Question 1

Solve the system of equations using Gauss-Jordan row reduction.   $\begin{aligned}
8 x + 4 z & = - 5 \
2 y + 5 z & = - 6 \
\frac { 4 } { 3 } y + \frac { 10 } { 3 } z & = - 2
\end{aligned}$

Accepted Answer

A)  $( 8,1,4 )$ 
B)  $( 8,4,0 )$ 
C)  $( - 1,0 , - 1 )$ 
D)  inconsistent 
E)  dependent 
A)  $( 8,1,4 )$ 
B)  $( 8,4,0 )$ 
C)  $( - 1,0 , - 1 )$ 
D)  inconsistent 
E)  dependent D

Question 2

The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, AZ and Toronto, Ontario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to outlets in Honolulu and Venice Beach. The Tucson plant, when operating at full capacity, can manufacture 620 Gladiator boards per week, while the Toronto plant, beset by labor disputes, can produce only 410 boards per week. The outlet in Honolulu orders 540 Gladiator boards per week, while Venice Beach orders 490 boards per week. Transportation costs are as follows:
Tucson to Honolulu: $10 per board; Tucson to Venice Beach: $5 per board;
Toronto to Honolulu: $20 per board; Toronto to Venice Beach: $10 per board.
a. If Tubular Ride Boogie Board Company has a transportation budget of $10,750 and is willing to assure full capacity production at both plants, how many Gladiator boards should be shipped from each manufacturing plant to each distribution outlet 
Tucson to Honolulu
__________
Tucson to Venice Beach
__________
Toronto to Honolulu
__________
Toronto to Venice Beach
__________
 
b. How many Gladiator boards should be shipped from each manufacturing plant to each distribution outlet to assure full capacity production at both plants for less money 
Tucson to Honolulu
__________
Tucson to Venice Beach
__________
Toronto to Honolulu
__________
Toronto to Venice Beach
__________

Accepted Answer

370; 250; 170; 240; 540; 80; 0; 410

Question 3

Use Gauss-Jordan row reduction to solve the given system of equations.  
  $\begin{aligned}
x + y + 5 z & = 3 \
y + 2 z + w & = 1 \
x + 3 y + 7 z + 2 w & = 4 \
x + y + 5 z + w & = 1
\end{aligned}$

Accepted Answer

A)  $\left( - \frac { 3 } { 2 } , 2 , \frac { 1 } { 2 } , - 2 \right)$ 
B)  $\left( - \frac { 3 } { 2 } , 4 , \frac { 1 } { 4 } , - 2 \right)$ 
C)  $\left( - \frac { 3 } { 2 } , 1 , \frac { 1 } { 2 } , - 2 \right)$ 
D)  $\left( - \frac { 3 } { 2 } , 2 , \frac { 1 } { 2 } , - 1 \right)$ 
E)  $\left( - \frac { 3 } { 4 } , 2 , \frac { 1 } { 2 } , - 2 \right)$ 
A)  $\left( - \frac { 3 } { 2 } , 2 , \frac { 1 } { 2 } , - 2 \right)$ 
B)  $\left( - \frac { 3 } { 2 } , 4 , \frac { 1 } { 4 } , - 2 \right)$ 
C)  $\left( - \frac { 3 } { 2 } , 1 , \frac { 1 } { 2 } , - 2 \right)$ 
D)  $\left( - \frac { 3 } { 2 } , 2 , \frac { 1 } { 2 } , - 1 \right)$ 
E)  $\left( - \frac { 3 } { 4 } , 2 , \frac { 1 } { 2 } , - 2 \right)$ A

Question 4

Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math holds 50 students and earns the college $1,000 in revenue per student. Each section of Applied Calculus holds 45 students and earns the college $1,500 per student, and each section of Computer Methods holds 10 students and earns the college $2,200 per student. Assuming that the college can offer a total of seven sections, wishes to accommodate 305 students, and wishes to bring in $339,500 in revenues, how many sections of each course should it offer 
Number of sections of Finite Math:
__________
Number of sections of Applied Calculus:
__________
Number of sections of Computer Methods:
__________

Accepted Answer

The answer of Urban Community College is planning to offer...

