Question 1

Which of the following three ordered triples are of the given form below.   Triple I :   Triple II :   Triple III :

Accepted Answer

A)  Only triple I and II are in the given form. 
B)  None of the triples are in the given form. 
C)  Only triple I and III are in the given form. 
D)  Only triple III is in the given form. 
E)  Only triple II is in the given form. 
A)  Only triple I and II are in the given form. 
B)  None of the triples are in the given form. 
C)  Only triple I and III are in the given form. 
D)  Only triple III is in the given form. 
E)  Only triple II is in the given form.

Question 2

A total of $50,000 is invested in two funds paying 6.5% and 7.5% simple interest.The total yearly interest is $3600.How much is invested at the 6.5% rate?

Accepted Answer

A)  $28,000 
B)  $12,000 
C)  $26,000 
D)  $15,000 
E)  $20,000 
A)  $28,000 
B)  $12,000 
C)  $26,000 
D)  $15,000 
E)  $20,000

Question 3

Solve the system by elimination.

Accepted Answer

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

Question 4

Solve the system of equations below by the substitution method.

Accepted Answer

A)    
B)    
C)    
D)    
E)  no solution 
A)    
B)    
C)    
D)    
E)  no solution

Question 5

A real estate company borrows $2,000,000.Some of the money is borrowed at 4%, some at 8%, and some at 11% simple annual interest.How much is borrowed at the 11% rate when the total annual interest is $130,000 and the amount borrowed at 4% is the same as the amount borrowed at 8%?

Accepted Answer

A)  $500,000 
B)  $200,000 
C)  $300,000 
D)  $600,000 
E)  $900,000 
A)  $500,000 
B)  $200,000 
C)  $300,000 
D)  $600,000 
E)  $900,000

Question 6

Find the maximum value of the objective function and where it occurs, if one exists. Objective function:   Constraints:

Accepted Answer

A)  The solution region is empty. There is no maximum value. 
B)  The maximum value is 1 and occurs at   
C)  The maximum value is 3 and occurs at   
D)  The maximum value is 12 and occurs at   
E)  The maximum value is 4 and occurs at   
A)  The solution region is empty. There is no maximum value. 
B)  The maximum value is 1 and occurs at   
C)  The maximum value is 3 and occurs at   
D)  The maximum value is 12 and occurs at   
E)  The maximum value is 4 and occurs at

Question 7

Solve the system by the method of elimination.

Accepted Answer

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

Question 8

Determine which of the following systems of equations is in row-echelon form. System I:   System II:   System III:

Accepted Answer

A)  None of the systems are in row-echelon form. 
B)  Only system II is in row-echelon form. 
C)  Only systems II and III are in row-echelon form. 
D)  All systems are in row-echelon form. 
E)  Only systems I and III are in row-echelon form. 
A)  None of the systems are in row-echelon form. 
B)  Only system II is in row-echelon form. 
C)  Only systems II and III are in row-echelon form. 
D)  All systems are in row-echelon form. 
E)  Only systems I and III are in row-echelon form.

Question 9

An investor has $300,000 to invest in two types of investments.Type A pays 5% annually and type B pays 7% annually.To have a well-balanced portfolio, the investor imposes the following conditions.At least one-third of the total portfolio is to be allocated to type A investments and at least one-third of the portfolio is to be allocated to type B investments.What is the optimal amount that should be invested in each investment?

Accepted Answer

A)  $100,000 in type A (5%), $200,000 in type B (7%) 
B)  $0 in type A (5%), $300,000 in type B (7%) 
C)  $200,000 in type A (5%), $100,000 in type B (7%) 
D)  $300,000 in type A (5%), $0 in type B (7%) 
E)  $110,000 in type A (5%), $190,000 in type B (7%) 
A)  $100,000 in type A (5%), $200,000 in type B (7%) 
B)  $0 in type A (5%), $300,000 in type B (7%) 
C)  $200,000 in type A (5%), $100,000 in type B (7%) 
D)  $300,000 in type A (5%), $0 in type B (7%) 
E)  $110,000 in type A (5%), $190,000 in type B (7%)

Question 10

Solve the system of equations below.

