Question 1

The chart below shows the amount spent by three U.S. airlines to fly one available seat one mile in the fourth quarter of 2000. $\begin{array} { | l | l | l | l | } 
\hline \text { Airline } & \text { United } & \text { American } & \text { SouthWest } \
\hline \text { Cost } & 11.3 \text { cents } & 11.0 \text { cents } & 7.8 \text { cents } \
\hline
\end{array}$ ?
Suppose that, on a 3000-mile New York-Los Angeles flight, United, American and SouthWest flew a total of 150 empty seats, costing them a total of $47,430. If United had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight 
United __________
American __________
SouthWest __________

Accepted Answer

The answer of The chart below shows the amount spent...

Question 2

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 $7,920 million budget to purchase new aircraft to seat a total of 19,000 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 
Number of Boeing 747s
__________
Number of Boeing 777s
__________
Number of European Airbus A321s
__________

Accepted Answer

The answer of Boeing 747s seat 400 passengers and are...

Question 3

This exercise is based on the following simplified model of the determination of the money stock.
  $\begin{array} { l } 
M = C + D \
C = 0.2 D \
R = 0.1 D \
H = R + C
\end{array}$ ,
 
where M - money stock
C - currency in circulation
R - bank reserves
D - deposits of the public
H - high-powered money
If the money stock were $108 billion, what would bank reserves have to be 
 
$____________billion

Accepted Answer

The answer of This exercise is based on the following...

Question 4

Use Gauss-Jordan row reduction to solve the system of equations.   $\begin{aligned}
1 x + 9 y + z & = 2 \
7 y + z & = 10
\end{aligned}$  
A) $( 1,2,0 )$
B) $( 0,0,2 )$
C) $( 0,0,3 )$
D) Redundant
E) Inconsistent

Accepted Answer

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

Question 5

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 6

You invested a total of $6,400 in three funds at the beginning of 2003, including an equal amount in PNF and CMBFX. You earned a total of $391 in interest for the year. How much did you invest in each of the three funds  Use the data given in the figure below. $$\begin{array} { | l | l | } 
\hline & \text { 2003 Yield } \
\hline \text { PNF (Pimco N. Y.) } & 6 \% \
\hline \text { CMBFX (Columbia Ore) } & 5 \% \
\hline \text { SFCOX } & 7 \% \
\hline
\end{array}$$  
PNF (Pimco N. Y.)
$__________
CMBFX (Columbia Ore)
$__________
SFCOX
$__________

Accepted Answer

The answer of You invested a total of $6,400 in...

Question 7

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 8

Use the table and the given X-ray absorption diagrams to identify the composition of each of the regions marked by a letter. The number in each region shows its absorption, and the number on each X-ray beam shows the total absorption for that beam. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Type } & \text { Air } & \text { Water } & \text { Gray matter } & \text { Tumor } & \text { Blood } & \text { Bone } \
\hline \text { Absorption } & 0 & 1,000 & 1,020 & 1,030 & 1,050 & 2,000 \
\hline
\end{array}$$      $a = 3070$ , $b = 5100$ , $c = 3060$ , $d = 1050$ 
x = __________
y = __________
z = __________
u = _________

Accepted Answer

The answer of Use the table and the given X-ray...

Question 9

Big Red Bookstore wants to ship books from its warehouses in Brooklyn and Queens to its stores, one on Long Island and one in Manhattan. Its warehouse in Brooklyn has 1,000 books and its warehouse in Queens has 2,000. Each store orders 1,500 books. It costs $1 to ship each book from Brooklyn to Manhattan and $2 to ship each book from Queens to Manhattan. It costs $5 to ship each book from Brooklyn to Long Island and $4 to ship each book from Queens to Long Island.
a. If Big Red has a transportation budget of $9,200 and is willing to spend all of it, how many books should Big Red ship from each warehouse to each store in order to fill all the orders 
Brooklyn to Manhattan __________
Queens to Manhattan __________
Brooklyn to Long Island __________
Queens to Long Island __________
 
b. How many books should Big Red ship from each warehouse to each store in order to fill all the orders for the minimum amount of money 
Brooklyn to Manhattan __________
Queens to Manhattan __________
Brooklyn to Long Island __________
Queens to Long Island __________

Accepted Answer

The answer of Big Red Bookstore wants to ship books...

Question 10

In the matrix of a system of linear equations, if one row of a matrix is a multiple of another row, then during the process of row reduction, one of those rows will eventually become all ones. Is statement

Accepted Answer

When one row is a multiple of another, during row reduction, one of those rows can be reduced to all zeros (not all ones) to eliminate redundancy, simplifying the system.

Question 11

Use the table and the given X-ray absorption diagrams to identify the composition of each of the regions marked by a letter. The number in each region shows its absorption, and the number on each X-ray beam shows the total absorption for that beam. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Type } & \text { Air } & \text { Water } & \text { Gray matter } & \text { Tumor } & \text { Blood } & \text { Bone } \
\hline \text { Absorption } & 0 & 1,000 & 1,020 & 1,030 & 1,050 & 2,000 \
\hline
\end{array}$$ ​  ​ $a = 3100$ , ​ $b = 3070$ ​, $c = 3080$ ​
x =
__________
y =
__________
z =
__________

Accepted Answer

The answer of Use the table and the given X-ray...

Question 12

In 2000, total revenues from sales of recorded rock, rap, and classical music amounted to $14.5 billion. Rock music brought in twice as much revenue as rap music and 900% the revenue of classical music. How much revenues were earned in each of the three categories of recorded music  (Round your answers to one decimal place.)
Rock
$__________ billion
Rap
$__________ billion
Classical music
$__________ billion

Accepted Answer

The answer of In 2000, total revenues from sales of...