Question 5

Use Gauss-Jordan row reduction to solve the system of equations.   $\begin{array} { l } 
9 x - 3 y = 24 \
- x + 2 y = 9
\end{array}$

Accepted Answer

A)  $( 7,5 )$ 
B)  $( 5,10 )$ 
C)  $( 7,7 )$ 
D)  $( 5,7 )$ 
E)  $( 6,7 )$ 
A)  $( 7,5 )$ 
B)  $( 5,10 )$ 
C)  $( 7,7 )$ 
D)  $( 5,7 )$ 
E)  $( 6,7 )$

Question 6

Boeing 747s seat 400 passengers and are priced at $200 million each, Boeing 777s seat 300 passengers and are priced at $160 million, and European Airbus A321s seat 200 passengers and are priced at $60 million. You are the purchasing manager of an airline company and have a $8,640 million budget to purchase new aircraft to seat a total of 20,800 passengers. Your company has a policy of supporting U.S. industries, and you have been required to spend twice as much on U.S.- manufactured aircraft as on foreign aircraft. Given the selection of three aircraft, how many of each should you order  ?

Accepted Answer

A) Number of Boeing 747s: 18 Number of Boeing 777s: 14
Number of European Airbus A321s: 45 
B)  Number of Boeing 747s: 18
Number of Boeing 777s: 16
Number of European Airbus A321s: 45 
C)  Number of Boeing 747s: 48
Number of Boeing 777s: 16
Number of European Airbus A321s: 16 
D)  Number of Boeing 747s: 16
Number of Boeing 777s: 16
Number of European Airbus A321s: 48 
E)  Number of Boeing 747s: 16
Number of Boeing 777s: 16
Number of European Airbus A321s: 45 
A) Number of Boeing 747s: 18 Number of Boeing 777s: 14
Number of European Airbus A321s: 45 
B)  Number of Boeing 747s: 18
Number of Boeing 777s: 16
Number of European Airbus A321s: 45 
C)  Number of Boeing 747s: 48
Number of Boeing 777s: 16
Number of European Airbus A321s: 16 
D)  Number of Boeing 747s: 16
Number of Boeing 777s: 16
Number of European Airbus A321s: 48 
E)  Number of Boeing 747s: 16
Number of Boeing 777s: 16
Number of European Airbus A321s: 45

Question 7

Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math holds 40 students and earns the college $1,300 in revenue per student. Each section of Applied Calculus holds 45 students and earns the college $1,600 per student, and each section of Computer Methods holds 15 students and earns the college $1,900 per student. Assuming that the college can offer a total of seven sections, wishes to accommodate 240 students, and wishes to bring in $357,000 in revenues, how many sections of each course should it offer  ?

Accepted Answer

A) Offer 2 sections of Finite Math, 2 sections of Applied Calculus, and 1 section of Computer Methods 
B)  Offer 2 sections of Finite Math, 3 sections of Applied Calculus, and 2 sections of Computer Methods 
C)  Offer 3 sections of Finite Math, 2 sections of Applied Calculus, and 2 sections of Computer Methods 
D)  Offer 5 sections of Finite Math, 1 section of Applied Calculus, and 1 section of Computer Methods 
E)  Offer 1 section of Finite Math, 5 sections of Applied Calculus, and 1 section of Computer Methods 
A) Offer 2 sections of Finite Math, 2 sections of Applied Calculus, and 1 section of Computer Methods 
B)  Offer 2 sections of Finite Math, 3 sections of Applied Calculus, and 2 sections of Computer Methods 
C)  Offer 3 sections of Finite Math, 2 sections of Applied Calculus, and 2 sections of Computer Methods 
D)  Offer 5 sections of Finite Math, 1 section of Applied Calculus, and 1 section of Computer Methods 
E)  Offer 1 section of Finite Math, 5 sections of Applied Calculus, and 1 section of Computer Methods

Question 8

If the addition or subtraction of two linear equations results in the equation $8 = 8$ , then the graphs of those equations are _______.

