Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…
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Textbook Question
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Chapter 3, Problem 11CT

Consider these two data sets:

Chapter 3, Problem 11CT, Consider these two data sets: One data set follows a linear pattern and one data set follows a

One data set follows a linear pattern and one data set follows a quadratic relation.

a. Draw a scatter diagram of each data set. Determine which is linear and which is quadratic. For the linear data, indicate whether the relation shows a positive or negative slope. For the quadratic relation, indicate whether the quadratic function of best fit will open up or down.

b. For the linear data set, find the line of best fit.

c. For the quadratic data set, find the quadratic function of best fit.

Expert Solution & Answer
Check Mark
To determine

To graph:

a. The scatter diagram for both the given sets, indicate the slope or if it opens up or down.

b. Find the line of best fit for the linear data.

c. Find the quadratic function of best fit.

Answer to Problem 11CT

a. The Set A has a linear relation with negative slope.

The Set B is having a quadratic relation where the function of best fit opens upwards.

b. The line of best fit for Set A is

y = −4.234x − 2.3617

c. The function of best fit the Set B is

y = 1.9928 x 2  + 0.2894x + 2.5031

Explanation of Solution

Given:

The given sets of data are

Precalculus Enhanced with Graphing Utilities, Chapter 3, Problem 11CT , additional homework tip 1

Graph:

The scatter diagram of Set A is

Precalculus Enhanced with Graphing Utilities, Chapter 3, Problem 11CT , additional homework tip 2

The scatter plot of Set B is

Precalculus Enhanced with Graphing Utilities, Chapter 3, Problem 11CT , additional homework tip 3

Interpretation:

We can draw the scatter diagram using Microsoft Excel.

Enter the values in the Excel work sheet and then select the Scatter plot from insert option.

Then to draw the functions of best fit, choose the Trend lines from the layout options.

a. The Set A has a linear relation with negative slope.

The Set B is having a quadratic relation where the function of best fit opens upwards.

b. The line of best fit for Set A is

y = −4.234x − 2.3617

c. The function of best fit the Set B is

y = 1.9928 x 2  + 0.2894x + 2.5031

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Chapter 3, Problem 10CT
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Chapter 3, Problem 1CR