Question 13

In November, 2003, the four organizations ranking 5 through 8 in home Internet users in the US were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 115 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that
   $\begin{array} { l } 
y - z = z - u \
x - y = 3 ( y - u ) + 1 \
x - y + z - u = 15
\end{array}$  
How large was the audience of each of the four companies in November, 2003 
eBay
__________ millions
The U.S. Government
__________ millions
Amazon
__________ millions
Lycos
__________ millions

Accepted Answer

The answer of In November, 2003, the four organizations ranking...

Question 14

Conan the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 545 victims consists of evil sorcerers, warriors, and orcs. These he has slain with a total of 580 mighty thrusts of his sword--evil sorcerers and warriors each requiring 2 thrusts (to the chest) and orcs each requiring 1 thrust (to the neck).When asked about the number of warriors he has slain, he replies, "The number of warriors I, the mighty Conan, have slain is four times the number of evil sorcerers that have fallen to my sword!" How many of each type of villain has he slain 
Evil sorcerers:
__________
Warriors:
__________
Orcs:
__________

Accepted Answer

The answer of Conan the Great has boasted to his...

Question 15

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 10 bread rolls, 15 defrosted beef patties, and 13 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bread roll, double cheeseburgers each require 2 beef patties, 1 bread roll, and 2 slices of cheese, and regular cheeseburgers each require 1 beef patty, 1 bread roll, and 1 slice of cheese. How many of each should you make 
Plain burgers:
__________
Double cheeseburgers:
__________
Regular cheeseburgers:
__________

Accepted Answer

The answer of You own a hamburger franchise and are...

Question 16

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 row of zeros in the reduced matrix does not necessarily mean the system cannot have a unique solution; it depends on the consistency of the system and the relationship between the number of equations, variables, and non-zero rows.

Question 17

Use Gauss-Jordan row reduction to solve the system.

$\begin{aligned}
3 x + y - 2 z = & - 4 \
2 x - 3 y + 2 z = & 11 \
x + y + z = & 3
\end{aligned}$  
A) $( 1 , - 1,3 )$
B) $\left( 9 , \frac { 2 } { 5 } , - 9 \right)$
C) $\left( 0,9 , \frac { 2 } { 5 } \right)$
D) $( 3,5 , - 5 )$
E) inconsistent

Accepted Answer

Solving the system using Gauss-Jordan row reduction, the solution is $x = 1$, $y = -1$, and $z = 3$.

Question 18

The chart below shows the amount spent by three U.S. airlines to fly one available seat one mile in the fourth quarter of 2000. $\begin{array} { | l | l | l | l | } 
\hline \text { Airline } & \text { Continental } & \text { SkyWest } & \text { SouthWest } \
\hline \text { Cost } & 9.8 \text { cents } & 20.3 \text { cents } & 7.8 \text { cents } \
\hline
\end{array}$ ?
Suppose that, on a 2000-mile Miami-Memphis flight, Continental, SkyWest, and SouthWest flew a total of 180 empty seats, costing them a total of $54,280. If SkyWest had twice as many empty seats as SouthWest, how many empty seats did each of these three airlines carry on its flight 
Continental __________
SkyWest __________
SouthWest __________

Accepted Answer

The answer of The chart below shows the amount spent...

Question 19

The Fancy French Perfume Company recently had its secret formula divulged. It turned out that it was using, as the three ingredients, rose oil, oil of fermented prunes, and alcohol. Moreover, each 18-ounce econo-size bottle contained 3 more ounces of alcohol than oil of fermented prunes, while the amount of alcohol was equal to the combined volume of the other two ingredients. How much of each ingredient did it use in an econo-size bottle 
Rose oil: __________
Oil of fermented prunes: __________
Alcohol: __________

Accepted Answer

The answer of The Fancy French Perfume Company recently had...

Question 20

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

The answer of The Tubular Ride Boogie Board Company has...

Quiz 4: Systems of Linear Equations and Matrices

Use Gauss-Jordan row reduction to solve the system of equations. $\begin{aligned}1 x + 9 y + z & = 2 \\7 y + z & = 10\end{aligned}$

In the matrix of a system of linear equations, if one row of a matrix is a multiple of another row, then during the process of row reduction, one of those rows will eventually become all ones. Is statement

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. $\begin{aligned}3 x + y - 2 z = & - 4 \\2 x - 3 y + 2 z = & 11 \\x + y + z = & 3\end{aligned}$

Quiz 4: Systems of Linear Equations and Matrices

Use Gauss-Jordan row reduction to solve the system of equations. 1x+9y+z=27y+z=10\begin{aligned}1 x + 9 y + z & = 2 \\7 y + z & = 10\end{aligned}1x+9y+z7y+z​=2=10​

In the matrix of a system of linear equations, if one row of a matrix is a multiple of another row, then during the process of row reduction, one of those rows will eventually become all ones. Is statement

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. 3x+y−2z=−42x−3y+2z=11x+y+z=3\begin{aligned}3 x + y - 2 z = & - 4 \\2 x - 3 y + 2 z = & 11 \\x + y + z = & 3\end{aligned}3x+y−2z=2x−3y+2z=x+y+z=​−4113​

Use Gauss-Jordan row reduction to solve the system of equations. $\begin{aligned}1 x + 9 y + z & = 2 \\7 y + z & = 10\end{aligned}$

Use Gauss-Jordan row reduction to solve the system. $\begin{aligned}3 x + y - 2 z = & - 4 \\2 x - 3 y + 2 z = & 11 \\x + y + z = & 3\end{aligned}$