tag:blogger.com,1999:blog-27593281306708636372024-02-20T15:03:55.510-08:00Mrs. OsawaruMrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.comBlogger237125tag:blogger.com,1999:blog-2759328130670863637.post-8057834752642471852020-05-14T11:11:00.001-07:002020-05-14T11:11:38.839-07:00Algebra 1 : Independent work:Geometry Preview<div class="XzvDs _208Ie tFDi5 blog-post-text-font blog-post-text-color _2QAo- _25MYV _6RI6N tFDi5" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background: 0px 0px rgb(255, 255, 255); border: 0px; box-sizing: inherit; direction: ltr; font-family: raleway, sans-serif; font-size: 18px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 1.5; outline: 0px; padding: 0px; vertical-align: baseline; white-space: pre-wrap;">
Segment Addition:</div>
<div class="XzvDs _208Ie tFDi5 blog-post-text-font blog-post-text-color _2QAo- _25MYV _6RI6N tFDi5" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background: 0px 0px rgb(255, 255, 255); border: 0px; box-sizing: inherit; direction: ltr; font-family: raleway, sans-serif; font-size: 18px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 1.5; outline: 0px; padding: 0px; vertical-align: baseline; white-space: pre-wrap;">
View Video: Number and Algebra in Deltamath</div>
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<a class="_2qJYG blog-link-hashtag-color _3Sq3W" href="https://www.educreations.com/lesson/view/line-segment-addition-postulate/54764855/?s=Z4H6el&ref=link" rel="noopener" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background: 0px 0px; border: 0px; box-sizing: inherit; color: #191919; cursor: pointer; font: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; vertical-align: baseline;" target="_top">https://www.educreations.com/lesson/view/line-segment-addition-postulate/54764855/?s=Z4H6el&ref=link</a></div>
<div class="XzvDs _208Ie tFDi5 blog-post-text-font blog-post-text-color _2QAo- _25MYV _6RI6N tFDi5" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background: 0px 0px rgb(255, 255, 255); border: 0px; box-sizing: inherit; direction: ltr; font-family: raleway, sans-serif; font-size: 18px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 1.5; outline: 0px; padding: 0px; vertical-align: baseline; white-space: pre-wrap;">
<br /></div>
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Assignment: </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB8PDT1bh3S1-5Q_d_pTap-dHQoT6dXNkIoYqzyD3apyohnHGv8L7a2kP6I4z_cu0Q3t1XDJzNz3Vr8sjXCsIy6F9q26qmKXgoioa2OpwWNQMNj12vZjDRUu1YLe4nj2fIxpTWxYDj_so/s1600/Segment+Addition+Postulate+worksheet+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="804" data-original-width="1600" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB8PDT1bh3S1-5Q_d_pTap-dHQoT6dXNkIoYqzyD3apyohnHGv8L7a2kP6I4z_cu0Q3t1XDJzNz3Vr8sjXCsIy6F9q26qmKXgoioa2OpwWNQMNj12vZjDRUu1YLe4nj2fIxpTWxYDj_so/s320/Segment+Addition+Postulate+worksheet+2.jpg" width="320" /></a></div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-68597630260470145222020-05-12T08:16:00.001-07:002020-05-12T08:16:55.336-07:00Algebra 1- The Segment Addition Postulate<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
Suppose XA = 3x and AY = 4x - 6. If A is the midpoint of XY, what is the length of XY?</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
3x 4x - 6<br />_________________________________<br />X A Y</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
The trick in this problem is to see that if A is the midpoint, then XA = AY.<br /><br />Since XA = AY, 3x = 4x - 6</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
Subtract 3x from both sides.<br /><br />3x - 3x = 4x - 3x - 6<br /><br />0 = x - 6<br /><br />Add 6 to both sides of the equation.<br /><br />0 + 6 = x - 6 + 6<br /><br />6 = x</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
To compute XA, you can either use 3x or 4x - 6<br /><br />Using 3x, we get XA = AY = 3 × 6 = 16</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
Using 4x - 6, we get XA = AY = 3 × 6 - 6 = 18 - 6 = 12</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
XY = XA + AY = 16 + 16 = 32</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
The length of XY is 32.</div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
Source:<a href="https://www.basic-mathematics.com/segment-addition-postulate.html" style="background-color: transparent;">https://www.basic-mathematics.com/segment-addition-postulate.html</a></div>
<div style="background-color: white; color: #666666; font-family: Cantarell, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 1.5em; margin-top: 1em;">
Assignment: </div>
<div class="separator" style="clear: both; text-align: center;">
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-14537276913034480522020-05-07T12:26:00.000-07:002020-05-07T12:26:26.190-07:00Instructional Video 5/5Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-30718195287613737242020-05-07T11:59:00.000-07:002020-05-07T11:59:04.715-07:00Algebra 1- Joint and marginal frequency tables re-teachingGood afternoon,<br />
Since we struggled with this concept, I will be reteaching it today.<br />
See you at the zoom call!Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-16156454314573742722020-05-05T09:33:00.003-07:002020-05-05T12:19:38.245-07:00Algebra 1- Joint and marginal frequency tables<h1 align="center" style="color: var(--b0Clr); font-family: champ, Verdana, Arial; font-size: 40px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: normal; margin: 18px 0px 5px; text-align: center; text-shadow: var(--h1Shadow);">
Relative Frequency</h1>
<div style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px; min-width: 150px;">
How often something happens divided by all outcomes.</div>
<div class="example" style="border-radius: 10px; box-shadow: 4px 4px 3px var(--b4Clr); color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px; margin: 20px 0px 30px 45px; overflow: hidden; padding: 5px 10px 1px;">
<div style="float: right; margin-bottom: 5px; margin-left: 10px; min-width: 150px;">
<img alt="Football Match" height="162" src="https://www.mathsisfun.com/data/images/football-match.jpg" width="200" /></div>
<h3 style="border-radius: 8px; color: var(--txtClr); font-size: 18px; font-weight: 400; margin: 2px -2px 12px; padding: 2px 8px;">
Example: Your team has won 9 games from a total of 12 games played:</h3>
<ul>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">the Frequency of winning is 9</li>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">the Relative Frequency of winning is 9/12 = 75%</li>
</ul>
</div>
<div style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px; min-width: 150px;">
All the Relative Frequencies add up to <span class="larger" style="color: var(--b3Clr); font-size: 17px;">1</span> (except for any rounding error).</div>
<div class="example" style="border-radius: 10px; box-shadow: 4px 4px 3px var(--b4Clr); color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px; margin: 20px 0px 30px 45px; overflow: hidden; padding: 5px 10px 1px;">
<div style="float: right; margin-bottom: 5px; margin-left: 10px; min-width: 150px;">
<img alt="road" height="117" src="https://www.mathsisfun.com/data/images/road.jpg" width="200" /></div>
<h3 style="border-radius: 8px; color: var(--txtClr); font-size: 18px; font-weight: 400; margin: 2px -2px 12px; padding: 2px 8px;">
Example: Travel Survey</h3>
<div style="min-width: 150px;">
92 people were asked how they got to work:</div>
<ul>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">35 used a car</li>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">42 took public transport</li>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">8 rode a bicycle</li>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">7 walked</li>
</ul>
<div style="min-width: 150px;">
The Relative Frequencies (to 2 decimal places) are:</div>
<ul>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">Car: 35/92 = <b>0.38</b></li>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">Public Transport: 42/92 = <b>0.46</b></li>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">Bicycle: 8/92 = <b>0.09</b></li>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">Walking: 7/92 = <b>0.08</b></li>
</ul>
<div align="center" class="larger" style="color: var(--b3Clr); font-size: 17px; min-width: 150px;">
0.38+0.46+0.09+0.08 = <b>1.01</b></div>
<div style="min-width: 150px;">
(It would be exactly 1 if we had used perfect accuracy)</div>
<div style="min-width: 150px;">
Source:<a href="https://www.mathsisfun.com/data/relative-frequency.html">https://www.mathsisfun.com/data/relative-frequency.html</a></div>
<div style="min-width: 150px;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 22.5pt; margin-bottom: 15.0pt; mso-outline-level: 2;">
<b><span style="color: black; font-family: "arial" , sans-serif; font-size: 18.0pt;">Assignment<o:p></o:p></span></b></div>
<div class="MsoNormal" style="background: white; line-height: 22.5pt; margin-bottom: 18.75pt;">
<span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt;"> </span><span style="color: black; font-family: "arial" , sans-serif; font-size: 12pt;">Each student in a random sample of students at a
local high school was categorized according to gender (male or female) and
whether they supported a proposal to increase the length of the school day by
30 minutes (oppose, support, no opinion). The following table summarizes the
data for this sample.</span></div>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; mso-padding-alt: 0in 0in 0in 0in; mso-yfti-tbllook: 1184; width: 670px;">
<tbody>
<tr style="height: 30.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td colspan="2" rowspan="2" style="background: #F1F1F1; border: solid white 1.5pt; height: 30.0pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "arial" , sans-serif; font-size: 12pt;"> </span><span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;"> <o:p></o:p></span></div>
</td>
<td colspan="4" style="background: #F1F1F1; border-left: none; border: solid white 1.5pt; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Opinion on Proposal
to Increase Length of School Day<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 30.0pt; mso-yfti-irow: 1;">
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Oppose<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Support<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">No Opinion<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Total<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 30.0pt; mso-yfti-irow: 2;">
<td rowspan="3" style="background: #F1F1F1; border-top: none; border: solid white 1.5pt; height: 30.0pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Gender<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Male<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">50<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">40<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">20<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">110<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 30.0pt; mso-yfti-irow: 3;">
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Female<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">40<o:p></o:p></span></div>
</td>
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<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">40<o:p></o:p></span></div>
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<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">10<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">90<o:p></o:p></span></div>
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<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">Total<o:p></o:p></span></div>
</td>
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<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">90<o:p></o:p></span></div>
</td>
<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">80<o:p></o:p></span></div>
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<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">30<o:p></o:p></span></div>
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<td style="background: #F1F1F1; border-bottom: solid white 1.5pt; border-left: none; border-right: solid white 1.5pt; border-top: none; height: 30.0pt; mso-border-left-alt: solid white 1.5pt; mso-border-top-alt: solid white 1.5pt; padding: 0in 0in 0in 0in;"><div class="MsoNormal" style="line-height: 22.5pt; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="color: #444444; font-family: "times new roman" , serif; font-size: 12.0pt;">200<o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt;">a.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal; line-height: normal;">
</span></span><!--[endif]--><span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt;">What proportion of the
students in this sample are male?<br />
<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 22.5pt; margin-bottom: .0001pt; margin: 0in; mso-list: l0 level1 lfo1; text-indent: 0in;">
<!--[if !supportLists]--><span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt;">b.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal; line-height: normal;">
</span></span><!--[endif]--><span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt;">What proportion of the
students in this sample support the proposal?<br />
<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 22.5pt; margin-bottom: .0001pt; margin: 0in; mso-list: l0 level1 lfo1; text-indent: 0in;">
<!--[if !supportLists]--><span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt;">c.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal; line-height: normal;">
</span></span><!--[endif]--><span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt;">What proportion of the
males in this sample support the proposal?<br />
<o:p></o:p></span></div>
<div style="min-width: 150px;">
<span style="color: black; font-family: "arial" , sans-serif; font-size: 12.0pt; line-height: 107%;">d. What proportion of the
students in this sample who support this proposal are female?<br />
