Question 1

Sketch the graph of the function   . ​

Accepted Answer

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

Question 2

Find the vertex of the graph of the equation   . ​

Accepted Answer

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

Question 3

If, in a monopoly market, the demand for a product is   , and the revenue function is   , where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent. ​

Accepted Answer

A) Price that will maximize revenue is  
) 
B) Price that will maximize revenue is  
) 
C) Price that will maximize revenue is  
) 
D) Price that will maximize revenue is  
) 
E) Price that will maximize revenue is  
) 
A) Price that will maximize revenue is  
) 
B) Price that will maximize revenue is  
) 
C) Price that will maximize revenue is  
) 
D) Price that will maximize revenue is  
) 
E) Price that will maximize revenue is  
)

Question 4

Suppose a company has fixed costs of $26,000 and variable costs of   dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is   dollars per unit. Find the break-even points. Round your answer to the nearest cent.

Accepted Answer

A) Break-even values are at  
And  
) 
B) Break-even values are at  
And  
) 
C) Break-even values are at  
And  
) 
D) Break-even values are at  
And  
) 
E) Break-even values are at  
And  
) 
A) Break-even values are at  
And  
) 
B) Break-even values are at  
And  
) 
C) Break-even values are at  
And  
) 
D) Break-even values are at  
And  
) 
E) Break-even values are at  
And  
)

Question 5

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places. ​   ​

Accepted Answer

A) linear;   
B) quadratic;   
C) power;   
D) cubic;   
E) quartic;   
A) linear;   
B) quadratic;   
C) power;   
D) cubic;   
E) quartic;

Question 6

Find the exact real solutions of the equation   , if they exist. ​

Accepted Answer

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

Question 7

An open-top box is constructed from a square piece of cardboard with sides of length 10 ft. The volume of such a box is given by   , where x is the height of the box. Find the volume of the box if its height is 2 ft. ​

Accepted Answer

A) 70.5 ft3 
B) 71.5 ft3 
C) 72 ft3 
D) 74 ft3 
E) 76.5 ft3 
A) 70.5 ft3 
B) 71.5 ft3 
C) 72 ft3 
D) 74 ft3 
E) 76.5 ft3

Question 8

The owner of a skating rink rents the rink for parties at $696 if 58 or fewer skaters attend, so that the cost per person is $12 if 58 attend. For each 5 skaters above 58, she reduces the price per skater by $0.50. Which table gives the revenue generated if 58, 68, and 78 skaters attend? ​

Accepted Answer

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

Question 9

Solve the equation   . ​

Accepted Answer

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

Question 10

The sensitivity S to a drug is related to the dosage x in milligrams by   . Use a graphing utility to determine what dosage gives maximum sensitivity. ​

Accepted Answer

A) 97 
B) 235,225 
C) 970, 0 
D) 970 
E) 485 
A) 97 
B) 235,225 
C) 970, 0 
D) 970 
E) 485

Question 11

Assume that sales revenues, in millions, for Continental Divide Mining can be described by   , where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places. ​

Accepted Answer

A) Maximum revenue is $9.463 million. 
B) Maximum revenue is $5.971 million. 
C) Maximum revenue is $3.672 million. 
D) Maximum revenue is $3.851 million. 
E) Maximum revenue is $16.986 million. 
A) Maximum revenue is $9.463 million. 
B) Maximum revenue is $5.971 million. 
C) Maximum revenue is $3.672 million. 
D) Maximum revenue is $3.851 million. 
E) Maximum revenue is $16.986 million.

Question 12

Multiply both sides of the equation   by the LCD, and then solve the resulting quadratic equation. ​

Accepted Answer

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

Question 13

When a stone is thrown upward, it follows a parabolic path given by a form of the equation   . If   represents ground level, find the equation of a stone that is thrown from ground level at   and lands on the ground 130 units away if the stone reaches a maximum height of 130 units. ​

Accepted Answer

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

Sketch the graph of the function .