Accepted Answer

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

Question 11

Maximize the object function   subject to the constraints

Accepted Answer

A)  The maximum value is 10 at   
B)  The maximum value is 4 at   
C)  The maximum value is 10 at   
D)  The maximum value is 12 at   
E)  The maximum value is 5 at   
A)  The maximum value is 10 at   
B)  The maximum value is 4 at   
C)  The maximum value is 10 at   
D)  The maximum value is 12 at   
E)  The maximum value is 5 at

Question 12

Which of the following systems of equations has as a solution the ordered triple   System I:   System II:   System III:

Accepted Answer

A)  Only system II has the ordered triple   as a solution. 
B)  Only systems I and II have the ordered triple   as a solution. 
C)  Each of the systems I, II, and III has the ordered triple   as a solution. 
D)  Only system III has the ordered triple   as a solution. 
E)  None of the systems has the ordered triple   as a solution. 
A)  Only system II has the ordered triple   as a solution. 
B)  Only systems I and II have the ordered triple   as a solution. 
C)  Each of the systems I, II, and III has the ordered triple   as a solution. 
D)  Only system III has the ordered triple   as a solution. 
E)  None of the systems has the ordered triple   as a solution.

Question 13

Find the least squares regression line y = ax + b for the points   by solving the system for a and b.   Points:   space

Accepted Answer

A)  y = 1.92x - 2.92 
B)  y = -0.15x + 1.92 
C)  y = -2.53x + 1.63 
D)  y = -2.92x + 1.92 
E)  y = 1.19x + 1.63 
A)  y = 1.92x - 2.92 
B)  y = -0.15x + 1.92 
C)  y = -2.53x + 1.63 
D)  y = -2.92x + 1.92 
E)  y = 1.19x + 1.63

Question 14

Determine which ordered pair is a solution of the system.

Accepted Answer

A)  (-4, -2) 
B)  (-8, 9) 
C)  (-8, -1) 
D)  (-2, 4) 
E)  (-4, 2) 
A)  (-4, -2) 
B)  (-8, 9) 
C)  (-8, -1) 
D)  (-2, 4) 
E)  (-4, 2)

Which of the following three ordered triples are of the given form below. Triple I : Triple II : Triple III :

A total of $50,000 is invested in two funds paying 6.5% and 7.5% simple interest.The total yearly interest is $3600.How much is invested at the 6.5% rate?

Solve the system by elimination.

Solve the system of equations below by the substitution method.

A real estate company borrows $2,000,000.Some of the money is borrowed at 4%, some at 8%, and some at 11% simple annual interest.How much is borrowed at the 11% rate when the total annual interest is $130,000 and the amount borrowed at 4% is the same as the amount borrowed at 8%?

Find the maximum value of the objective function and where it occurs, if one exists. Objective function: Constraints:

Solve the system by the method of elimination.

Determine which of the following systems of equations is in row-echelon form. System I: System II: System III:

Solve the system of equations below.

Maximize the object function subject to the constraints

Which of the following systems of equations has as a solution the ordered triple System I: System II: System III:

Find the least squares regression line y = ax + b for the points by solving the system for a and b. Points: space

Determine which ordered pair is a solution of the system.

Fundamental Concepts of Algebra

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Polynomial and Rational Functions

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Exam 5: Systems of Equations and Inequalities

Which of the following three ordered triples are of the given form below. Triple I : Triple II : Triple III :

A total of $50,000 is invested in two funds paying 6.5% and 7.5% simple interest.The total yearly interest is $3600.How much is invested at the 6.5% rate?

Solve the system by elimination.

Solve the system of equations below by the substitution method.

A real estate company borrows $2,000,000.Some of the money is borrowed at 4%, some at 8%, and some at 11% simple annual interest.How much is borrowed at the 11% rate when the total annual interest is $130,000 and the amount borrowed at 4% is the same as the amount borrowed at 8%?

Find the maximum value of the objective function and where it occurs, if one exists. Objective function: Constraints:

Solve the system by the method of elimination.

Determine which of the following systems of equations is in row-echelon form. System I: System II: System III:

Solve the system of equations below.

Maximize the object function subject to the constraints

Which of the following systems of equations has as a solution the ordered triple System I: System II: System III:

Find the least squares regression line y = ax + b for the points by solving the system for a and b. Points: space

Determine which ordered pair is a solution of the system.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Sequences, Series, and Probability

Filters