Accepted Answer

A) equal 
B)  parallel 
C)  not parallel 
D)  perpendicular 
E)  none of these 
A) equal 
B)  parallel 
C)  not parallel 
D)  perpendicular 
E)  none of these

Question 9

A system of three equations in two unknowns corresponds to three lines in the plane. Describe several ways that these lines might be positioned if the system has no solutions

Accepted Answer

The lines may be parallel, or two lines

Question 10

In a certain month, Nortel (NT) stock started and ended the month valued at $4.70 a share, and Altria Group (MO) increased from $48 to $52 a share. If you invested a total of $5,458 in these stocks at the beginning of this month and sold them for $5,858 at the end of this month, how many shares of each stock did you buy  ?

Accepted Answer

A) 130 shares of NT and 120 shares of MO 
B)  140 shares of NT and 100 shares of MO 
C)  101 shares of NT and 254 shares of MO 
D)  100 shares of NT and 140 shares of MO 
E)  130 shares of NT and 470 shares of MO 
A) 130 shares of NT and 120 shares of MO 
B)  140 shares of NT and 100 shares of MO 
C)  101 shares of NT and 254 shares of MO 
D)  100 shares of NT and 140 shares of MO 
E)  130 shares of NT and 470 shares of MO

Question 11

Use Gauss-Jordan row reduction to solve the given system of equations.
​
​ $\begin{aligned}
x + y + 5 z & = 1 \
y + 2 z + w & = 1 \
x + 3 y + 7 z + 2 w & = 2 \
x + y + 5 z + w & = 1
\end{aligned}$

Accepted Answer

The answer of Use Gauss-Jordan row reduction to solve the...

Question 12

Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Is Frans' statement

Accepted Answer

A) True 
 B)False

Question 13

Use Gauss-Jordan row reduction to solve the system of equations.
​ $\begin{array} { l } 
8 x - y = 12 \
8 x + 8 y = 3
\end{array}$

Accepted Answer

The answer of Use Gauss-Jordan row reduction to solve the...

Question 14

In November 2003, the four companies with the largest number of home Internet users in the US were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 282 million users. Taking x to be the Microsoft audience in millions, ?y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that
  $\begin{array} { l } 
z - u = 3 ( x - y ) + 6 \
x + y = 52 + z + u \
x - y + z - u = 42
\end{array}$  
How large was the audience of each of the four companies in November, 2003 
Microsoft
__________ millions
Time Warner
__________ millions
Yahoo
__________ millions
Google
__________ millions

Accepted Answer

The answer of In November 2003, the four companies with...

Question 15

The U.S. Senate has 100 members. For a bill to pass with a super majority, at least twice as many senators must vote for the bill as against it. If 96 senators vote, how many must vote for a bill for it to pass with a super majority 
 
__________ senators must vote for the bill.

Accepted Answer

The answer of The U.S. Senate has 100 members. For...

Question 16

You invested a total of $6,800 in three funds at the beginning of 2003, including an equal amount in PNF and CMBFX. You earned a total of $407 in interest for the year. How much did you invest in each of the three funds  Use the data given in the figure below. $$\begin{array} { | l | l | } 
\hline & 2003 \text { Yield } \
\hline \text { PNF (Pimco N. Y.) } & 6 \% \
\hline \text { CMBFX (Columbia Ore) } & 5 \% \
\hline \text { SFCOX } & 7 \% \
\hline
\end{array}$$

