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Practice_Final
You scored 75 out of 100
Question 1
Your answer is CORRECT.
Give the slope of the line passing through the points ( 8 , 1 ) and ( -8 , 1 ).
a)
b)
c)
d)
e)
f)
None of the above.
Question 2
Your answer is INCORRECT.
Give the equation of the line that passes through the points ( -1 , 1 ) and ( 1 , 2 ).
a)
b)
c)
d)
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e)
f)
None of the above.
Question 3
Your answer is CORRECT.
Suppose you buy a piece of office equipment for $10,000. After 3 years you sell it for a scrap
value of $3,000. The equipment is depreciated linearly over 3 years. The value of the piece of
equipment after 1 years is (rounded to the nearest whole dollar)
a)
$8,250
b)
$7,667
c)
$9,222
d)
$3,000
e)
$9,300
f)
None of the above.
Question 4
Your answer is CORRECT.
A manufacturer has a monthly fixed cost of $80,000 and a production cost of $19 for each unit
produced. The product sells for $28 per unit. Find the break-even quantity.
a)
b)
c)
d)
e)
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f)
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None of the above.
Question 5
Your answer is CORRECT.
A company has fixed monthly costs of $90,000 and production costs on its product of $23 per
unit. The company sells its product for $73 per unit. The cost function, revenue function and
profit function for this situation are
a)
b)
c)
d)
e)
f)
None of the above.
Question 6
Your answer is CORRECT.
A manufacturer has a monthly fixed cost of $30,000.00 and a production cost of $12 for each unit
produced. The product sells for $19 per unit. If the manufacturer produces and sells 5,000 units
one month, then his profit is
a)
$950,000
b)
$65,000
c)
$5,000
d)
$30,000
e)
$600,000
f)
None of the above.
Question 7
Your answer is INCORRECT.
Which of the following matrices are in row-reduced form?
(Note: The dotted vertical line in each matrix should be a single vertical line.)
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I.
II.
III.
a)
I and III only
b)
None of them
c)
I and II only
d)
II and III only
e)
All of them
f)
None of the above.
Question 8
Your answer is INCORRECT.
Given that the augmented matrix in row-reduced form below is equivalent to the augmented
matrix of a system of linear equations. Determine whether the system has a solution and find the
solution(s) to the system, if they exist.
(Note: The dotted vertical line in the matrix above should be a single vertical line.)
a)
x = -10, y = -5
b)
No solution
c)
x = -10+ z, y = -5, z = any real number
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d)
x = -10- z, y = -5, z = any real number
e)
x = -10, y = 5, z = -10
f)
None of the above.
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Question 9
Your answer is CORRECT.
Use the Gauss-Jordan elimination process on the following system of linear equations to find the
value of z.
a)
b)
c)
d)
e)
f)
None of the above.
Question 10
Your answer is CORRECT.
Use Gauss-Jordan elimination process to solve the following system of linear equations.
a)
x = -3, y = 6, z = 4
b)
x = -2, y = 3, z = 3
c)
x = 0, y = 5, z = 2
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d)
No solution.
e)
Infinitely many solutions.
f)
None of the above.
Question 11
Your answer is CORRECT.
Perform the indicated operation, if possible.
4
+ 10
a)
b)
c)
d)
e)
f)
None of the above.
Question 12
Your answer is CORRECT.
Solve for x.
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+
=
a)
b)
c)
d)
e)
f)
None of the above.
Question 13
Your answer is CORRECT.
Let A =
and B =
. Compute the product AB, if possible.
a)
b)
c)
d)
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e)
f)
None of the above.
Question 14
Your answer is CORRECT.
Find the inverse of the given matrix, if it exists.
a)
b)
c)
d)
e)
f)
None of the above.
Question 15
Your answer is CORRECT.
A company produces two types of the jackets; windbreakers and rainbreakers. The company has
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at most 67 hours of finishing time per week and 64 hours of packaging time per week. Each
windbreaker jacket takes 45 minutes of finishing time and 22 minutes of packaging time per
week, whereas each rainbreaker jacket takes 68 minutes of finshing time and 35 minutes of
packaging time per week. The company's profit for each windbreaker and rainbreaker jacket is 24
and 41, respectively. Let x denote the number of windbeaker jackets they should produce and y
denote the number of rainbreaker jackets they should produce. The company wants to maximize
profit. Set up the Linear Programming Problem for this situation.
a)
Max P = 24x + 41y s.t. 68x + 45y< 67 , 35x + 22y< 64 , x> 0 , y> 0
b)
Max P = 41x + 24y s.t. 68x + 45y< 4020 , 35x + 22y< 3840 , x> 0 , y> 0
c)
Max P = 41x + 24y s.t. 45 x + 68y> 4020 , 22x + 35y> 3840 , x> 0 , y> 0
d)
Max P = 24x + 41y s.t. 45 x + 68y< 4020 , 22 x + 35 y< 3840 , x> 0 , y> 0
e)
Max P = 24x + 41y s.t. 45 x + 68y< 67 , 22x + 35y< 64 , x> 0 , y> 0
f)
None of the above.
