Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
10th Edition
ISBN: 9780134673301
Author: Waits, Foley, Kennedy, Bock Demana
Publisher: PEARSON
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Chapter P, Problem 33RE
Solution

a.

The scatter plot of the given data.

  Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition, Chapter P, Problem 33RE , additional homework tip  1

Given:

The table shows for average SAT math score, y , in selected years x ,

    Year200820092010201120122013201420152016
    Annual Average cost514514515514514514513511508

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2y1x2x1
  • The slope of a line is defined as rise over run

Calculation:

The scatter plot of the given data is shown below:

  Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition, Chapter P, Problem 33RE , additional homework tip  2

b.

The linear equation for average SAT math score, y , in terms of the year x using the points 2008,514 and 2016,508 .

  y=0.75x2008+514

Given:

The table shows for average SAT math score, y , in selected years x ,

    Year200820092010201120122013201420152016
    Annual Average cost514514515514514514513511508

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2y1x2x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the linear equation, first find the slope of the line using the points 2008,514 and 2016,508 as shown below

  m=y2y1x2x1=50851420162008=68=0.75

Now, substitute m=0.75 and x1,y1=2008,514 into the point-slope form of the line and simplify further as shown below

  yy1=mxx1y514=0.75x2008y=0.75x2008+514

Thus, the linear equation for average SAT math score is y=0.75x2008+514 .

The graph on the scatter plot is shown below:

  Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition, Chapter P, Problem 33RE , additional homework tip  3

c.

The average SAT score in 2020 using the equation found in part (b).

  505

Given:

The linear equation that gives the average SAT score in year x is y=0.75x2008+514 .

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2y1x2x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the average SAT score in 2020, substitute x=2020 into the given equation and simplify further as shown below

  y=0.75x2008+514=0.7520202008+514=0.7512+514=9+514=505

Thus, the average SAT score in 2020 is 505 .

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

Ch. P.1 - Prob. 1ECh. P.1 - Prob. 2ECh. P.1 - Prob. 3ECh. P.1 - Prob. 4ECh. P.1 - Prob. 5ECh. P.1 - Prob. 6ECh. P.1 - Prob. 7ECh. P.1 - Prob. 8ECh. P.1 - Prob. 9ECh. P.1 - Prob. 10ECh. P.1 - Prob. 11ECh. P.1 - Prob. 12ECh. P.1 - Prob. 13ECh. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - Prob. 17ECh. P.1 - Prob. 18ECh. P.1 - Prob. 19ECh. P.1 - Prob. 20ECh. P.1 - Prob. 21ECh. P.1 - Prob. 22ECh. P.1 - Prob. 23ECh. P.1 - Prob. 24ECh. P.1 - Prob. 25ECh. P.1 - Prob. 26ECh. P.1 - Prob. 27ECh. P.1 - Prob. 28ECh. P.1 - Prob. 29ECh. P.1 - Prob. 30ECh. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Prob. 33ECh. P.1 - Prob. 34ECh. P.1 - Prob. 35ECh. P.1 - Prob. 36ECh. P.1 - Prob. 37ECh. P.1 - Prob. 38ECh. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Prob. 42ECh. P.1 - Prob. 43ECh. P.1 - Prob. 44ECh. P.1 - Prob. 45ECh. P.1 - Prob. 46ECh. P.1 - Prob. 47ECh. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - Prob. 50ECh. P.1 - Prob. 51ECh. P.1 - Prob. 52ECh. P.1 - Prob. 53ECh. P.1 - Prob. 54ECh. P.1 - Prob. 55ECh. P.1 - Prob. 56ECh. P.1 - Prob. 57ECh. P.1 - Prob. 58ECh. P.1 - Prob. 59ECh. P.1 - Prob. 60ECh. P.1 - Prob. 61ECh. P.1 - Prob. 62ECh. P.1 - Prob. 63ECh. P.1 - In Exercises 63 and 64, use scientific notation to...Ch. P.1 - Prob. 65ECh. P.1 - Prob. 66ECh. P.1 - Prob. 67ECh. P.1 - Prob. 68ECh. P.1 - Prob. 69ECh. P.1 - Prob. 70ECh. P.1 - Prob. 71ECh. P.1 - Prob. 72ECh. P.1 - Prob. 73ECh. P.1 - Prob. 74ECh. P.1 - Prob. 75ECh. P.1 - Prob. 76ECh. P.2 - Prob. 1QRCh. P.2 - Prob. 2QRCh. P.2 - Prob. 3QRCh. P.2 - Prob. 4QRCh. P.2 - Prob. 5QRCh. P.2 - Prob. 6QRCh. P.2 - Prob. 7QRCh. P.2 - Prob. 8QRCh. P.2 - Prob. 9QRCh. P.2 - Prob. 10QRCh. P.2 - Prob. 1ECh. P.2 - Prob. 2ECh. P.2 - Prob. 3ECh. P.2 - Prob. 4ECh. P.2 - Prob. 5ECh. P.2 - Prob. 6ECh. P.2 - Prob. 7ECh. P.2 - Prob. 8ECh. P.2 - Prob. 9ECh. P.2 - Prob. 10ECh. 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