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-32631794923860413362020-05-01T09:30:00.000-07:002020-05-01T09:30:38.891-07:00Algebra 1 Instructional video 4/30<div class="separator" style="clear: both; text-align: center;">
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<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-25106503236664685582020-05-01T09:21:00.001-07:002020-05-01T09:30:26.381-07:002 way table<div class="wikiContent faded-content" id="articleMain" style="background-color: white; box-sizing: border-box; color: #555555; font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; position: relative;">
<div id="transcriptMain" ng-non-bindable="" style="box-sizing: border-box;">
<h2 id="section---TwoWayTable" style="box-sizing: border-box; color: inherit; font-family: inherit; font-size: 26px; line-height: 1.1; margin-bottom: 10px; margin-top: 20px;">
Two-Way Table</h2>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
Do you believe in Martians? Here is a survey of 100 college students asking that very question: <i style="box-sizing: border-box;">Do you believe in Martians?</i></div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
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<table border="1" class="wikitable" style="background-color: transparent; border-collapse: collapse; border-spacing: 0px; box-sizing: border-box;"><tbody style="box-sizing: border-box;">
<tr class="odd" style="background-color: #eeeeee; box-sizing: border-box;"><th style="box-sizing: border-box; padding: 5px; text-align: left;">Gender</th><th style="box-sizing: border-box; padding: 5px; text-align: left;">Yes</th><th style="box-sizing: border-box; padding: 5px; text-align: left;">No</th></tr>
<tr style="box-sizing: border-box;"><td style="box-sizing: border-box; padding: 5px;">Male</td><td style="box-sizing: border-box; padding: 5px;">10</td><td style="box-sizing: border-box; padding: 5px;">32</td></tr>
<tr class="odd" style="background-color: #eeeeee; box-sizing: border-box;"><td style="box-sizing: border-box; padding: 5px;">Female</td><td style="box-sizing: border-box; padding: 5px;">38</td><td style="box-sizing: border-box; padding: 5px;">20</td></tr>
<tr style="box-sizing: border-box;"><td style="box-sizing: border-box; padding: 5px;">Total</td><td style="box-sizing: border-box; padding: 5px;">48</td><td style="box-sizing: border-box; padding: 5px;">52</td></tr>
</tbody></table>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
This type of table is called a <span style="box-sizing: border-box; font-weight: 700;">two-way or contingency table</span>.</div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
A two-way or contingency table is a statistical table that shows the observed number or frequency for two variables, the rows indicating one category and the columns indicating the other category. The row category in this example is gender - male or female. The column category is their choice, yes or no.</div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
There is a lot of information we can learn from this small table. Let's look at a couple questions you could see on a test.</div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
<i style="box-sizing: border-box;">How many males were asked?</i> Let's look across the male row. Ten said 'yes' and 32 said 'no.' That would be a total of 42 males.</div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
<i style="box-sizing: border-box;">How many college students believe in Martians?</i> Look down the Yes column. Ten males and 38 females said 'yes.' That would be a total of 48 college students.</div>
<h2 id="section---Example2" style="box-sizing: border-box; color: inherit; font-family: inherit; font-size: 26px; line-height: 1.1; margin-bottom: 10px; margin-top: 20px;">
Example #2</h2>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
A recent survey of 100 college students asked if they prefer to drink tea, coffee, or an energy drink during finals week. Here is the table created from that survey.</div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
</div>
<table border="1" class="wikitable" style="background-color: transparent; border-collapse: collapse; border-spacing: 0px; box-sizing: border-box;"><tbody style="box-sizing: border-box;">
<tr class="odd" style="background-color: #eeeeee; box-sizing: border-box;"><th style="box-sizing: border-box; padding: 5px; text-align: left;">Gender</th><th style="box-sizing: border-box; padding: 5px; text-align: left;">Tea</th><th style="box-sizing: border-box; padding: 5px; text-align: left;">Coffee</th><th style="box-sizing: border-box; padding: 5px; text-align: left;">Energy Drink</th></tr>
<tr style="box-sizing: border-box;"><td style="box-sizing: border-box; padding: 5px;">Male</td><td style="box-sizing: border-box; padding: 5px;">2</td><td style="box-sizing: border-box; padding: 5px;">15</td><td style="box-sizing: border-box; padding: 5px;">39</td></tr>
<tr class="odd" style="background-color: #eeeeee; box-sizing: border-box;"><td style="box-sizing: border-box; padding: 5px;">Female</td><td style="box-sizing: border-box; padding: 5px;">18</td><td style="box-sizing: border-box; padding: 5px;">20</td><td style="box-sizing: border-box; padding: 5px;">6</td></tr>
<tr style="box-sizing: border-box;"><td style="box-sizing: border-box; padding: 5px;">Total</td><td style="box-sizing: border-box; padding: 5px;">20</td><td style="box-sizing: border-box; padding: 5px;">35</td><td style="box-sizing: border-box; padding: 5px;">45</td></tr>
</tbody></table>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
Let's look at a couple questions you could see on a test.</div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
<i style="box-sizing: border-box;">How many college students drink tea given that they are a female?</i> In this question, we're looking for tea drinkers that are female. Let's look at the female row and tea column. The answer is 18.</div>
<div style="box-sizing: border-box; line-height: 1.5; margin-bottom: 10px;">
<i style="box-sizing: border-box;">How many students drink tea or are male?</i> In this question, we're looking for all tea drinkers united with all males. To figure out the answer, let's highlight the Tea column and Male row. We do have an overlap at Tea and Male, so be sure not to add that twice. So our answer is Total Tea drinkers 20 plus Total Males 56 minus the overlap of 2. 20 + 56 - 2 = 74. There are 74 students that are tea drinkers or male.</div>
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<span class="icon-unlock" style="box-sizing: border-box; font-family: "icomoon important"; line-height: 1; speak: none;"></span>Source:https://study.com/academy/lesson/what-is-a-two-way-table.html</div>
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Assignment: quizziz code: <span style="background-color: #f2f2f2; color: #292a3a; font-family: "Open Sans", sans-serif, Helvetica, Arial; font-size: 28px; font-weight: 700; letter-spacing: 8px;">898765</span></div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-8003812792387082102020-04-28T10:41:00.000-07:002020-04-28T10:41:53.389-07:00Instructional Video 4/28/2020<div class="separator" style="clear: both; text-align: center;">
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<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-5358087816146099492020-04-28T09:00:00.004-07:002020-04-28T09:11:24.252-07:005 number summary<div class="text" style="background-color: white; color: #404040; font-family: Arial, Helvetica, sans-serif; font-size: 14px; line-height: 1.6em; margin-bottom: 1.2em; margin-top: 1.2em;">
You only need the five values listed above (min, <span class="math" style="font-family: "times new roman" , "times" , serif; font-size: 15.4px;">Q<span style="bottom: -0.25em; font-size: 11.55px; line-height: 0; position: relative; vertical-align: baseline;">1</span>, Q<span style="bottom: -0.25em; font-size: 11.55px; line-height: 0; position: relative; vertical-align: baseline;">2</span>, Q<span style="bottom: -0.25em; font-size: 11.55px; line-height: 0; position: relative; vertical-align: baseline;">3</span></span>, and max) in order to draw your box-and-whisker plot. This set of five values has been given the name "the five-number summary".</div>
<div class="text" style="background-color: white; color: #404040; font-family: Arial, Helvetica, sans-serif; font-size: 14px; line-height: 1.6em; margin-bottom: 1.2em; margin-top: 1.2em;">
<h3 id="x-ck12-NmQyZWE1ZTEyNjFlODlkZTc0YmMyNTljZGFiN2IyNmM.-zkb" style="border-top: 1px solid rgb(230, 230, 230); box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 1.6875em; line-height: 1.4; margin: 2em 0px 0.4em; padding: 15px 0px 0px; text-rendering: optimizelegibility;">
Examples</h3>
<h4 style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 1.4375em; line-height: 1.4; margin: 0.2em 0px 0.5em; padding: 0px; text-rendering: optimizelegibility;">
Example 1</h4>
<div id="x-ck12-N2ViZWMwMjFlNjc2MjM5NjJiZDU1OTE4MWFkMmU4ZWU.-xln" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
Earlier you were asked to compute the five number summary for 0, 0, 1, 2, 63, 61, 27, 13. It helps to order the data.</div>
<div id="x-ck12-YTg0ZTc3Njc4Nzg5OWM3YTRhMGNkYTcxYWY2OTkyMDM.-5u9" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
0, 0, 1, 2, 13, 27, 61, 63</div>
<ul id="x-ck12-OWNmNTA2ZTA4MTdhMzgyZmMwMzA0MWEyMWI4OGNlM2Y.-bwe" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; list-style-position: inside; margin-bottom: 1.25em; margin-left: 20px !important; margin-right: 0px; margin-top: 0px; padding: 0px 0px 0px 10px;">
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">Since there are 8 observations, the median is the average of the <span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="4%5E%7Bth%7D" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-12-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-112" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.789em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.565em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.23em, 1001.4em, 2.626em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-113" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-114" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.23em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.072em, 1001.23em, 4.3em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.23em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.96em, 1001.23em, 4.188em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.903em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-115" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-116" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-117" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.23em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-118" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">4</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.505em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.406em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-119" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-120" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-121" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; font-size: 12.6694px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">t</span><span class="mi" id="MathJax-Span-122" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; font-size: 12.6694px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">h</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.378em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.372em; width: 0px;"></span></span></nobr></span></span> and <span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="5%5E%7Bth%7D" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-13-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-123" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.789em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.565em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.23em, 1001.4em, 2.626em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-124" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-125" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.23em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.072em, 1001.23em, 4.3em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.23em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.96em, 1001.23em, 4.188em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.903em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-126" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-127" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-128" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.23em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-129" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">5</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.505em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.406em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-130" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-131" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-132" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; font-size: 12.6694px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">t</span><span class="mi" id="MathJax-Span-133" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; font-size: 12.6694px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">h</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.378em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.372em; width: 0px;"></span></span></nobr></span></span> observations: <span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="%5Cfrac%7B2%2B13%7D%7B2%7D%3D7.5" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-14-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-134" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 6.755em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 6.03em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.728em, 1005.81em, 3.128em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-135" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-136" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.695em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.57em, 1005.64em, 4.969em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.695em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.514em, 1005.64em, 4.858em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-137" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-138" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-139" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.114em; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.849em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1002.68em, 4.244em, -999.997em); left: 25.5208px; line-height: normal; margin: 0px 0px 0px -1.336em; max-width: 64em !important; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-140" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-141" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-142" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-143" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">13</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 25.5208px; line-height: normal; margin: 0px 0px 0px -0.22em; max-width: 64em !important; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-144" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.84em, 1002.85em, 1.23em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -1.281em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 2.849em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.063em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-145" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-146" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">7.5</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.378em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></span></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">The lowest observation is 0.