Question 1

Solve the system by the addition method. ​   ​

Accepted Answer

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

Question 2

Solve the system by the Gauss-Jordan method.
​

Accepted Answer

The answer of Solve the system by the Gauss-Jordan method.
​...

Question 3

An after-shave lotion is 50% alcohol. If you have 4 fluid ounces of the lotion, how much water must be added to reduce the mixture to 10% alcohol? ​

Accepted Answer

A)  32 oz 
B)  16 oz 
C)  200 oz 
D)  20 oz 
E)  4 oz 
A)  32 oz 
B)  16 oz 
C)  200 oz 
D)  20 oz 
E)  4 oz B

Question 4

Solve the system by the Gauss-Jordan method. ​   ​

Accepted Answer

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

Question 5

Solve the system by the Gauss-Jordan method.
​

Accepted Answer

The answer of Solve the system by the Gauss-Jordan method.
​...

Question 6

Given the matrix, perform elementary row operation to obtain a 1 in the row 1, column 1 position.
​

Accepted Answer

The answer of Given the matrix, perform elementary row operation...

Question 7

An after-shave lotion is 40% alcohol. If you have 15 fluid ounces of the lotion, how much water must be added to reduce the mixture to 30% alcohol?
​
__________ ounces of water

Accepted Answer

The answer of An after-shave lotion is 40% alcohol. If...

Question 8

Solve the system by graphing. ​   ​   ​

Accepted Answer

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

Question 9

Decide which of the points below is a feasible solution for the given constraints. ​   ​

Accepted Answer

A)  ( -1, 3 ) 
B)  ( -3, 3 ) 
C)  ( 2, 1 ) 
D)  ( 3, 3 ) 
E)  none of these choices 
A)  ( -1, 3 ) 
B)  ( -3, 3 ) 
C)  ( 2, 1 ) 
D)  ( 3, 3 ) 
E)  none of these choices

Question 10

The Thompson Company manufactures two industrial products, standard ($55 profit per item) and economy ($25 profit per item). These items are built using machine time and manual labor. The standard product requires 4 hr of machine time and 3 hr of manual labor. The economy model requires 4 hr of machine time and no manual labor. If the week's supply of manual labor is limited to 600 hr and machine time to 12,000 hr, how much of each type of product should be produced each week to maximize the profit?
​
__________ standard models and __________ economy models.

Accepted Answer

The answer of The Thompson Company manufactures two industrial products,...

Question 11

If row 7 of a matrix [A] is multiplied by 4 and then added to row 4 of [A], then the correct notation is *Row (4,[A],7,4). Decide whether the statement is true or false.
​

Accepted Answer

A) True 
 B)False

Question 12

Solve the system by the Gauss-Jordan method.
​

Accepted Answer

The answer of Solve the system by the Gauss-Jordan method.
​...

Question 13

If row 5 of a matrix [C] is multiplied by -3 and then added to row 6 of [C], then the correct notation is Row+(-3,[C],6,5). Decide whether the statement is true or false.

Accepted Answer

A) True 
 B)False

Question 14

A collection of coins has a value of $4.12. There is the same number of nickels and dimes but four fewer pennies than nickels or dimes. How many pennies are in the collection if there are 74 coins? ​

Accepted Answer

A)  15 pennies 
B)  32 pennies 
C)  22 pennies 
D)  4 pennies 
E)  34 pennies 
A)  15 pennies 
B)  32 pennies 
C)  22 pennies 
D)  4 pennies 
E)  34 pennies

Question 15

A plane with a tail wind makes its 1,440-mile flight in 4 hours. The return flight against the wind takes a half hour longer. What is the wind speed? Round to one decimal place, if required.
​
__________ mph

Accepted Answer

The answer of A plane with a tail wind makes...

Question 16

The Thompson Company manufactures two industrial products, standard ($45 profit per item) and economy ($30 profit per item). These items are built using machine time and manual labor. The standard product requires 2 hr of machine time and 1 hr of manual labor. The economy model requires 2 hr of machine time and no manual labor. If the week's supply of manual labor is limited to 900 hr and machine time to 9,000 hr, how much of each type of product should be produced each week to maximize the profit? ​

Accepted Answer

A)  no standard models and 4,500 economy models 
B)  900 standard models and 3,600 economy models 
C)  900 standard models and 2,250 economy models 
D)  4,500 standard models and no economy models 
E)  2,250 standard models and 2,250 economy models 
A)  no standard models and 4,500 economy models 
B)  900 standard models and 3,600 economy models 
C)  900 standard models and 2,250 economy models 
D)  4,500 standard models and no economy models 
E)  2,250 standard models and 2,250 economy models

Question 17

Find the matrix [A]([B] + [C]), if
​   ,
​   , and
​   ​

Accepted Answer

The answer of Find the matrix [A]([B] + [C]), if
​...

Question 18

Find the product [ A ][ B ], if ​   ​
​

Accepted Answer

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

Question 19

Write a linear programming model, including the objective function and the set of constraints for the following problem. DO NOT SOLVE, but be sure to define all your variables. ​
Brown Bros., Inc., is an investment company doing an analysis of the pension fund for a certain company. The fund has a maximum of $10 million to invest in two places: no more than $8 million in stocks yielding 12%, and at least $2 million in long-term bonds yielding 9%. The stock-to-bond investment ratio cannot be more than 2 to 1. How should Brown Bros. advise its client so that the investments yield the maximum yearly return?
​
DENOTE:
​
X = amount invested in stock (in millions of dollars)
Y = amount invested in bonds (in millions of dollars)
​

Accepted Answer

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

Question 20

Solve the system by solving the corresponding matrix equation with an inverse. ​   ​
​

Accepted Answer

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

Solve the system by the addition method.