Accepted Answer

A) PNF (Pimco N. Y.): $2,500 CMBFX (Columbia Ore): $2,500
SFCOX : $2,200 
B)  PNF (Pimco N. Y.): $2,500
CMBFX (Columbia Ore): $2,500
SFCOX : $1,800 
C)  PNF (Pimco N. Y.): $2,200
CMBFX (Columbia Ore): $2,200
SFCOX : $2,400 
D)  PNF (Pimco N. Y.): $2,300
CMBFX (Columbia Ore): $2,300
SFCOX : $2,200 
E)  PNF (Pimco N. Y.): $2,300
CMBFX (Columbia Ore): $2,300
SFCOX : $1,800 
A) PNF (Pimco N. Y.): $2,500 CMBFX (Columbia Ore): $2,500
SFCOX : $2,200 
B)  PNF (Pimco N. Y.): $2,500
CMBFX (Columbia Ore): $2,500
SFCOX : $1,800 
C)  PNF (Pimco N. Y.): $2,200
CMBFX (Columbia Ore): $2,200
SFCOX : $2,400 
D)  PNF (Pimco N. Y.): $2,300
CMBFX (Columbia Ore): $2,300
SFCOX : $2,200 
E)  PNF (Pimco N. Y.): $2,300
CMBFX (Columbia Ore): $2,300
SFCOX : $1,800

Question 17

Use Gauss-Jordan row reduction to solve the system of equations.
​ $\begin{array} { l } 
7 x - 3 y = - 10 \
- x + 9 y = 70
\end{array}$

Accepted Answer

The answer of Use Gauss-Jordan row reduction to solve the...

Question 18

The traffic through downtown East Podunk flows through the one-way system shown below:     
 $a = 400$ , $b = 50$ , $c = 400$  
Traffic counters find that 400 vehicles enter town from the west each hour and 400 leave town toward the east each hour. Also, 50 cars drive down Canal Street each hour.
 
Write down the general solution of the associated system of linear equations. Is it possible to determine the number of vehicles on each street per hour

Accepted Answer

A)   $\begin{array} { l } 
x = 400 - w \
y = 450 - w \
z = 50 + w \
50 \leq w \leq 400
\end{array}$ 
B)  $\begin{array} { l } 
x = 390 - w \
y = 470 - w \
z = 80 + w \
80 \leq w \leq 390
\end{array}$ 
C)  $\begin{array} { l } 
x = 470 - w \
y = 390 - w \
z = - 80 + w \
80 \leq w \leq 390
\end{array}$ 
D)   $\begin{array} { l } 
x = 400 - w \
y = 470 - w \
z = 50 + w \
400 \leq w \leq 470
\end{array}$ 
E)    $\begin{array} { l } 
x = 450 - w \
y = 400 - w \
z = - 50 + w \
50 \leq w \leq 400
\end{array}$ 
A)   $\begin{array} { l } 
x = 400 - w \
y = 450 - w \
z = 50 + w \
50 \leq w \leq 400
\end{array}$ 
B)  $\begin{array} { l } 
x = 390 - w \
y = 470 - w \
z = 80 + w \
80 \leq w \leq 390
\end{array}$ 
C)  $\begin{array} { l } 
x = 470 - w \
y = 390 - w \
z = - 80 + w \
80 \leq w \leq 390
\end{array}$ 
D)   $\begin{array} { l } 
x = 400 - w \
y = 470 - w \
z = 50 + w \
400 \leq w \leq 470
\end{array}$ 
E)    $\begin{array} { l } 
x = 450 - w \
y = 400 - w \
z = - 50 + w \
50 \leq w \leq 400
\end{array}$

Question 19

Find all solutions of the given system and check your answer graphically.   $$\begin{aligned}
\frac { x } { 5 } - \frac { y } { 2 } & = 1 \
\frac { x } { 3 } + y & = - 2
\end{aligned}$$

Accepted Answer

A)  $\left( - \frac { 1 } { 7 } , - \frac { 2 } { 33 } \right)$ 
B)  $( 1 , - 2 )$ 
C)  $( 0 , - 2 )$ 
D)  No solutions 
E)  An infinite number of solutions 
A)  $\left( - \frac { 1 } { 7 } , - \frac { 2 } { 33 } \right)$ 
B)  $( 1 , - 2 )$ 
C)  $( 0 , - 2 )$ 
D)  No solutions 
E)  An infinite number of solutions

Question 20

Find all solutions of the given system and choose the graph of the system that shows the solutions.

