Question 1

Find the least squares regression line for the points   . Round numerical values in your answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    C

Question 2

Suppose an agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre) and the amount of fertilizer x (in hundreds of pounds per acre). The results are shown in the table. Determine the least squares regression line for the data using the regression capabilities of a graphing utility, and then use this model to estimate the yield for a fertilizer application of 160 pounds per acre. Round your answer to one decimal place.

Accepted Answer

A)  37.3 bushels per acre 
B)  39.7 bushels per acre 
C)  35.6 bushels per acre 
D)  38.4 bushels per acre 
E)  39.3 bushels per acre 
A)  37.3 bushels per acre 
B)  39.7 bushels per acre 
C)  35.6 bushels per acre 
D)  38.4 bushels per acre 
E)  39.3 bushels per acre D

Question 3

Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 640 cubic feet. The cost of wall paint is $0.076 per square foot and the cost of ceiling paint is $0.19 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Find the room dimensions that result in a minimum cost for the paint. Round your answers to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    A

Question 4

The least squares regression line for the points shown in the graph is   . Calculate S, the sum of the squared errors.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Find the least squares regression line for the points   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Suppose a trough with trapezoidal cross sections is formed by turning up the edges of a 30-inch-wide sheet of aluminum (see figure). Find the cross section of maximum area.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 360 cubic feet. The cost of wall paint is $0.054 per square foot and the cost of ceiling paint is $0.18 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Identify the room dimensions that result in a minimum cost for the paint and use these dimensions to find the minimum cost for the paint. Round your answer to the nearest cent.

Accepted Answer

A)  $54.00 
B)  $8.64 
C)  $7.00 
D)  $19.44 
E)  $21.60 
A)  $54.00 
B)  $8.64 
C)  $7.00 
D)  $19.44 
E)  $21.60

Question 8

Find the minimum distance from the point   to the plane   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Suppose an agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre) and the amount of fertilizer x (in hundreds of pounds per acre). The results are shown in the table. Use the regression capabilities of a graphing utility to find the least squares regression line for the data.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

The material for constructing the base of an open box costs 1.5 times as much per unit area as the material for constructing the sides. For a fixed amount of money $150.00, find the dimensions of the box of largest volume that can be made.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Find three positive numbers x, y, and z whose sum is 30 and the sum of the squares is a minimum.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Suppose a store manager wants to know the demand y for an energy bar as a function of price x. The daily sales for three different prices of the energy bar are shown in the table. Determine the least squares regression line for the data using the regression capabilities of a graphing utility, and then use this model to estimate the demand when the price is $1.59.

Accepted Answer

A)  202 
B)  166 
C)  190 
D)  151 
A)  202 
B)  166 
C)  190 
D)  151

Question 13

A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue from   units of running shoes and   units of basketball shoes is:   , where   and   are in thousands of units. Find   and   so as to maximize the revenue.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Find the least squares regression line for the points shown in the graph.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Suppose a store manager wants to know the demand y for an energy bar as a function of price x. The daily sales for three different prices of the energy bar are shown in the table. Use the regression capabilities of a graphing utility to find the least squares regression line for the data.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Find the minimum distance from the point   to the surface   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Find three positive numbers x, y, and z whose sum is 24 and product is a maximum.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Suppose a corporation manufactures candles at two locations. The cost of producing   units at location 1 is   and the cost of producing   units at location 2 is   . The candles sell for $43 per unit. Find the quantity that should be produced at each location to maximize the profit   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Exam 13: Section 10: Functions of Several Variables

Find the least squares regression line for the points . Round numerical values in your answer to two decimal places.

The least squares regression line for the points shown in the graph is . Calculate S, the sum of the squared errors.

Find the least squares regression line for the points .

Suppose a trough with trapezoidal cross sections is formed by turning up the edges of a 30-inch-wide sheet of aluminum (see figure). Find the cross section of maximum area.

Find the minimum distance from the point to the plane .

The material for constructing the base of an open box costs 1.5 times as much per unit area as the material for constructing the sides. For a fixed amount of money $150.00, find the dimensions of the box of largest volume that can be made.

Find three positive numbers x, y, and z whose sum is 30 and the sum of the squares is a minimum.

A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue from units of running shoes and units of basketball shoes is: , where and are in thousands of units. Find and so as to maximize the revenue.

Find the least squares regression line for the points shown in the graph.

Suppose a store manager wants to know the demand y for an energy bar as a function of price x. The daily sales for three different prices of the energy bar are shown in the table. Use the regression capabilities of a graphing utility to find the least squares regression line for the data.

Find the minimum distance from the point to the surface .

Find three positive numbers x, y, and z whose sum is 24 and product is a maximum.

Suppose a corporation manufactures candles at two locations. The cost of producing units at location 1 is and the cost of producing units at location 2 is . The candles sell for $43 per unit. Find the quantity that should be produced at each location to maximize the profit .

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series

Section 5: Infinite Series

Section 6: Infinite Series

Section 7: Infinite Series

Section 8: Infinite Series

Section 9: Infinite Series

Section 10: Infinite Series