</li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">The highest observation is 63.</li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">The middle of the lower half is <span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="%5Cfrac%7B0%2B1%7D%7B2%7D%3D0.5" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-15-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-147" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 6.197em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.527em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.728em, 1005.3em, 3.128em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-148" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-149" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.193em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.57em, 1005.14em, 4.969em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.193em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.514em, 1005.14em, 4.858em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-150" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-151" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-152" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.114em; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.347em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1002.18em, 4.244em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -1.113em; max-width: 64em !important; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-153" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-154" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">0</span><span class="mo" id="MathJax-Span-155" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-156" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -0.22em; max-width: 64em !important; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-157" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.84em, 1002.35em, 1.23em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -1.281em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 2.347em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.063em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-158" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-159" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">0.5</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.378em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></span></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">The middle of the upper half is <span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="%5Cfrac%7B27%2B61%7D%7B2%7D%3D44" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-16-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-160" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 7.034em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 6.253em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.728em, 1006.03em, 3.128em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-161" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-162" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.918em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.57em, 1005.92em, 4.969em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.918em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.514em, 1005.92em, 4.858em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-163" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-164" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-165" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.114em; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.351em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1003.18em, 4.244em, -999.997em); left: 30.0208px; line-height: normal; margin: 0px 0px 0px -1.616em; max-width: 64em !important; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-166" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-167" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">27</span><span class="mo" id="MathJax-Span-168" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-169" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">61</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 30.0208px; line-height: normal; margin: 0px 0px 0px -0.22em; max-width: 64em !important; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-170" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.84em, 1003.35em, 1.23em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -1.281em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 3.351em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.063em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-171" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-172" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">44</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.441em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></span></li>
</ul>
<div id="x-ck12-NWE2Nzg2OGY5MGZlODFkNjAyYTk1ZjZkYzk2ODE2MDc.-4hi" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
The five number summary is 0, 0.5, 7.5, 44, 63</div>
<h4 style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 1.4375em; line-height: 1.4; margin: 0.2em 0px 0.5em; padding: 0px; text-rendering: optimizelegibility;">
Example 2</h4>
<div id="x-ck12-Yjk2Y2EyOWYwOWE5NTg5YzhhODA2Y2MwNTQ2MjU4MjE.-plb" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
Create a set of data that meets the following five number summary:</div>
<div id="x-ck12-NmRiZmM1OTExNGQ3YTc0YWM2YjMxNGM5NzNjZDU1MWI.-gzo" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
{2, 5, 9, 18, 20}</div>
<div id="x-ck12-ZGI2ZTM2MWNjNWU4ZDZlMGI4YTU0MmQ4NDJkYWVlYjE.-we8" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
<span style="box-sizing: border-box;">Suppose there are 8 data points. The lowest point must be 2 and the highest point must be 20. The middle two points must average to be 9 so they could be 8 and 10. The second and third points must average to be 5 so they could be 4 and 6. The sixth and seventh points need to average to be 18 so they could be 18 and 18. Here is one possible answer:</span></div>
<div id="x-ck12-MGJiODQ0NDk0YzY4NzNiM2M0YjA5ZWExMDhlYWNlZjc.-fql" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
<span style="box-sizing: border-box;">2, 4, 6, 8, 10, 18, 18, 20</span></div>
<h4 style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 1.4375em; line-height: 1.4; margin: 0.2em 0px 0.5em; padding: 0px; text-rendering: optimizelegibility;">
Example 3</h4>
<div id="x-ck12-NjFiYmJiYzliOTZlNzY2ZDMzY2MyOWQ1OGI5MGE1NDg.-x0h" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
Compute the five number summary for the following data:</div>
<div id="x-ck12-NDczOTkzNzA1YmM3Zjk4ODBhYmUwMDk5OTcyMmZkYTU.-vuf" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9, 10, 15</div>
<div id="x-ck12-Njc4NmQ2MTNlNTllZGRiZmE0NzI2ZjRkODI2NjU0ZWE.-7bk" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
There are 20 observations.</div>
<ul id="x-ck12-ZGMzOGUxMjVkMWUwMzE3NTY5ZTVjMWNkOTRiZWUxMmQ.-1bt" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; list-style-position: inside; margin-bottom: 1.25em; margin-left: 20px !important; margin-right: 0px; margin-top: 0px; padding: 0px 0px 0px 10px;">
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">Lower : 1</li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q1%20%3A%20%5Cfrac%7B2%2B3%7D%7B2%7D%3D2.5" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-17-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-173" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 8.652em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.704em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.728em, 1007.48em, 3.128em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-174" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-175" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.369em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.57em, 1007.31em, 4.969em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.369em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.514em, 1007.31em, 4.858em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-176" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-177" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-178" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-179" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-180" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mfrac" id="MathJax-Span-181" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.114em; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.347em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1002.18em, 4.244em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -1.113em; max-width: 64em !important; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-182" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-183" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-184" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-185" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -0.22em; max-width: 64em !important; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-186" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.84em, 1002.35em, 1.23em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -1.281em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 2.347em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.063em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-187" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-188" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2.5</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.378em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></span></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q2%20%3A%20%5Cfrac%7B4%2B5%7D%7B2%7D%3D4.5" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-18-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-189" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 8.652em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.704em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.728em, 1007.48em, 3.128em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-190" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-191" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.369em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.57em, 1007.31em, 4.969em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.369em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.514em, 1007.31em, 4.858em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.903em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-192" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-193" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-194" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-195" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-196" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mfrac" id="MathJax-Span-197" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.114em; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.347em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1002.18em, 4.244em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -1.113em; max-width: 64em !important; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-198" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-199" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">4</span><span class="mo" id="MathJax-Span-200" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-201" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">5</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -0.22em; max-width: 64em !important; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-202" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.84em, 1002.35em, 1.23em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -1.281em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 