$\begin{array} { l } 
x - y = 0 \
x + y = - 18
\end{array}$

Accepted Answer

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

Solve the system of equations using Gauss-Jordan row reduction. 8x+4z =-5 2y+5z =-6 y+z =-2

Use Gauss-Jordan row reduction to solve the given system of equations. x+y+5z =3 y+2z+w =1 x+3y+7z+2w =4 x+y+5z+w =1

Use Gauss-Jordan row reduction to solve the system of equations. 9x-3y=24 -x+2y=9

If the addition or subtraction of two linear equations results in the equation $8 = 8$ , then the graphs of those equations are _______.

A system of three equations in two unknowns corresponds to three lines in the plane. Describe several ways that these lines might be positioned if the system has no solutions

Use Gauss-Jordan row reduction to solve the given system of equations. x+y+5z =1 y+2z+w =1 x+3y+7z+2w =2 x+y+5z+w =1

Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Is Frans' statement

Use Gauss-Jordan row reduction to solve the system of equations. 8x-y=12 8x+8y=3

The U.S. Senate has 100 members. For a bill to pass with a super majority, at least twice as many senators must vote for the bill as against it. If 96 senators vote, how many must vote for a bill for it to pass with a super majority __________ senators must vote for the bill.

Use Gauss-Jordan row reduction to solve the system of equations. 7x-3y=-10 -x+9y=70

Find all solutions of the given system and check your answer graphically. - =1 +y =-2

Find all solutions of the given system and choose the graph of the system that shows the solutions. x-y=0 x+y=-18

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 4: Systems of Linear Equations and Matrices

Solve the system of equations using Gauss-Jordan row reduction. 8x+4z =-5 2y+5z =-6 y+z =-2

Use Gauss-Jordan row reduction to solve the given system of equations. x+y+5z =3 y+2z+w =1 x+3y+7z+2w =4 x+y+5z+w =1

Use Gauss-Jordan row reduction to solve the system of equations. 9x-3y=24 -x+2y=9

If the addition or subtraction of two linear equations results in the equation 8=88 = 88=8 , then the graphs of those equations are _______.

A system of three equations in two unknowns corresponds to three lines in the plane. Describe several ways that these lines might be positioned if the system has no solutions

Use Gauss-Jordan row reduction to solve the given system of equations. ​ ​ x+y+5z =1 y+2z+w =1 x+3y+7z+2w =2 x+y+5z+w =1

Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Is Frans' statement

Use Gauss-Jordan row reduction to solve the system of equations. ​ 8x-y=12 8x+8y=3

The U.S. Senate has 100 members. For a bill to pass with a super majority, at least twice as many senators must vote for the bill as against it. If 96 senators vote, how many must vote for a bill for it to pass with a super majority __________ senators must vote for the bill.

Use Gauss-Jordan row reduction to solve the system of equations. ​ 7x-3y=-10 -x+9y=70

Find all solutions of the given system and check your answer graphically. - =1 +y =-2

Find all solutions of the given system and choose the graph of the system that shows the solutions. x-y=0 x+y=-18

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

If the addition or subtraction of two linear equations results in the equation $8 = 8$ , then the graphs of those equations are _______.

Use Gauss-Jordan row reduction to solve the given system of equations. x+y+5z =1 y+2z+w =1 x+3y+7z+2w =2 x+y+5z+w =1

Use Gauss-Jordan row reduction to solve the system of equations. 8x-y=12 8x+8y=3

Use Gauss-Jordan row reduction to solve the system of equations. 7x-3y=-10 -x+9y=70