Chapter 3 Solutions

Precalculus Enhanced with Graphing Utilities

Ch. 3.1 - Graph y=2x3 . (pp. 32-35)Ch. 3.1 - Find the slope of the line joining the points (...Ch. 3.1 - Find the average rate of change of f(x)=3 x 2 2 ,...Ch. 3.1 - Solve: 6x900=15x+2850 . (pp. A44-A46)Ch. 3.1 - If f( x )= x 2 4 , find f( 2 ) . (pp. 60-62)Ch. 3.1 - True or False The graph of the function f( x )= x...Ch. 3.1 - For the graph of the linear function f( x )=mx+b ,...Ch. 3.1 - If the slope m of the graph of a linear function...Ch. 3.1 - True or False The slope of a nonvertical line is...Ch. 3.1 - True or False The average rate of change of f( x...
Ch. 3.1 - What is the only type of function that has a...Ch. 3.1 - A car has 12,500 miles on its odometer. Say the...Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - Suppose that f( x )=4x1 and g(x)=2x+5 . a. Solve...Ch. 3.1 - Suppose that f( x )=3x+5 and g(x)=2x+15 . a. Solve...Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - Car Rentals The cost C , in dollars, of a one-day...Ch. 3.1 - Phone Charges The monthly cost C , in dollars, for...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Taxes The function T( x )=0.15(x9225)+922.50...Ch. 3.1 - Competitive Balance Tax In 2011, major league...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Cost Function The simplest cost function is the...Ch. 3.1 - Cost Function Refer to Problem 47. Suppose that...Ch. 3.1 - Truck Rentals A truck rental company rents a truck...Ch. 3.1 - International Calling A cell phone company offers...Ch. 3.1 - Developing a Linear Model from Data How many songs...Ch. 3.1 - Developing a Linear Model from Data The following...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Under what circumstances is a linear function f( x...Ch. 3.1 - Explain how the graph of f( x )=mx+b can be used...Ch. 3.2 - Plot the points ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 )...Ch. 3.2 - Find an equation of the line containing the points...Ch. 3.2 - A _____________ is used to help us to see what...Ch. 3.2 - If the Independent variable in a line of best fit...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - Prob. 17AYUCh. 3.2 - Prob. 18AYUCh. 3.2 - Prob. 19AYUCh. 3.2 - Prob. 20AYUCh. 3.2 - Prob. 21AYUCh. 3.2 - Prob. 22AYUCh. 3.2 - Prob. 23AYUCh. 3.2 - Prob. 24AYUCh. 3.2 - Prob. 25AYUCh. 3.3 - List the intercepts of the equation y= x 2 9 ....Ch. 3.3 - Prob. 2AYUCh. 3.3 - To complete the square of x 2 5x , you add the...Ch. 3.3 - To graph y= (x4) 2 you shift the graph of y= x 2...Ch. 3.3 - The graph of a quadratic function is called a(n)...Ch. 3.3 - The vertical line passing through the vertex of a...Ch. 3.3 - The x-coordinate of the vertex of f( x )=a x 2...Ch. 3.3 - True or False The graph of f( x )=2 x 2 +3x4 opens...Ch. 3.3 - True or False The y-coordinate of the vertex of f(...Ch. 3.3 - True or False If the discriminant b 2 4ac=0 , the...Ch. 3.3 - If b 2 4ac0 , which of the following conclusions...Ch. 3.3 - If the graph of f( x )=a x 2 +bx+c,a0 , has a...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - The graph of the function f( x )=a x 2 +bx+c has...Ch. 3.3 - The graph of the function f(x)=a x 2 +bx+c has...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Suppose that f(x)= x 2 +4x21 . (a) What is the...Ch. 3.3 - Suppose that f( x )= x 2 +2x8 . (a) What is the...Ch. 3.3 - Find the point on the line y=x that is closest to...Ch. 3.3 - Find the point on the line y=x+1 that is closest...Ch. 3.3 - Maximizing Revenue Suppose that the manufacturer...Ch. 3.3 - Maximizing Revenue The John Deere company has...Ch. 3.3 - Minimizing Marginal Cost The marginal cost of a...Ch. 3.3 - Minimizing Marginal Cost (See Problem 91.) The...Ch. 3.3 - Business The monthly revenue R achieved by selling...Ch. 3.3 - Business The daily revenue R achieved by selling x...Ch. 3.3 - Stopping Distance An accepted relationship between...Ch. 3.3 - Birthrate for Unmarried Women In the United...Ch. 3.3 - Let f( x )=a x 2 +bx+c , where a,b,andc are odd...Ch. 3.3 - Make up a quadratic function that opens down and...Ch. 3.3 - On one set of coordinate axes, graph the family of...Ch. 3.3 - On one set of coordinate axes, graph the family of...Ch. 3.3 - State the circumstances that cause the graph of a...Ch. 3.3 - Why does the graph of a quadratic function open up...Ch. 3.3 - Can a quadratic function have a range of ( , ) ?...Ch. 3.3 - What are the possibilities for the number of times...Ch. 3.4 - Translate the following sentence into a...Ch. 3.4 - Use a graphing utility to find the line of best...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Enclosing a Rectangular Field David has 400 yards...Ch. 3.4 - Enclosing a Rectangular Field Beth has 3000 feet...