Solve the system by the Gauss-Jordan method.

An after-shave lotion is 50% alcohol. If you have 4 fluid ounces of the lotion, how much water must be added to reduce the mixture to 10% alcohol?

Solve the system by the Gauss-Jordan method.

Solve the system by the Gauss-Jordan method.

Given the matrix, perform elementary row operation to obtain a 1 in the row 1, column 1 position.

An after-shave lotion is 40% alcohol. If you have 15 fluid ounces of the lotion, how much water must be added to reduce the mixture to 30% alcohol? __________ ounces of water

Solve the system by graphing.

Decide which of the points below is a feasible solution for the given constraints.

If row 7 of a matrix [A] is multiplied by 4 and then added to row 4 of [A], then the correct notation is *Row (4,[A],7,4). Decide whether the statement is true or false.

Solve the system by the Gauss-Jordan method.

If row 5 of a matrix [C] is multiplied by -3 and then added to row 6 of [C], then the correct notation is Row+(-3,[C],6,5). Decide whether the statement is true or false.

A collection of coins has a value of $4.12. There is the same number of nickels and dimes but four fewer pennies than nickels or dimes. How many pennies are in the collection if there are 74 coins?

A plane with a tail wind makes its 1,440-mile flight in 4 hours. The return flight against the wind takes a half hour longer. What is the wind speed? Round to one decimal place, if required. __________ mph

Find the matrix [A]([B] + [C]), if , , and

Find the product [ A ][ B ], if

Solve the system by solving the corresponding matrix equation with an inverse.

The Nature of Problem Solving

The Nature of Sets

The Nature of Logic

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Measurement

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Voting and Apportionment

Filters

Exam 16: The Nature of Mathematical Systems

Solve the system by the addition method. ​ ​

Solve the system by the Gauss-Jordan method. ​

An after-shave lotion is 50% alcohol. If you have 4 fluid ounces of the lotion, how much water must be added to reduce the mixture to 10% alcohol? ​

Solve the system by the Gauss-Jordan method. ​ ​

Solve the system by the Gauss-Jordan method. ​

Given the matrix, perform elementary row operation to obtain a 1 in the row 1, column 1 position. ​

An after-shave lotion is 40% alcohol. If you have 15 fluid ounces of the lotion, how much water must be added to reduce the mixture to 30% alcohol? ​ __________ ounces of water

Solve the system by graphing. ​ ​ ​

Decide which of the points below is a feasible solution for the given constraints. ​ ​

If row 7 of a matrix [A] is multiplied by 4 and then added to row 4 of [A], then the correct notation is *Row (4,[A],7,4). Decide whether the statement is true or false. ​

Solve the system by the Gauss-Jordan method. ​

If row 5 of a matrix [C] is multiplied by -3 and then added to row 6 of [C], then the correct notation is Row+(-3,[C],6,5). Decide whether the statement is true or false.

A collection of coins has a value of $4.12. There is the same number of nickels and dimes but four fewer pennies than nickels or dimes. How many pennies are in the collection if there are 74 coins? ​

A plane with a tail wind makes its 1,440-mile flight in 4 hours. The return flight against the wind takes a half hour longer. What is the wind speed? Round to one decimal place, if required. ​ __________ mph

Find the matrix [A]([B] + [C]), if ​ , ​ , and ​ ​

Find the product [ A ][ B ], if ​ ​ ​

Solve the system by solving the corresponding matrix equation with an inverse. ​ ​ ​

The Nature of Problem Solving

The Nature of Sets

The Nature of Logic

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Measurement

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Voting and Apportionment

Filters

Solve the system by the addition method.

Solve the system by the Gauss-Jordan method.

An after-shave lotion is 50% alcohol. If you have 4 fluid ounces of the lotion, how much water must be added to reduce the mixture to 10% alcohol?

Solve the system by the Gauss-Jordan method.

Solve the system by the Gauss-Jordan method.

Given the matrix, perform elementary row operation to obtain a 1 in the row 1, column 1 position.

An after-shave lotion is 40% alcohol. If you have 15 fluid ounces of the lotion, how much water must be added to reduce the mixture to 30% alcohol? __________ ounces of water

Solve the system by graphing.

Decide which of the points below is a feasible solution for the given constraints.

If row 7 of a matrix [A] is multiplied by 4 and then added to row 4 of [A], then the correct notation is *Row (4,[A],7,4). Decide whether the statement is true or false.

Solve the system by the Gauss-Jordan method.

A collection of coins has a value of $4.12. There is the same number of nickels and dimes but four fewer pennies than nickels or dimes. How many pennies are in the collection if there are 74 coins?

A plane with a tail wind makes its 1,440-mile flight in 4 hours. The return flight against the wind takes a half hour longer. What is the wind speed? Round to one decimal place, if required. __________ mph

Find the matrix [A]([B] + [C]), if , , and

Find the product [ A ][ B ], if

Solve the system by solving the corresponding matrix equation with an inverse.