2.347em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.063em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-203" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-204" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">4.5</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.441em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></span></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q3%20%3A%20%5Cfrac%7B6%2B7%7D%7B2%7D%3D6.5" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-19-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-205" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 8.652em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.704em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.728em, 1007.48em, 3.128em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-206" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-207" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.369em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.57em, 1007.31em, 4.969em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.369em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.514em, 1007.31em, 4.858em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-208" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-209" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-210" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-211" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-212" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mfrac" id="MathJax-Span-213" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.114em; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.347em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1002.24em, 4.244em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -1.113em; max-width: 64em !important; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-214" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-215" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">6</span><span class="mo" id="MathJax-Span-216" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-217" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">7</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 21.0208px; line-height: normal; margin: 0px 0px 0px -0.22em; max-width: 64em !important; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-218" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.84em, 1002.35em, 1.23em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -1.281em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 2.347em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.063em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-219" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-220" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">6.5</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.441em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></span></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">Upper : 15</li>
</ul>
<h4 style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 1.4375em; line-height: 1.4; margin: 0.2em 0px 0.5em; padding: 0px; text-rendering: optimizelegibility;">
Example 4</h4>
<div id="x-ck12-YzU2OTA1ZjNmY2EyMDNlZjc5NTljZTg1YTY5NjliYjI.-ufa" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
Compute the five number summary for the following data:</div>
<div id="x-ck12-ZGFhZWQ5NjlkZTYyODBhMGM4MDI3NzU5ZmY1YjkzYWI.-vtk" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
4, 8, 11, 11, 12, 14, 16, 20, 21, 25</div>
<div id="x-ck12-MjRkNWM4MmY3NDExMjk5MzljNjk3ZTM2YTRkZDY4YjQ.-rnz" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
There are 10 observations total in this set of data. </div>
<ul id="x-ck12-MTFlNTBkM2QwNDBmMjJmODkxMmJkZGZjNDZjMzdlMGU.-apg" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; list-style-position: inside; margin-bottom: 1.25em; margin-left: 20px !important; margin-right: 0px; margin-top: 0px; padding: 0px 0px 0px 10px;">
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">Lowest value (minimum) : 4</li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q1%20%3A%2011" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-20-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-221" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 3.909em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.463em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.286em, 1003.24em, 2.57em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-222" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-223" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1003.07em, 4.411em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1003.07em, 4.355em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-224" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-225" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-226" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-227" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-228" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mn" id="MathJax-Span-229" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">11</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr></span></span> <em style="box-sizing: border-box; line-height: inherit;">(Note that this is the median of the first half of the data - 4, 8, 11, 11, 12)</em></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q2%20%3A%20%5Cfrac%7B12%2B14%7D%7B2%7D%3D13" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-21-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-230" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 9.434em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 8.429em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.728em, 1008.21em, 3.128em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-231" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-232" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 8.094em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.57em, 1008.04em, 4.969em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 8.094em;"><span style="border: 0px; box-sizing: border-box; clip: rect(2.514em, 1008.04em, 4.858em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.903em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-233" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-234" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-235" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-236" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-237" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mfrac" id="MathJax-Span-238" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.114em; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.351em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1003.18em, 4.244em, -999.997em); left: 30.0208px; line-height: normal; margin: 0px 0px 0px -1.616em; max-width: 64em !important; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-239" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-240" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">12</span><span class="mo" id="MathJax-Span-241" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-242" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.226em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">14</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1000.45em, 4.188em, -999.997em); left: 30.0208px; line-height: normal; margin: 0px 0px 0px -0.22em; max-width: 64em !important; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-243" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.84em, 1003.35em, 1.23em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -1.281em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 3.351em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.063em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-244" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-245" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">13</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.441em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></span> <em style="box-sizing: border-box; line-height: inherit;">(Note that this is the median of the full set of data)</em></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q3%20%3A%2020" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-22-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-246" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 3.909em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.463em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.286em, 1003.24em, 2.57em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-247" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-248" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1003.07em, 4.411em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1003.07em, 4.355em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-249" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-250" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-251" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-252" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-253" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mn" id="MathJax-Span-254" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">20</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr></span></span> <em style="box-sizing: border-box; line-height: inherit;">(Note that this is the median of the second half of the data - 14, 16, 20, 21, 25)</em></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">Upper value (maximum) : 25</li>
</ul>
<div id="x-ck12-YzgyZjJiYjAxM2NmNDkxN2ZiMzRkNTBjZmI3ZDc2MGY.-ogp" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
<span style="box-sizing: border-box;">T</span>he five number summary is 4, 11, 13, 20, 25.</div>
<h4 id="x-ck12-YzZkYTM4ZDY1NjE3MmU3M2QwMTlmOWI5ZjljNTk1ZTY.-jz9" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 1.4375em; line-height: 1.4; margin: 0.2em 0px 0.5em; padding: 0px; text-rendering: optimizelegibility;">
Example 5</h4>
<div id="x-ck12-ZjcyOTkxYzgwOWFiMjY5M2MwZjg3ZTQxODRhNjY0ZDE.-2zx" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
Compute the five number summary for the following data:</div>
<div id="x-ck12-YTk0NTRmNzJlMWFjYTg5NTMzZjcwZGQ4ZWNjNmE0ZGU.-re6" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
3, 7, 10, 14, 19, 19, 23, 27, 29</div>
<div class="" id="x-ck12-NmMyNDM2MmZmZDg0ODA1ZjA4Zjk5MDQ1MjQyNTMzNGM.-lsi" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; overflow-y: hidden; padding: 0px; text-rendering: optimizelegibility;">
There are 9 observations total. To calculate <span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q1" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-23-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-255" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.844em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.621em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.286em, 1001.4em, 2.57em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-256" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-257" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.286em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1001.23em, 4.411em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.286em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1001.23em, 4.355em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-258" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-259" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-260" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-261" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr></span></span> and <span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q3" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-24-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-262" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.844em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.621em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.286em, 1001.4em, 2.57em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-263" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-264" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.286em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1001.23em, 4.411em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.286em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1001.23em, 4.355em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-265" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-266" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-267" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-268" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr></span></span>, you should include the median in both the lower half and upper half calculations.</div>
<ul id="x-ck12-ZTFkOTA5NzZiNzI5NzA5YzMxMTRlMTU4MGNkY2Q0Yjg.-z2l" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; list-style-position: inside; margin-bottom: 1.25em; margin-left: 20px !important; margin-right: 0px; margin-top: 0px; padding: 0px 0px 0px 10px;">
