College Algebra with Modeling & Visualization (5th Edition)
College Algebra with Modeling & Visualization (5th Edition)
5th Edition
ISBN: 9780321826138
Author: Gary K. Rockswold
Publisher: PEARSON
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Chapter 2, Problem 1EDE
To determine

  1. Estimated height of female with 12-inch humerus.
  2. Plot for ordered pairs (x,y) for both sexes and corresponding relationship.
  3. For 1-inch increase in the length of humerus, corresponding increase in heights for both sexes.
  4. Determination of linear functions that model the data.
  5. Use the linear functions to get estimation of height for given values of length of humerus.

Expert Solution & Answer
Check Mark

Answer to Problem 1EDE

Solution:

  1. 62.8 inch
  2. Plot
  3. College Algebra with Modeling & Visualization (5th Edition), Chapter 2, Problem 1EDE

  4. For 1-inch increase in length of humerus corresponding increase in height is 3.1-inches for female and 3-inches for male.
  5. The linear functions that model these data for female and male are f(x)=3.1x+25.6 and g(x)=3x+29 respectively.
  6. The range for the height a female when the humerous is between 9.7 to 10.1 is 55.67 to 56.91 inches, and the range for the height a male when the humerous is between 9.7 to 10.1 is 58.1 to 59.3 inches.

Explanation of Solution

a) From the given table we can observe that the estimated height of a female with 12-inch humerous is 62.8 inches.

b) From the given table we get the ordered pairs for female as (8, 50.4),

  (9, 53.5),

  (10, 56.6),

  (11, 59.7),

  (12, 62.8), and (13, 65.9) , and for male as (8, 53),

  (9, 56),

  (10, 59),

  (11, 62),

  (12, 65),

  (13, 68) , and (14, 71) . Now, plotting these points on we get the graph as shown below.

From the graph we can observe that all the points for female lie on a straight line and for male as well the points lie on a straight line. Therefore, we can say that the relation between the humerous and height of male or female is linear as for each 1-inch increase in the humerous the height of male or female increases by constant amount.

c) From the table we can observe that for 1-inch increase in humerous for female corresponds to 3.1 inches increase in the height, and for 1-inch increase in humerous for male corresponds to 3 inches in increase in the height.

d) For female, each 1-inch increase in humerous causes 3.1-inches increase in height so, the linear relation for female can be written as shown below.

  f(x)=3.1x+c

Now, Substitute x=8 and y=50.4 in the above equation and solve for c .

  f(x)=3.1x+c50.4=3.1(8)+cc=25.6

Substitute the value of c in f to get the relation for female.

  f(x)=3.1x+25.6

Similarly, for male, each 1-inch increase in humerous causes 3-inches increase in height so, the linear relation for male can be written as shown below.

  g(x)=3x+k

Now, for the point (8, 53.0) , we have x=8 and g(8)=53 . Use these values in the equation for g and solve it for k .

  g(x)=3x+k53=3(8)+k53=24+kk=29

Now, substitute the value of k in the equation for g to get the relation for male.

  g(x)=3x+29

Thus, the required linear functions that model these data for female and male are

  f(x)=3.1x+25.6 and g(x)=3x+29 respectively.

e) When x=9.7 , f(9.7)=3.1(9.7)+25.6 = 55.67 and g(9.7)=3(9.7)+29 = 58.1 .

When x=10.1 , f(10.1)=3.1(10.1)+25.6 = 56.91 and g(10.1)=3(10.1)+29 = 59.3 .

Therefore, the range for the height a female when the humerous is between 9.7 to 10.1 is 55.67 to 56.91 inches, and the range for the height a male when the humerous is between 9.7 to 10.1 is 58.1 to 59.3 inches.

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Chapter 2 Solutions

College Algebra with Modeling & Visualization (5th Edition)