Question 16
Your answer is INCORRECT.
Given the following linear programming problem, find the optimal solution.
Maximize
10 x + y< 10
5 x + 4 y< 20
x> 0
y> 0
a)
b)
c)
d)
e)
f)
None of the above.
Question 17
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Your answer is CORRECT.
Mr. Smith wishes to retire in 11 years. When he retires he would like to have $500,000 in his
bank account. Mr. Smith's bank pays 6% per year compounded annually. How much should he
deposit now to attain his goal?
a)
$263,397.76
b)
$263,396.76
c)
$263,393.76
d)
$263,394.76
e)
$263,395.76
f)
None of the above.
Question 18
Your answer is CORRECT.
Jennifer bought a brand new treadmill on a credit plan at BeFit Exercise Equipment. BeFit will
charge her 16% per year compounded monthly. If her monthly payments will be $150 for 4 years,
how much was the original price of the treadmill?
a)
$5,291.82
b)
$5,290.82
c)
$5,292.82
d)
$5,289.82
e)
$5,295.82
f)
None of the above.
Question 19
Your answer is CORRECT.
You borrowed $11,000 from your bank to build a small cabin on your property. The bank will
charge 10% per year compounded quarterly. You decide to pay off this loan in 3 years by making
quarterly payments. How much are your quarterly payments?
a)
$1,052.36
b)
$1,072.36
c)
$1,102.36
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d)
$1,062.36
e)
$1,032.36
f)
None of the above.
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Question 20
Your answer is CORRECT.
The manager of a manufacturing company knows that they will need a new machine in one of
their factories. The new machine will cost them $12,500. The manager has determined that they
can afford to pay 10% of the cost of the machine in cash. They can then finance the rest through a
credit union. The credit union will charge 2% per year compounded monthly. How much are their
monthly payments for 4 years?
a)
$317.03
b)
$244.07
c)
$225.32
d)
$250.36
e)
$271.19
f)
None of the above.
Question 21
Your answer is CORRECT.
Given the following Venn diagram, find n[ ( Ac B)c ].
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a)
20
b)
84
c)
32
d)
65
e)
51
f)
None of the above.
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Question 22
Your answer is CORRECT.
(Car Sales) Of the cars sold during the month of July, 95 had air conditioning, 102 had automatic
transmission, and 73 had power steering. 7 cars had all three of these extras. 25 cars had none of
these extras. 21 cars had only air conditioning, 55 cars had only automatic transmissions, and 35
cars had only power steering. 9 cars had both automatic transmission and power steering. How
many cars had exactly two of the given options?
a)
104
b)
76
c)
2
d)
69
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e)
86
f)
None of the above.
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Question 23
Your answer is CORRECT.
A license plate consists of 3 letters followed by 3 digits. How many license plates are possible if
the 1st letter can't be O, and letters and digits may repeat.
a)
12,320,100
b)
16,900,000
c)
15,625,000
d)
17,576,000
e)
11,390,625
f)
None of the above.
Question 24
Your answer is INCORRECT.
Suzy randomly picks marbles form a bag containing 18 identical marbles. How many possible
outcomes are there of she selects 7 marbles?
a)
31,834
b)
160,392,960
c)
31,804
d)
31,864
e)
31,824
f)
None of the above.
Question 25
Your answer is CORRECT.
An urn contains 5 blue balls and 4 orange balls. In how many ways can we select 1 blue balls and
2 orange balls from the urn?
a)
17
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b)
56
c)
20
d)
13
e)
30
f)
None of the above.
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Question 26
Your answer is CORRECT.
A business organization needs to make up a 5 member fund-raising committee. The organization
has 10 accounting majors and 8 finance majors. In how many ways can the fund-raising
committee be formed if at most 1 accounting major is on the committee?
a)
756
b)
66
c)
56
d)
700
e)
10
f)
None of the above.
Question 27
Your answer is CORRECT.