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">Lowest value (minimum) : 3</li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q1%20%3A%2010" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-25-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-269" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 3.909em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.463em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.286em, 1003.24em, 2.57em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-270" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-271" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1003.07em, 4.411em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1003.07em, 4.355em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-272" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-273" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-274" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-275" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-276" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mn" id="MathJax-Span-277" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">10</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr></span></span> <em style="box-sizing: border-box; line-height: inherit;">(this is the median of 3, 7, 10, 14, 19)</em></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q2%20%3A%2019" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-26-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-278" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 3.909em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.463em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.286em, 1003.24em, 2.57em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-279" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-280" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1003.07em, 4.411em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1003.07em, 4.355em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-281" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-282" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-283" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-284" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-285" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mn" id="MathJax-Span-286" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">19</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr></span></span></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;"><span class="x-ck12-mathEditor" data-contenteditable="false" data-edithtml="" data-math-class="x-ck12-math" data-mathmethod="inline" data-tex="Q3%20%3A%2023" style="background-color: inherit !important; box-sizing: border-box; margin-right: -1px; width: auto !important;"><span class="MathJax" id="MathJax-Element-27-Frame" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: 64em !important; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-287" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 3.909em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 17.92px; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.463em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.286em, 1003.24em, 2.57em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -2.174em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-288" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtable" id="MathJax-Span-289" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0.17em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.184em, 1003.07em, 4.411em, -999.997em); left: 0em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; top: -4.015em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.128em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1003.07em, 4.355em, -999.997em); line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: absolute; right: 0em; top: -3.959em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mtd" id="MathJax-Span-290" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-291" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-292" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">Q</span><span class="mn" id="MathJax-Span-293" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-294" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">:</span><span class="mn" id="MathJax-Span-295" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px 0px 0px 0.282em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">23</span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.021em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.179em; line-height: normal; margin: 0px; max-width: 64em !important; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; max-width: 64em !important; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr></span></span> <em style="box-sizing: border-box; line-height: inherit;">(this is the median of 19, 19, 23, 27, 29)</em></li>
<li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px;">Upper value (maximum) : 29</li>
</ul>
<div id="x-ck12-NjRkOTEyZTUwNzg3MTM0OGRhNWVkNjA3NmFlOWZiOGU.-jj8" style="box-sizing: border-box; color: #56544d; direction: ltr; font-family: ProximaNova, "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 9px; padding: 0px; text-rendering: optimizelegibility;">
<span style="box-sizing: border-box;">T</span>he five number summary is 3, 10, 19, 23, 29.</div>
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<span style="font-family: "times new roman", times, serif; font-size: 15.4px;">Assignment: </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1AqgW0UaEhiENiYiHL3eLFYUsy9Kq9qP8AOqHARzBMiAaHGndn9qy-7bb58Zsa4YwBIkNDdL04-g0XOlvm7B-UobWJ_0wN7xvSIq4us2noayuqnJ3orFS3iknsljpSzbuBc-v9d5Ro58/s1600/5+number+summary.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1236" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1AqgW0UaEhiENiYiHL3eLFYUsy9Kq9qP8AOqHARzBMiAaHGndn9qy-7bb58Zsa4YwBIkNDdL04-g0XOlvm7B-UobWJ_0wN7xvSIq4us2noayuqnJ3orFS3iknsljpSzbuBc-v9d5Ro58/s320/5+number+summary.jpg" width="247" /></a></div>
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<span class="math" style="color: purple; font-family: "times new roman" , "times" , serif; font-size: 15.4px; font-weight: 700;">Sources: </span><span style="color: purple; font-family: arial, helvetica, sans-serif; font-weight: 700;">https://www.purplemath.com/modules/boxwhisk2.htm</span></div>
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<a href="https://www.ck12.org/c/statistics/five-number-summary/lesson/Five-Number-Summary-PCALC/">https://www.ck12.org/c/statistics/five-number-summary/lesson/Five-Number-Summary-PCALC/</a></div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-13224601580330906942020-04-23T08:56:00.000-07:002020-04-23T08:56:15.340-07:00Data Distribution Algebra 1 Thursday 4/23/2020Objectives:<br />
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<span style="font-weight: normal;"><span style="color: black; font-family: "verdana";">Describe the central tendency of a data
set.</span></span><span style="font-weight: normal;"><span style="color: black; font-family: "verdana";">Create and interpret box-and-whisker
plots. </span></span></div>
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<span style="font-weight: normal;"><span style="color: black; font-family: "verdana";">Zoom Call @ 1p.m</span></span></div>
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<span style="font-weight: normal;"><span style="color: black; font-family: "verdana";">Assignment:</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVkA9jThdFJ95MWqIui_tZLBiOe0zlZjlKuqhgZiDeQjKAsohTeVEUKR7G0DhDlguTkvt1yzLPynQf5rGO-WpnyxnBrzAAPQqSQ8SUqbcDZ80JWudY-YMDPZIAcoL7ng0ozaajSns5lw8/s1600/data+distribution+worksheet.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1214" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVkA9jThdFJ95MWqIui_tZLBiOe0zlZjlKuqhgZiDeQjKAsohTeVEUKR7G0DhDlguTkvt1yzLPynQf5rGO-WpnyxnBrzAAPQqSQ8SUqbcDZ80JWudY-YMDPZIAcoL7ng0ozaajSns5lw8/s320/data+distribution+worksheet.jpg" width="242" /></a></div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-81554297012921907922020-04-23T08:49:00.000-07:002020-04-23T08:49:50.633-07:00Algebra 1 Instructional Video on April 21, 2020 <span id="goog_1950336648"></span><span id="goog_1950336649"></span><br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-77243667819059663462020-04-21T09:30:00.002-07:002020-04-21T09:51:36.001-07:00Algebra 1 Arithmetic and Geometric Sequences April 21, 2020<div style="overflow: auto;">
We will continue working on sequences today:<br />
Here are some notes. Your classwork<br />
Arithmetic Sequences<br />
Example:<br />
<table align="center" style="border-collapse: collapse;"><tbody>
<tr><td style="border: solid 2px var(--bgClr); padding: 5px;"><span class="large" style="color: var(--a4Clr); font-size: 19px;">1, 4, 7, 10, 13, 16, 19, 22, 25, ...</span></td></tr>
</tbody></table>
Its Rule is <b>x<sub>n</sub> = 3n-2</b></div>
<ul style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px;">
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;"><b>a</b> is the first term, and</li>
</ul>
<ul style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px;">
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;"><b>d</b> is the difference between the terms (called the <b>"common difference"</b>)</li>
</ul>
Geometric Sequences<br />
Example:<br />
<table align="center" style="border-collapse: collapse;"><tbody>
<tr><td style="border: solid 2px var(--bgClr); padding: 5px;">2, 4, 8, 16, 32, 64, 128, 256<span class="large" style="color: var(--a4Clr); font-size: 19px;">, ...</span></td></tr>
</tbody></table>
Its Rule is <b>x<sub>n</sub> = 2<sup>n</sup></b><br />
<ul style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px;">
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;"><b>a</b> is the first term, and</li>
</ul>
<ul style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px;">
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;"><b>r</b> is the factor between the terms (called the <b>"common ratio"</b>)</li>
</ul>
<ul>
<li style="color: var(--b4Clr); list-style-type: disc; padding-bottom: 7px;">When <b>r=0</b>, we get the sequence {a,0,0,...} which is not geometric</li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiinNfdcZbnkU1UDHDanBm09ZYZaOziTtqSxcsruEIxWhLb5ZJao5e7wS6PmrjzB3FstFCjGACVIzMG22tP1P-AVy7EuFARQHwutdPoL7gCQOYcmiMuPc5gLQJwP_j3-tW9Zm96Nor9cHc/s1600/Comparing+Arithmetic+and+Geometric+Sequences+worksheet-page-001.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1237" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiinNfdcZbnkU1UDHDanBm09ZYZaOziTtqSxcsruEIxWhLb5ZJao5e7wS6PmrjzB3FstFCjGACVIzMG22tP1P-AVy7EuFARQHwutdPoL7gCQOYcmiMuPc5gLQJwP_j3-tW9Zm96Nor9cHc/s320/Comparing+Arithmetic+and+Geometric+Sequences+worksheet-page-001.jpg" width="247" /></a></div>
is posted after the notes. See you at the zoom call at 1 p.m.<br />
<h4 style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px; min-width: 150px;">
<span style="font-weight: normal;">In an <a href="https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html" style="border-radius: 10px; border: solid 2px var(--b2Clr); padding: 3px;">Arithmetic Sequence</a> the difference between one term and the next is a constant.<br />In other words, we just add some value each time ... on to infinity.<br />This sequence has a difference of 3 between each number.<br />In General we can write an arithmetic sequence like this:<br />{a, a+d, a+2d, a+3d, ... }<br />where:<br />And we can make the rule:<br /><span class="large" style="color: var(--a4Clr); font-size: 19px;">x<sub>n</sub> = a + d(n-1)</span>(We use "n-1" because d is not used in the 1st term).</span></h4>
<h4 style="color: #333333; font-family: Verdana, Arial, Tahoma, sans-serif; font-size: 15px; min-width: 150px;">
<span style="font-weight: normal;"><br />In a <a href="https://www.mathsisfun.com/algebra/sequences-sums-geometric.html" style="border-radius: 10px; border: solid 2px var(--b2Clr); padding: 3px;">Geometric Sequence</a> each term is found by multipl<div class="separator" style="clear: both; text-align: center;">
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ying the previous term by a constant.<br />This sequence has a factor of 2 between each number.<br />In General we can write a geometric sequence like this:<br />{a, ar, ar<sup>2</sup>, ar<sup>3</sup>, ... }<br />where:<br />Note: r should not be 0.<br />And the rule is:<br />x<sub>n</sub> = ar<sup>(n-1)</sup>(We use "n-1" because <span class="large" style="color: var(--a4Clr); font-size: 19px;">ar<sup>0</sup></span> is the 1st term)<br />source:<br /><a href="https://www.mathsisfun.com/algebra/sequences-series.html">https://www.mathsisfun.com/algebra/sequences-series.html</a></span></h4>
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Assignment:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI6lV_FKvalfgq6fB6oVnMKxgq4q3Tp8Zp55BcXUxzDKV7VQ3X33xm3ZEbLA8Htz2swschVXS0hEokg68ub_q2QwPbfIGTQgW7QlvK6lXduMffDM5vxX5PMtnaFcs5PsIXCz3ypUtl2fU/s1600/Comparing+Arithmetic+and+Geometric+Sequences+worksheet-page-001.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1237" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI6lV_FKvalfgq6fB6oVnMKxgq4q3Tp8Zp55BcXUxzDKV7VQ3X33xm3ZEbLA8Htz2swschVXS0hEokg68ub_q2QwPbfIGTQgW7QlvK6lXduMffDM5vxX5PMtnaFcs5PsIXCz3ypUtl2fU/s320/Comparing+Arithmetic+and+Geometric+Sequences+worksheet-page-001.jpg" width="247" /></a></div>