Ch. 2.1 - Find the slope-intercept form for the line in the...Ch. 2.1 - Find the slope-intercept form for the line in the...Ch. 2.1 - Find the slope-intercept form for the line in the...Ch. 2.1 - Prob. 14ECh. 2.1 - Concepts Match the given equation to its graph (a-...Ch. 2.1 - Concepts Match the given equation to its graph (a-...Ch. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Concepts Match the given equation to its graph (a-...Ch. 2.1 - Concepts Match the given equation to its graph (a-...Ch. 2.1 - Prob. 21ECh. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Prob. 32ECh. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Prob. 45ECh. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Find the slope-intercept form for the line...Ch. 2.1 - Prob. 48ECh. 2.1 - Find an equation of the line satisfying the...Ch. 2.1 - Find an equation of the line satisfying the...Ch. 2.1 - Find an equation of the line satisfying the...Ch. 2.1 - Find an equation of the line satisfying the...Ch. 2.1 - Prob. 53ECh. 2.1 - Find an equation of the line satisfying the...Ch. 2.1 - Find an equation of the line satisfying the...Ch. 2.1 - Prob. 56ECh. 2.1 - Determine the x- and y-intercepts on the graph of...Ch. 2.1 - Determine the x- and y-intercepts on the graph of...Ch. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - Determine the x- and y-intercepts on the graph of...Ch. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - Prob. 69ECh. 2.1 - Prob. 70ECh. 2.1 - Prob. 71ECh. 2.1 - Prob. 72ECh. 2.1 - Prob. 73ECh. 2.1 - Prob. 74ECh. 2.1 - The table lists data that are exactly linear. 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Solve the inequality...Ch. 2.3 - (Refer to Example 2.) Solve the inequality...Ch. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - (Refer to Example 2.) Solve the inequality...Ch. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Use the given graph of y = ax + b to solve each...Ch. 2.3 - Use the given graph of y = ax + b to solve each...Ch. 2.3 - Use the given graph of y = ax + b to solve each...Ch. 2.3 - Use the given graph of y = ax + b to solve each...Ch. 2.3 - x-Intercept Method (Refer to Example 4.) Use the...Ch. 2.3 - x-Intercept Method (Refer to Example 4.) Use the...Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Solve the linear inequality graphically. Write the...Ch. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Solve the compound linear inequality graphically....Ch. 2.3 - Solve the compound linear inequality graphically....Ch. 2.3 - Solve the compound linear inequality graphically....Ch. 2.3 - The graphs of two linear functions f and g are...Ch. 2.3 - Use the figure to solve each equation or...Ch. 2.3 - Assume y1represents a linear function with the set...Ch. 2.3 - Assume y1 represents a linear function with the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve each inequality numerically. Write the...Ch. 2.3 - Solve the inequality. Approximate the end points...Ch. 2.3 - Prob. 80ECh. 2.3 - Solve the inequality. Approximate the end points...Ch. 2.3 - Solve the inequality. 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(a) Determine the...Ch. 2.4 - Complete the following for f(x). (a) Determine the...Ch. 2.4 - Complete the following for f(x). (a) Determine the...Ch. 2.4 - Complete the following for f(x). (a) Determine the...Ch. 2.4 - Graph f. 37. fx=12x+1if4x212xif2x123x+43if1x4Ch. 2.4 - Graph f. 38. fx=3212xif3x12xif1x212x5if2x3Ch. 2.4 - Use f(x) to complete the following....Ch. 2.4 - Use g(x) to complete the following....Ch. 2.4 - Use the graph of y = f(x) to write a...Ch. 2.4 - Use the graph of y = f(x) to write a...Ch. 2.4 - Housing Market One way to describe the housing...Ch. 2.4 - High School Dropouts The table lists the...Ch. 2.4 - Complete the following. (a) Use dot mode to graph...Ch. 2.4 - Complete the following. (a) Use dot mode to graph...Ch. 2.4 - Complete the following. (a) Use dot mode to graph...Ch. 2.4 - Complete the following. 