Given P(A) = 0.36, P(B) = 0.40 and P(A Bc) = 0.17. Find P(A B).
a)
b)
c)
d)
e)
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f)
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None of the above.
Question 28
Your answer is CORRECT.
A fair coin is tossed 26 times. What is the probability that at most 23 tails occur?
a)
0.000039
b)
0.999995
c)
0.999956
d)
0.000005
e)
0.000044
f)
None of the above.
Question 29
Your answer is INCORRECT.
An experiment consists of choosing a colored urn with equally likely probability and then
drawing a ball from that urn. In the brown urn, there are 24 brown balls and 11 white balls. In the
yellow urn, there are 18 yellow balls and 8 white balls. In the white urn, there are 18 white balls
and 16 blue balls. What is the probability of choosing the yellow urn and a white ball?
a)
b)
c)
d)
e)
f)
None of the above.
Question 30
Your answer is CORRECT.
A recording company obtains the blank CDs used to produce its labels from three compact disk
manufacturers: I, II, and III. The quality control department of the company has determined that
1% of the compact disks produced by manufacturer I are defective, 7% of those produced by
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manufacturer II are defective, and 3% of those produced by manufacturer III are defective.
Manufacturers I, II, and III supply 36%, 20%, and 44%, respectively, of the compact disks used
by the company. What is the probability that a randomly selected label produced by the company
will contain a defective compact disk?
a)
b)
c)
d)
e)
f)
None of the above.
Question 31
Your answer is INCORRECT.
King Mattress purchases Sleep-n-Air mattresses from three different distributors. The probability
of getting a defective mattress from Distributor A, B, or C is 0.43, 0.40, and 0.11, respectively.
Assuming an equal probability of making a purchase from either distributor A, B, or C. If King
Mattress sells a defective mattress, what is the probability that it came from Distributor C?
a)
b)
c)
d)
e)
f)
None of the above.
Question 32
Your answer is CORRECT.
Find the expected value of the random variable X having the following probability distribution.
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x
-1 5
7
8
12
P(X=x) 3/13 7/26 1/13 5/13 1/26
a)
5.1723
b)
0.2497
c)
0.1897
d)
5.1923
e)
5.1823
f)
None of the above.
Question 33
Your answer is CORRECT.
Consider the following binomial experiment. The probability that a green jelly bean is chosen at
random from a large package of jelly beans is 3/8. Sally chooses 12 jelly beans, what is the
probability that at most 2 will be green jelly beans?
a)
0.1075
b)
0.8865
c)
0.2600
d)
0.1135
e)
0.5000
f)
None of the above.
Question 34
Your answer is CORRECT.
Consider the following binomial experiment. The probability that a fuse produced by a certain
company will be defective is 1/4. If 500 fuses are produced each day, how many can we expect to
find each day that are defective ?
a)
123
b)
122
c)
126
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d)
125
e)
129
f)
None of the above.
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Question 35
Your answer is CORRECT.
Let Z be a standard normal variable. Find P(Z > -.66).
a)
b)
c)
d)
e)
f)
None of the above.
Question 36
Your answer is CORRECT.
Let Z be a standard normal variable. Find the value of z if z satisfies P(Z > z) = 0.6331.
a)
b)
c)
d)
e)
f)
None of the above.
Question 37
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Your answer is INCORRECT.
Let Z be a standard normal variable. Find P(.5 < Z < 2.51).
a)
b)
c)
d)
e)
f)
None of the above.
Question 38
Your answer is INCORRECT.
Endure All, a manufacturer of batteries claims that the lifetime of their batteries is normally
distributed with a mean of 500 hr. and a standard deviation of 40 hr. What is the probability that
an Endure All battery selected at random will last more than 550 hours?
a)
b)
c)
d)
e)
f)
None of the above.
Question 39
Your answer is CORRECT.
Use the appropriate normal distribution to approximate the resulting binomial distributions. A
convenience store owner claims that 55% of the people buying from her store, on a certain day of
the week, buy coffee during their visit. A random sample of 35 customers is made. If the store
owner's claim is correct, what is the probability that fewer than 20 customers in the sample buy
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coffee during their visit on that certain day of the week?
a)
b)
c)
d)
e)
f)
None of the above.
Question 40
Your answer is INCORRECT.
Use the normal distribution to approximate the following binomial distribution. You claim that
73% of the voters in your district will vote for you. If the district has 350 voters, what is the
probability that at least 275 will actually vote for you?
a)
b)
c)
d)
e)
f)
None of the above.
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