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Or Login to quizziz.com : activity code is <span style="background-color: #f2f2f2; color: #292a3a; font-family: "Open Sans", sans-serif, Helvetica, Arial; font-size: 28px; font-weight: 700; letter-spacing: 8px; text-align: center;">229092</span></div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-23464603694130339972020-04-20T06:34:00.001-07:002020-04-20T06:34:17.497-07:00CRM Week of April 20, 2020 <strong style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;"><u>Week 5</u><br /><br />Monday 4/20 - Quantitative vs. Qualitative and Correlation vs. Causation</strong><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><a href="https://youtu.be/ZtppTPL-fBQ" style="background-color: white; color: #2b2b2b; font-family: Montserrat; font-size: 16px; text-decoration-line: none; transition: color 200ms ease-in 0s;" target="_blank">https://youtu.be/ZtppTPL-fBQ</a><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Qualitative and Quantitative practice worksheet on the "College Readiness Math" tab<br />Correlation worksheet on the "College Readiness Math" tab<br /></span><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><strong style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Tuesday 4/21 - Fluency Tables</strong><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><a href="https://youtu.be/hPYna_KWEF0" style="background-color: white; color: #2b2b2b; font-family: Montserrat; font-size: 16px; text-decoration-line: none; transition: color 200ms ease-in 0s;" target="_blank">https://youtu.be/hPYna_KWEF0</a><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Two-way variables </span><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">worksheet on the "College Readiness Math" tab</span><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><strong style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Wednesday 4/22 - Shape of graphs</strong><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><a href="https://youtu.be/pbuoYK6UGs0" style="background-color: white; color: #2b2b2b; font-family: Montserrat; font-size: 16px; text-decoration-line: none; transition: color 200ms ease-in 0s;" target="_blank">https://youtu.be/pbuoYK6UGs0</a><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Best measure of center and spread</span><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;"> </span><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">worksheet on the "College Readiness Math" tab</span><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><strong style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Thursday 4/23 - Unit 8 Study Guide<br /><br />Friday 4/24 - Make up day (no classes)</strong><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Make up any work or Unit 8 quiz. </span><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><strong style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;"><u>Week 6</u><br /><br />Monday 4/27 - Unit 5 Test<br /><br />Tuesday 4/28 - Unit 6 Test<br /><br />Wednesday 4/29 - Unit 7 Test<br /><br />Thursday 4/30 - Unit 8 Test<br /><br />Friday 5/1 - Make Up Day (no classes)</strong><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><span style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">Make up any tests you need to take. </span><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><br style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;" /><strong style="background-color: white; color: #9b9b9b; font-family: Montserrat; font-size: 16px;">WE ARE FINISHED!!! WE WOULD HAVE TAKEN THIS TIME TO REVIEW FOR SENIOR FINALS. LET ME KNOW IF YOU NEED HELP WITH ANYTHING. </strong>Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-83716858180780005392020-04-16T11:44:00.000-07:002020-04-16T11:44:43.307-07:00Instructional Video Thursday April 16, 2020<div class="separator" style="clear: both; text-align: center;">
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<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-72987696209374755722020-04-16T08:22:00.001-07:002020-04-16T08:22:42.309-07:00Algebra 1 April 16, 2020<br />
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Sequences</div>
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Online Book: Khan Academy - use the button below for specific lesson. Please look at arithmetic and geometric sequences, lessons and activities (recursive and explicit for both)</div>
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Notes: Use the Anchor Charts to assist with instruction.</div>
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Assignment: </div>
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Zoom call is today @ 1 p.m.</div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-78730057938055701832020-04-14T11:36:00.000-07:002020-04-14T11:36:09.105-07:00Instructional video 4/14/2020<div class="separator" style="clear: both; text-align: center;">
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<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-31602125816505047082020-04-14T07:47:00.001-07:002020-04-14T07:47:38.108-07:00Algebra 1 week of April 14, 2014<div class="paragraph" style="background-color: white; color: #666666; font-family: Muli !important; font-size: 16px; line-height: 1.8em; margin: 0px; overflow-wrap: break-word; padding: 0px;">
<strong>Monday 4.13 & Tuesday 4.14</strong><br />Mixed Review (Linear, Quadratic, Exponential)<br />Notes: Use the PowerPoint Applications of all 3 functions below.<br />Assignment: Complete the worksheet below.</div>
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<a href="http://pebblebrookalgebra1.weebly.com/uploads/1/2/9/2/129208817/applications_of_all_3_functions.pptx" style="color: rgba(51, 51, 51, 0.6); text-decoration-line: none; transition: color 200ms ease-in 0s;" title="Download file: applications_of_all_3_functions.pptx"><img height="36" src="http://www.weebly.com/weebly/images/file_icons/xls.png" style="border: 0px; float: left; left: 0px; margin: 0px 15px 15px 0px; position: relative; top: 0px;" width="36" /></a><div style="float: left; position: relative;">
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<tr><td colspan="2"><b>applications_of_all_3_functions.pptx</b></td></tr>
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<a href="http://pebblebrookalgebra1.weebly.com/uploads/1/2/9/2/129208817/applications_of_all_3_functions.pptx" style="color: rgba(51, 51, 51, 0.6); font-weight: bold; text-decoration-line: none; transition: color 200ms ease-in 0s;" title="Download file: applications_of_all_3_functions.pptx">Download File</a></div>
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<a href="http://pebblebrookalgebra1.weebly.com/uploads/1/2/9/2/129208817/phs_zombie_outbreak.docx" style="color: rgba(51, 51, 51, 0.6); text-decoration-line: none; transition: color 200ms ease-in 0s;" title="Download file: phs_zombie_outbreak.docx"><img height="36" src="http://www.weebly.com/weebly/images/file_icons/rtf.png" style="border: 0px; float: left; left: 0px; margin: 0px 15px 15px 0px; position: relative; top: 0px;" width="36" /></a><div style="float: left; position: relative;">
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<tr><td colspan="2"><b>phs_zombie_outbreak.docx</b></td></tr>
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<a href="http://pebblebrookalgebra1.weebly.com/uploads/1/2/9/2/129208817/phs_zombie_outbreak.docx" style="color: rgba(51, 51, 51, 0.6); font-weight: bold; text-decoration-line: none; transition: color 200ms ease-in 0s;" title="Download file: phs_zombie_outbreak.docx">Download File</a></div>
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<strong>Wednesday 4.15 & Thursday 4.16</strong><br />Sequences<br />Online Book: Khan Academy - use the button below for specific lesson. Please look at arithmetic and geometric sequences, lessons and activities (recursive and explicit for both)<br />Notes: Use the Anchor Charts to assist with instruction.<br />Assignment: Check for understanding activity on zoom call</div>
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<a class="wsite-button wsite-button-small wsite-button-normal" href="https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences" style="background: none; color: rgb(34, 34, 34) !important; cursor: pointer; display: inline-block; font-size: 14px !important; height: auto; padding: 0px; text-decoration-line: none !important; transition: color 200ms ease-in 0s;" target="_blank"><span class="wsite-button-inner" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 2px solid rgba(38, 38, 38, 0.6); color: rgba(38, 38, 38, 0.6) !important; display: block; float: left; font-family: Roboto, sans-serif; font-size: 13px !important; font-weight: 700; height: auto; letter-spacing: 0.02em; line-height: 1.5em; padding: 8px 16px; text-transform: uppercase; transition: all 400ms ease-in 0s;">KHAN ACADEMY - SEQUENCES</span></a><div style="height: 10px; overflow: hidden;">
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<a href="http://pebblebrookalgebra1.weebly.com/uploads/1/2/9/2/129208817/linquadexp_tables.pdf" style="color: rgba(51, 51, 51, 0.6); text-decoration-line: none; transition: color 200ms ease-in 0s;" title="Download file: linquadexp_tables.pdf"><img height="36" src="http://www.weebly.com/weebly/images/file_icons/pdf.png" style="border: 0px; float: left; left: 0px; margin: 0px 15px 15px 0px; position: relative; top: 0px;" width="36" /></a><div style="float: left; position: relative;">
<table style="font-family: tahoma; font-size: 12px; line-height: 0.9;"><tbody>
<tr><td colspan="2"><b>linquadexp_tables.pdf</b></td></tr>
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<a href="http://pebblebrookalgebra1.weebly.com/uploads/1/2/9/2/129208817/linquadexp_tables.pdf" style="color: rgba(51, 51, 51, 0.6); font-weight: bold; text-decoration-line: none; transition: color 200ms ease-in 0s;" title="Download file: linquadexp_tables.pdf">Download File</a></div>
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<strong>Friday 4.17</strong><br />Optional Tutoring Day<br />Please see your teacher's blog for more information.</div>
Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-25105294424310259712020-04-13T12:39:00.000-07:002020-04-13T12:39:03.018-07:00Week of April 13, 2020 CRM<div class="container" style="color: #393939; font-family: "Noto Sans", sans-serif; font-size: 16px;">
<main class="main main--marketing" role="main" style="background: rgb(255, 255, 255); padding: 3.75em 0px 0px;"><div class="layout-field layout-region layout-region--hotmath" style="box-sizing: border-box; clear: both; float: none; margin: 0px auto; max-width: 1050px; padding: 0px 10px; position: relative; width: 1050px;">
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Graphing Exponential Functions</h1>
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A simple exponential function to graph is <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>y</mi><mo>=</mo><msup><mn>2</mn><mi>x</mi></msup></mrow></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 3.581em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.876em;"><span style="border: 0px; clip: rect(1.515em, 1002.88em, 2.724em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-3" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-4" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-5" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.305em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="msup" id="MathJax-Span-6" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.305em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.96em;"><span style="border: 0px; clip: rect(3.178em, 1000.46em, 4.136em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.979em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-7" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.507em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.383em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>y</mi><mo>=</mo><msup><mn>2</mn><mi>x</mi></msup></mrow></math></span></span> .</div>
<div style="margin-bottom: 1em;">
</div>
<table border="1" cellpadding="0" cellspacing="0" style="margin: 0px 0px 1em; width: 278px;"><tbody>
<tr><td width="47"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-9" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-10" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></td><td align="center" width="28"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>3</mn></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-12" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.565em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.263em;"><span style="border: 0px; clip: rect(1.565em, 1001.21em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-13" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-14" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.003em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>3</mn></math></span></span></td><td align="center" width="34"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>2</mn></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-16" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.565em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.263em;"><span style="border: 0px; clip: rect(1.565em, 1001.21em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-17" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-18" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-19" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>2</mn></math></span></span></td><td align="center" width="30"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>1</mn></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-20" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.565em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.263em;"><span style="border: 0px; clip: rect(1.565em, 1001.21em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-21" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-22" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-23" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>1</mn></math></span></span></td><td align="center" width="27"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-24" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-25" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-26" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">0</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.003em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span></span></td><td align="center" width="28"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" id="MathJax-Element-7-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-27" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-28" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-29" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span></td><td align="center" width="28"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>" id="MathJax-Element-8-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-30" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-31" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-32" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span></td><td align="center" width="28"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>" id="MathJax-Element-9-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-33" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-34" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-35" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.003em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span></td></tr>