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Analyzing the Motion of a Projectile A projectile...Ch. 3.4 - Analyzing the Motion of a Projectile A projectile...Ch. 3.4 - Suspension Bridge A suspension bridge with weight...Ch. 3.4 - Architecture A parabolic arch has a span of 120...Ch. 3.4 - Constructing Rain Gutters A rain gutter is to be...Ch. 3.4 - Norman Windows A Norman window has the shape of a...Ch. 3.4 - Constructing a Stadium A track-and-field playing...Ch. 3.4 - Architecture A special window has the shape of a...Ch. 3.4 - Chemical Reactions A self-catalytic chemical...Ch. 3.4 - Calculus: Simpson's Rule The figure shows the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Life Cycle Hypothesis An individuals income varies...Ch. 3.4 - Height of a Rail A shot-putter throws a hall at an...Ch. 3.4 - Which Model? The following data represent the...Ch. 3.4 - Which Model? An engineer collects the following...Ch. 3.4 - Which Model? The following data represent the...Ch. 3.4 - Which Model? A cricket makes a chirping noise by...Ch. 3.4 - Refer to Example 1 in this section. Notice that if...Ch. 3.5 - Solve the inequality 3x27 .Ch. 3.5 - Write (2,7] using inequality notation.Ch. 3.5 - (a) f( x )0 (b) f( x )0Ch. 3.5 - (a) g( x )0 (b) g( x )0Ch. 3.5 - (a) g( x )f( x ) (b) f( x )g( x )Ch. 3.5 - (a) f( x )g( x ) (b) f( x )g( x )Ch. 3.5 - x 2 3x100Ch. 3.5 - x 2 +3x100Ch. 3.5 - x 2 4x0Ch. 3.5 - x 2 +8x0Ch. 3.5 - x 2 90Ch. 3.5 - x 2 10Ch. 3.5 - x 2 +x12Ch. 3.5 - x 2 +7x12Ch. 3.5 - 2 x 2 5x+3Ch. 3.5 - 6 x 2 6+5xCh. 3.5 - x 2 x+10Ch. 3.5 - x 2 +2x+40Ch. 3.5 - 4 x 2 +96xCh. 3.5 - 25 x 2 +1640xCh. 3.5 - 6( x 2 1 )5xCh. 3.5 - 2( 2 x 2 3x )9Ch. 3.5 - What is the domain of the function f( x )= x 2 16...Ch. 3.5 - What is the domain of the function f( x )= x3 x 2...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Revenue Suppose that the manufacturer of a gas...Ch. 3.5 - Revenue The John Deere company has found that the...Ch. 3.5 - Artillery A projectile Fired from the point ( 0,0...Ch. 3.5 - Runaway Car Using Hooke's Law, we can show that...Ch. 3.5 - Show that the inequality ( x4 ) 2 0 has exactly...Ch. 3.5 - Show that the inequality ( x2 ) 2 0 has one real...Ch. 3.5 - Explain why the inequality x 2 +x+10 has all real...Ch. 3.5 - Explain why the inequality x 2 x+10 has the empty...Ch. 3.5 - Explain the circumstances under which the...Ch. 3 - In Problems 1-3: (a) Determine the slope and...Ch. 3 - In Problems 1-3: (a) Determine the slope and...Ch. 3 - In Problems 1-3: (a) Determine the slope and...Ch. 3 - In Problems 4 and 5, determine whether the...Ch. 3 - In Problems 4 and 5, determine whether the...Ch. 3 - In Problems 6-8, graph each quadratic function...Ch. 3 - In Problems 6-8, graph each quadratic function...Ch. 3 - In Problems 6-8, graph each quadratic function...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 15-17, determine whether the given...Ch. 3 - In Problems 15-17, determine whether the given...Ch. 3 - In Problems 15-17, determine whether the given...Ch. 3 - In Problems 18-19, solve each quadratic...Ch. 3 - In Problems 18-19, solve each quadratic...Ch. 3 - 20. In Problems 20 and 21, find the quadratic...Ch. 3 - 21. In Problems 20 and 21, find the quadratic...Ch. 3 - 22. Sales Commissions Bill has just been offered a...Ch. 3 - 23. Demand Equation the price p (in dollars) and...Ch. 3 - 24. Enclosing the Most Area with a Fence A farmer...Ch. 3 - 25. Minimizing Marginal Cost Callaway Golf Company...Ch. 3 - 26. Maximizing Area A rectangle has one vertex on...Ch. 3 - 27. Parabolic Arch Bridge A horizontal bridge is...Ch. 3 - 28. Bono Length Research performed at NASA, led by...Ch. 3 - 29. Advertising A small manufacturing firm...Ch. 3 - For the linear function f( x )=4x+3 , a. Find the...Ch. 3 - Determine whether the given function is linear or...Ch. 3 - Graph f(x)= (x3) 2 2 using transformations.Ch. 3 - In Problems 4 and 5, a. Determine whether the...Ch. 3 - In Problems 4 and 5, a. Determine whether the...Ch. 3 - Determine the quadratic function for the given...Ch. 3 - Determine whether f( x )=-2 x 2 +12x+3 has a...Ch. 3 - Solve, x 2 10x+240 .Ch. 3 - The weekly rental cost of a 20-foot recreational...Ch. 3 - The price p (in dollars) and the quantity x sold...Ch. 3 - Consider these two data sets: One data set follows...Ch. 3 - Find the distance between the points P=( 1,3 ) and...Ch. 3 - Which of the following points are on the graph of,...Ch. 3 - Solve the inequality 5x+30 and graph the solution...Ch. 3 - Find the equation of the line containing the...Ch. 3 - Find the equation of the line perpendicular to the...Ch. 3 - Graph the equation x 2 + y 2 4x+8y5=0 .Ch. 3 - Does the following relation represent a function?...Ch. 3 - For the function f defined by f( x )= x 2 4x+1 ,...Ch. 3 - Find the domain of h(z)= 3z1 6z7 .Ch. 3 - Is the following graph the graph of a function?Ch. 3 - Consider the function f(x)= x x+4 . a. Is the...Ch. 3 - Is the function f(x)= x 2 2x+1 even, odd, or...Ch. 3 - Approximate the local maximum values and local...Ch. 3 - If f(x)=3x+5 and g(x)=2x+1 , a. Solve f(x)=g( x )...Ch. 3 - For the graph of the function f , a. Find the...

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