Find the vertex of the graph of the equation .

If, in a monopoly market, the demand for a product is , and the revenue function is , where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent.

Suppose a company has fixed costs of $26,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the break-even points. Round your answer to the nearest cent.

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places.

Find the exact real solutions of the equation , if they exist.

An open-top box is constructed from a square piece of cardboard with sides of length 10 ft. The volume of such a box is given by , where x is the height of the box. Find the volume of the box if its height is 2 ft.

The owner of a skating rink rents the rink for parties at $696 if 58 or fewer skaters attend, so that the cost per person is $12 if 58 attend. For each 5 skaters above 58, she reduces the price per skater by $0.50. Which table gives the revenue generated if 58, 68, and 78 skaters attend?

Solve the equation .

The sensitivity S to a drug is related to the dosage x in milligrams by . Use a graphing utility to determine what dosage gives maximum sensitivity.

Assume that sales revenues, in millions, for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places.

Multiply both sides of the equation by the LCD, and then solve the resulting quadratic equation.

When a stone is thrown upward, it follows a parabolic path given by a form of the equation . If represents ground level, find the equation of a stone that is thrown from ground level at and lands on the ground 130 units away if the stone reaches a maximum height of 130 units.

Algebraic Concepts

Linear Equations and Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 3: Quadratic and Other Special Functions

Sketch the graph of the function . ​

Find the vertex of the graph of the equation . ​

If, in a monopoly market, the demand for a product is , and the revenue function is , where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent. ​

Suppose a company has fixed costs of $26,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the break-even points. Round your answer to the nearest cent.

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places. ​ ​

Find the exact real solutions of the equation , if they exist. ​

An open-top box is constructed from a square piece of cardboard with sides of length 10 ft. The volume of such a box is given by , where x is the height of the box. Find the volume of the box if its height is 2 ft. ​

The owner of a skating rink rents the rink for parties at $696 if 58 or fewer skaters attend, so that the cost per person is $12 if 58 attend. For each 5 skaters above 58, she reduces the price per skater by $0.50. Which table gives the revenue generated if 58, 68, and 78 skaters attend? ​

Solve the equation . ​

The sensitivity S to a drug is related to the dosage x in milligrams by . Use a graphing utility to determine what dosage gives maximum sensitivity. ​

Assume that sales revenues, in millions, for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places. ​

Multiply both sides of the equation by the LCD, and then solve the resulting quadratic equation. ​

When a stone is thrown upward, it follows a parabolic path given by a form of the equation . If represents ground level, find the equation of a stone that is thrown from ground level at and lands on the ground 130 units away if the stone reaches a maximum height of 130 units. ​

Algebraic Concepts

Linear Equations and Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Sketch the graph of the function .

Find the vertex of the graph of the equation .

If, in a monopoly market, the demand for a product is , and the revenue function is , where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent.

Determine what type of function best models the data given below, and find the equation that is the best fit for the data. Round your final values to four decimal places.

Find the exact real solutions of the equation , if they exist.

An open-top box is constructed from a square piece of cardboard with sides of length 10 ft. The volume of such a box is given by , where x is the height of the box. Find the volume of the box if its height is 2 ft.

The owner of a skating rink rents the rink for parties at $696 if 58 or fewer skaters attend, so that the cost per person is $12 if 58 attend. For each 5 skaters above 58, she reduces the price per skater by $0.50. Which table gives the revenue generated if 58, 68, and 78 skaters attend?

Solve the equation .

The sensitivity S to a drug is related to the dosage x in milligrams by . Use a graphing utility to determine what dosage gives maximum sensitivity.

Assume that sales revenues, in millions, for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places.

Multiply both sides of the equation by the LCD, and then solve the resulting quadratic equation.

When a stone is thrown upward, it follows a parabolic path given by a form of the equation . If represents ground level, find the equation of a stone that is thrown from ground level at and lands on the ground 130 units away if the stone reaches a maximum height of 130 units.