<tr><td><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mn>2</mn><mi>x</mi></msup></math>" id="MathJax-Element-10-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-36" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 3.581em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.876em;"><span style="border: 0px; clip: rect(1.515em, 1002.88em, 2.724em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-37" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-38" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-39" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.305em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="msup" id="MathJax-Span-40" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.305em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.96em;"><span style="border: 0px; clip: rect(3.178em, 1000.46em, 4.136em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.979em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-41" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.507em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.383em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-42" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mn>2</mn><mi>x</mi></msup></math></span></span></td><td align="center"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>8</mn></mfrac></math>" id="MathJax-Element-11-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-43" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.809em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; clip: rect(1.363em, 1000.66em, 2.926em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-44" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-45" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.103em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.456em;"><span style="border: 0px; clip: rect(3.38em, 1000.3em, 4.136em, -999.997em); left: 4.52083px; line-height: normal; margin: 0px 0px 0px -0.199em; padding: 0px; position: absolute; top: -4.383em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-46" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.38em, 1000.3em, 4.136em, -999.997em); left: 4.52083px; line-height: normal; margin: 0px 0px 0px -0.199em; padding: 0px; position: absolute; top: -3.627em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-47" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">8</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.859em, 1000.46em, 1.212em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.258em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0.003em; width: 0.456em;"></span><span style="border: 0px; display: inline-block; height: 1.061em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.559em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>8</mn></mfrac></math></span></span></td><td align="center"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac></math>" id="MathJax-Element-12-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-48" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.809em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; clip: rect(1.363em, 1000.66em, 2.926em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-49" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-50" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.103em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.456em;"><span style="border: 0px; clip: rect(3.38em, 1000.3em, 4.136em, -999.997em); left: 4.52083px; line-height: normal; margin: 0px 0px 0px -0.199em; padding: 0px; position: absolute; top: -4.383em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-51" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.38em, 1000.36em, 4.136em, -999.997em); left: 4.52083px; line-height: normal; margin: 0px 0px 0px -0.199em; padding: 0px; position: absolute; top: -3.576em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-52" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">4</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.859em, 1000.46em, 1.212em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.258em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0.003em; width: 0.456em;"></span><span style="border: 0px; display: inline-block; height: 1.061em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.559em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac></math></span></span></td><td align="center"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-13-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-53" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.809em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; clip: rect(1.363em, 1000.66em, 2.876em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-54" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-55" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.103em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.456em;"><span style="border: 0px; clip: rect(3.38em, 1000.3em, 4.136em, -999.997em); left: 4.52083px; line-height: normal; margin: 0px 0px 0px -0.199em; padding: 0px; position: absolute; top: -4.383em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-56" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.38em, 1000.3em, 4.136em, -999.997em); left: 4.52083px; line-height: normal; margin: 0px 0px 0px -0.199em; padding: 0px; position: absolute; top: -3.627em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-57" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 14.0269px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 3.984em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.859em, 1000.46em, 1.212em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.258em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0.003em; width: 0.456em;"></span><span style="border: 0px; display: inline-block; height: 1.061em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.497em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span></span></td><td align="center"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" id="MathJax-Element-14-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-58" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-59" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-60" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span></td><td align="center"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>" id="MathJax-Element-15-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-61" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-62" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-63" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span></td><td align="center"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>" id="MathJax-Element-16-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-64" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-65" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-66" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">4</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span></span></td><td align="center"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>" id="MathJax-Element-17-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 16px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-67" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.565em, 1000.46em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-68" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-69" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">8</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.003em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></span></span></td></tr>
</tbody></table>
<div style="margin-bottom: 1em;">
</div>
<div style="margin-bottom: 1em;">
<img src="https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/graphing-exponential-and-logarithmic-functions/graph1.gif" style="border-style: none; height: auto; max-width: 100%; vertical-align: bottom;" /></div>
<div style="margin-bottom: 1em;">
Notice that the graph has the <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" id="MathJax-Element-18-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-70" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-71" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-72" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span> -axis as an <a href="https://www.varsitytutors.com/hotmath/hotmath_help/topics/asymptotes.html" style="background-color: transparent; color: #007ac0; text-decoration-line: none;">asymptote </a>on the left, and increases very fast on the right.</div>
<div style="margin-bottom: 1em;">
Changing the <a href="https://www.varsitytutors.com/hotmath/hotmath_help/topics/exponents.html" style="background-color: transparent; color: #007ac0; text-decoration-line: none;">base </a>changes the shape of the graph.</div>
<div style="margin-bottom: 1em;">
<img src="https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/graphing-exponential-and-logarithmic-functions/graph2.gif" style="border-style: none; height: auto; max-width: 100%; vertical-align: bottom;" /></div>
<div style="margin-bottom: 1em;">
Replacing <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" id="MathJax-Element-19-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-73" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-74" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-75" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span> with <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mi>x</mi></math>" id="MathJax-Element-20-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-76" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.716em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.363em;"><span style="border: 0px; clip: rect(1.767em, 1001.31em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-77" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-78" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mi" id="MathJax-Span-79" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>x</mi></math></span></span> reflects the graph across the <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>" id="MathJax-Element-21-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-80" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.724em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-81" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-82" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span> -axis; replacing <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>" id="MathJax-Element-22-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-83" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.724em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-84" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-85" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span> with <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mi>y</mi></math>" id="MathJax-Element-23-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-86" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 1.565em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.263em;"><span style="border: 0px; clip: rect(1.767em, 1001.26em, 2.724em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-87" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-88" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mi" id="MathJax-Span-89" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>y</mi></math></span></span> reflects it across the <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" id="MathJax-Element-24-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-90" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-91" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-92" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span> -axis.</div>
<div style="margin-bottom: 1em;">
<img src="https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/graphing-exponential-and-logarithmic-functions/graph3.gif" style="border-style: none; height: auto; max-width: 100%; vertical-align: bottom;" /></div>
<div style="margin-bottom: 1em;">
Replacing <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" id="MathJax-Element-25-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-93" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-94" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-95" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.691em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span> with <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>h</mi></math>" id="MathJax-Element-26-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-96" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 2.876em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.321em;"><span style="border: 0px; clip: rect(1.515em, 1002.32em, 2.623em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-97" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-98" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-99" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.204em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-100" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.204em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">h</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.066em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.184em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>h</mi></math></span></span> <a href="https://www.varsitytutors.com/hotmath/hotmath_help/topics/transformations-of-graphs.html" style="background-color: transparent; color: #007ac0; text-decoration-line: none;">translates </a>the graph <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>" id="MathJax-Element-27-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-101" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.515em, 1000.56em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-102" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-103" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">h</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.003em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></span></span> units to the left.</div>
<div style="margin-bottom: 1em;">
<img src="https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/graphing-exponential-and-logarithmic-functions/graph4.gif" style="border-style: none; height: auto; max-width: 100%; vertical-align: bottom;" /></div>
<div style="margin-bottom: 1em;">