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Super Bowl Ads The table lists the cost in...Ch. 2.4 - Women in Politics The table lists the percentage P...Ch. 2.4 - Prob. 71ECh. 2.4 - Prob. 72ECh. 2.4 - Prob. 73ECh. 2.4 - Prob. 74ECh. 2.4 - Prob. 1EDECh. 2.4 - Prob. 2EDECh. 2.4 - Prob. 3EDECh. 2.4 - Prob. 4EDECh. 2.4 - Prob. 5EDECh. 2.4 - Prob. 1CBCCh. 2.4 - Prob. 2CBCCh. 2.4 - Prob. 3CBCCh. 2.4 - Prob. 4CBCCh. 2.4 - Prob. 5CBCCh. 2.5 - Exercises 1-8: Let a ? 0. 1. Solve | x | = 3.Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Graph by hand. (a) Find the x-intercept. (b)...Ch. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - (Refer to Example 1.) Do the following. (a) Graph...Ch. 2.5 - Prob. 15ECh. 2.5 - (Refer to Example 1.) Do the following. (a) Graph...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Solve the absolute value equation. 19. | -2x | = 4Ch. 2.5 - Solve the absolute value equation. 20. . ? 3x ?...Ch. 2.5 - Prob. 21ECh. 2.5 - Solve the absolute value equation. 22. | -3x - 2 |...Ch. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Solve the absolute value equation. 26. | 6x - 9 |...Ch. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Solve the absolute value equation. 32. | 3 - 3x |...Ch. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Solve the absolute value equation. 36. | x - 3 | =...Ch. 2.5 - Prob. 37ECh. 2.5 - Solve the absolute value equation. 38....Ch. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - The graphs of f and g are shown. Solve each...Ch. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Solve the equation (a) graphically, (b)...Ch. 2.5 - Solve the equation (a) graphically, (b)...Ch. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Solve the inequality. Write the solution in...Ch. 2.5 - Prob. 56ECh. 2.5 - Solve the inequality. Write the solution in...Ch. 2.5 - Solve the inequality. Write the solution in...Ch. 2.5 - Prob. 59ECh. 2.5 - Solve the inequality. Write the solution in...Ch. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Prob. 69ECh. 2.5 - Prob. 70ECh. 2.5 - Prob. 71ECh. 2.5 - Prob. 72ECh. 2.5 - Prob. 73ECh. 2.5 - Human Cannonball A human cannonball plans to...Ch. 2.5 - Prob. 75ECh. 2.5 - Dew Point and Altitude The dew point decreases as...Ch. 2.5 - Prob. 77ECh. 2.5 - Prob. 78ECh. 2.5 - Prob. 79ECh. 2.5 - Prob. 80ECh. 2.5 - Prob. 81ECh. 2.5 - Prob. 82ECh. 2.5 - Prob. 83ECh. 2.5 - Prob. 84ECh. 2.5 - Prob. 85ECh. 2.5 - Prob. 86ECh. 2.5 - Prob. 87ECh. 2.5 - Prob. 88ECh. 2.5 - Prob. 89ECh. 2.5 - Prob. 90ECh. 2.5 - Prob. 1EDECh. 2.5 - Prob. 2EDECh. 2.5 - Prob. 1CBCCh. 2.5 - Prob. 2CBCCh. 2.5 - Prob. 3CBCCh. 2.5 - Prob. 4CBCCh. 2.5 - Prob. 5CBCCh. 2 - Prob. 1EDECh. 2 - Prob. 2EDECh. 2 - A Puzzle Three people leave for a city 15 miles...Ch. 2 - Prob. 4EDECh. 2 - Prob. 1CRECh. 2 - Prob. 2CRECh. 2 - Prob. 3CRECh. 2 - Prob. 4CRECh. 2 - Prob. 5CRECh. 2 - Prob. 6CRECh. 2 - Prob. 7CRECh. 2 - Prob. 8CRECh. 2 - Prob. 9CRECh. 2 - Prob. 10CRECh. 2 - Prob. 11CRECh. 2 - Prob. 12CRECh. 2 - Prob. 13CRECh. 2 - Write a formula for a function f that computes the...Ch. 2 - Prob. 15CRECh. 2 - Prob. 16CRECh. 2 - Prob. 17CRECh. 2 - Prob. 18CRECh. 2 - Prob. 19CRECh. 2 - Prob. 20CRECh. 2 - Prob. 21CRECh. 2 - Write an equation of a line satisfying the given...Ch. 2 - Write an equation of a line satisfying the given...Ch. 2 - Prob. 24CRECh. 2 - Prob. 25CRECh. 2 - Prob. 26CRECh. 2 - Prob. 27CRECh. 2 - Prob. 28CRECh. 2 - Prob. 29CRECh. 2 - Prob. 30CRECh. 2 - Prob. 31CRECh. 2 - Prob. 32CRECh. 2 - Prob. 33CRECh. 2 - Prob. 34CRECh. 2 - Prob. 35CRECh. 2 - Prob. 36CRECh. 2 - Prob. 37CRECh. 2 - Prob. 38CRECh. 2 - Prob. 39CRECh. 2 - Prob. 40CRECh. 2 - Prob. 41CRECh. 2 - Prob. 42CRECh. 2 - Prob. 43CRECh. 2 - Prob. 44CRECh. 2 - Prob. 45CRECh. 2 - Prob. 46CRECh. 2 - Prob. 47CRECh. 2 - Prob. 48CRECh. 2 - Prob. 49CRECh. 2 - Prob. 50CRECh. 2 - Prob. 51CRECh. 2 - Prob. 52CRECh. 2 - Prob. 53CRECh. 2 - Prob. 54CRECh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Find the slope-intercept form of the equation of a...Ch. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RE
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