Replacing <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>" id="MathJax-Element-28-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-104" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.658em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.507em;"><span style="border: 0px; clip: rect(1.767em, 1000.51em, 2.724em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-105" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-106" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 0.941em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span> with <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>&#x2212;</mo><mi>k</mi></math>" id="MathJax-Element-29-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-107" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 2.724em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.17em;"><span style="border: 0px; clip: rect(1.515em, 1002.17em, 2.724em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-108" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-109" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-110" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.204em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mi" id="MathJax-Span-111" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.204em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">k</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.253em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>−</mo><mi>k</mi></math></span></span> (which is the same as adding <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>" id="MathJax-Element-30-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-112" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.515em, 1000.56em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-113" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-114" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">k</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.003em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></span></span> to the right side) translates the graph <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>" id="MathJax-Element-31-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-115" role="math" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.708em;"><span style="border: 0px; display: inline-block; font-size: 19.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.557em;"><span style="border: 0px; clip: rect(1.515em, 1000.56em, 2.523em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.366em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-116" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-117" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">k</span></span><span style="border: 0px; display: inline-block; height: 2.371em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.003em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></span></span> units up.</div>
<div style="margin-bottom: 1em;">
<img src="https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/graphing-exponential-and-logarithmic-functions/graph5.gif" style="border-style: none; height: auto; max-width: 100%; vertical-align: bottom;" /></div>
<div style="margin-bottom: 1em;">
Source:<a href="https://www.varsitytutors.com/hotmath/hotmath_help/topics/graphing-exponential-functions">https://www.varsitytutors.com/hotmath/hotmath_help/topics/graphing-exponential-functions</a></div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-16356103960252984572020-04-01T06:36:00.000-07:002020-04-01T07:10:19.143-07:00Algebra 1 , Wednesday April 1, 2020<div class="MsoNormal" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: normal; margin-bottom: 0in;">
<b>Wednesday 4/01/2020<o:p></o:p></b></div>
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Characteristics of Exponential Functions<o:p></o:p></div>
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<b>Online Book:</b> Holt McDougal Analytic Geometry<o:p></o:p></div>
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Module 12<o:p></o:p></div>
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Lesson 2<o:p></o:p></div>
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<b>Notes:</b><br />
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<b>Assignment:</b> </div>
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<span style="color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif;"><span style="font-size: 13.2px;"> x</span></span><br />
<span style="color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif;"><span style="font-size: 13.2px;">Graph and determine the characteristics of 1. y = 2 using a table of values.</span></span><br />
<span style="color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif;"><span style="font-size: 13.2px;"> x</span></span><br />
<span style="color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif;"><span style="font-size: 13.2px;"> 2. </span></span>y = (1/2)</div>
Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-84033702841438787422020-03-31T10:06:00.000-07:002020-03-31T10:06:10.347-07:00Algebra 1 Instructional video for Tuesday March, 30 2020<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dyNPZRd5VWAqS_VGVhWwIK40J64RQsQpj0T2OBhVHC-oIali1ZoWDyt7zGBSGttbqiL1jrEFCoCelav4jisAg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-66047093856334865262020-03-31T07:30:00.001-07:002020-03-31T07:30:26.967-07:00Algebra 1 , Tuesday March 31, 2020<br />
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<b>Tuesday 3/31/2020<o:p></o:p></b></div>
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Characteristics of Quadratic functions<o:p></o:p></div>
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<b>Online Book:</b> Khan Academy – <a href="http://www.khanacademy.org/" style="color: #888888; text-decoration-line: none;">www.khanacademy.org</a> – search features of quadratic functions<o:p></o:p></div>
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<a href="https://youtu.be/o-g5GuBgNVA" style="color: #888888; text-decoration-line: none;">https://youtu.be/o-g5GuBgNVA</a><o:p></o:p></div>
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<b>Notes:</b> Use the PowerPoint Characteristics of Quadratic Functions<o:p></o:p></div>
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<b>Assignment:</b> <div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKXfSMS_lJMLtW-mixyQyjFurrlEcyKFGVk70q9kUs3sMMYaoD1mckjNgPQl5lHJ6A1zV3U6YoQQhtmLYgAUwzYhyYINpq7ic2AkWAW8G-e2GIUDNp_rB54iDgXxekLnI623IROyc6USM/s1600/9.1_Identifying_Quadratic_Functions-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1237" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKXfSMS_lJMLtW-mixyQyjFurrlEcyKFGVk70q9kUs3sMMYaoD1mckjNgPQl5lHJ6A1zV3U6YoQQhtmLYgAUwzYhyYINpq7ic2AkWAW8G-e2GIUDNp_rB54iDgXxekLnI623IROyc6USM/s320/9.1_Identifying_Quadratic_Functions-1.jpg" width="247" /></a></div>
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Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-33922981186254644222020-03-30T08:53:00.000-07:002020-03-30T08:53:44.893-07:00Algebra 1 Instructional video for Monday March, 30 2020<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzgEOno1jCzgYv1rXnlfFYr7jSRN0k2VmuGxleYQFyLSkvXS1w8bT_ZfiKpL-W6cFbY-EAEshBZLMDrUPU0bg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-57586236968976858982020-03-30T07:17:00.002-07:002020-03-30T07:17:42.076-07:00Algebra 1 Week of March 30, 2020<br />
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<b>Monday 3/30/2020<o:p></o:p></b></div>
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Characteristics of Linear Equations<o:p></o:p></div>
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<b>Online Book:</b> Holt McDougal Coordinate Algebra<o:p></o:p></div>
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<span style="mso-tab-count: 1;"> </span>Module 10<o:p></o:p></div>
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<span style="mso-tab-count: 1;"> </span>Lesson 1<o:p></o:p></div>
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<b>Notes &</b><b>Assignment:</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFgPQQCJ0brrYQYc2vKvpyFtSbsVWeHrYO1vaCoLfbrJQky1tNOS5Wk7TCj6K8ED9U5V1tg19vPfflPzROwN2feqW3OQ-7BK2fuU0x57_GJY8L9k0WhPxq3l2OdtJ9ZGil7YDdSdYeTjY/s1600/linear+equations+review_mastery-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1215" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFgPQQCJ0brrYQYc2vKvpyFtSbsVWeHrYO1vaCoLfbrJQky1tNOS5Wk7TCj6K8ED9U5V1tg19vPfflPzROwN2feqW3OQ-7BK2fuU0x57_GJY8L9k0WhPxq3l2OdtJ9ZGil7YDdSdYeTjY/s320/linear+equations+review_mastery-1.jpg" width="242" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2Dc2u783nxK-Uy9ANMPbk3-iCNzI9SGPJPN__JFmzMnt2cRqRn6HUYhVhPdMfB7f858NIeNn7BBEjqHcL6gSoTxHNQzD7qiKWOxQ3dyBq0OCMjWXbKTTQwI8JfjVFUSavJnnMk6zFAVI/s1600/linear+equations+reading_strategies-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1215" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2Dc2u783nxK-Uy9ANMPbk3-iCNzI9SGPJPN__JFmzMnt2cRqRn6HUYhVhPdMfB7f858NIeNn7BBEjqHcL6gSoTxHNQzD7qiKWOxQ3dyBq0OCMjWXbKTTQwI8JfjVFUSavJnnMk6zFAVI/s320/linear+equations+reading_strategies-1.jpg" width="242" /></a></div>
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Instructional video will be posted after the zoom class. Kindly join the zoom class at 10.30a.m on Mondays- Wednesdays for instruction. The zoom id is :6134333209 .</div>
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I look forward to seeing you!</div>
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<b>Tuesday 3/31/2020<o:p></o:p></b></div>
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Characteristics of Quadratic functions<o:p></o:p></div>
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<b>Online Book:</b> Khan Academy – <a href="http://www.khanacademy.org/">www.khanacademy.org</a>
– search features of quadratic functions<o:p></o:p></div>
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<span style="mso-tab-count: 1;"> </span><a href="https://youtu.be/o-g5GuBgNVA">https://youtu.be/o-g5GuBgNVA</a><o:p></o:p></div>
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<b>Notes:</b> Use the PowerPoint Characteristics of Quadratic Functions<o:p></o:p></div>
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<b>Assignment:</b> <o:p></o:p></div>
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<b>Wednesday 4/01/2020<o:p></o:p></b></div>
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Characteristics of Exponential Functions<o:p></o:p></div>
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<b>Online Book:</b> Holt McDougal Analytic Geometry<o:p></o:p></div>
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<span style="mso-tab-count: 1;"> </span>Module 12<o:p></o:p></div>
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<span style="mso-tab-count: 1;"> </span>Lesson 2<o:p></o:p></div>
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<b>Notes:</b> Use the PowerPoint Characteristics of Exponential
Functions<o:p></o:p></div>
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<b>Assignment:</b> Worksheet on Characteristics of Exponential
Functions<o:p></o:p></div>
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<b>Thursday 04/02/2020<o:p></o:p></b></div>
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Optional Tutoring Days – See Instructors’ Blog<o:p></o:p></div>
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<b>Online Book:</b> <o:p></o:p></div>
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<b>Friday 04/03/2020<o:p></o:p></b></div>
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Optional Tutoring Days – See Instructors’ Blog<o:p></o:p></div>
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<b>Online Book:</b> <o:p></o:p></div>
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<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-12476013732786741442020-03-27T10:16:00.000-07:002020-03-27T10:16:05.476-07:00Algebra 1 Instructional video for Friday March, 27 2020<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzm_0Gyh8C2zrYpEzZh9cdLdCIuROP8aGzwH43ePtkXueQYawM7LBXJga8zjQaw-HW1NDpjmQCc4tTLAwj6DQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<br />Mrs. Osawaru's Bloghttp://www.blogger.com/profile/12884909675706022426noreply@blogger.com0tag:blogger.com,1999:blog-2759328130670863637.post-59557465823798438842020-03-27T08:16:00.000-07:002020-03-27T08:16:04.819-07:00Algebra 1, Friday March 27, 2020<span style="background-color: white; color: #666666; font-family: Muli; font-size: 16px;">Friday 3.27 <strong>Transforming Exponential Function</strong></span><br style="background-color: white; color: #666666; font-family: Muli; font-size: 16px;" /><strong style="background-color: white; color: #666666; font-family: Muli; font-size: 16px;"></strong><span style="background-color: white; color: #666666; font-family: Muli; font-size: 16px;">Holt McDougal Coordinate Algebra Module 13 - Extension 13.2 pg 358 - 360; </span><br />
<span style="background-color: white; color: #666666; font-family: Muli; font-size: 16px;">Notes: Copy Transformations of Exponential Functions Table;</span><br />
<strong style="color: #666666; font-family: Muli; font-size: 16px;">Transforming Exponential Function ppt: </strong><a href="http://pebblebrookalgebra1.weebly.com/lesson-323--327.html">http://pebblebrookalgebra1.weebly.com/lesson-323--327.html</a><br />
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Activity:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLTPi6x81pBrPSbcgykO8shCsNRX3gZF5wWoVE06DYeGgqx63lMvOzBkGnNh329Jp6XTub8TpICNR1iJGN6Y6gkCzFcmbtEMSt5iF3_pJW5Iivtmxo3hXEfK7mUE6tPINuIxo_4PcWX7Q/s1600/Transforming+exponential+function+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1003" data-original-width="784" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLTPi6x81pBrPSbcgykO8shCsNRX3gZF5wWoVE06DYeGgqx63lMvOzBkGnNh329Jp6XTub8TpICNR1iJGN6Y6gkCzFcmbtEMSt5iF3_pJW5Iivtmxo3hXEfK7mUE6tPINuIxo_4PcWX7Q/s320/Transforming+exponential+function+1.jpg" width="250" /></a></div>
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