Instructions This is an open-book exam. You may refer to you.docx

Instructions:
This is an open-book exam. You may refer to your text and
other course materials as you work on the exam, and you may
use a calculator.
Record your answers and work in this document.
There are 25 problems.
Problems #1-12 are multiple choice. Record your choice for
each problem.
Problems #13-15 are short answer. Record your answer for each
problem.
Problems #16-25 are short answer with work required when
directed. When requested, show all work and write all answers
in the spaces allotted on the following pages. You may type
your work using plain-text formatting or an equation editor, or
you may hand-write your work and scan it. In either case, show
work neatly and correctly, following standard mathematical
conventions. Each step should follow clearly and completely
from the previous step. If necessary, you may attach extra
pages.
MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13. (a)
(b)

(c)
(d)
14. (a)
(b)
(c)
15. (a)
(b)
(c)
SHORT ANSWER with Work Shown. Record your answers and
work.
Problem Number
Solution

16
Answers:
(a)
(b)
(c)
Work for (a), (b), and (c):

17
Answer:
Work:
18
Answer:
Work:
19

Answers:
(a)
(b)
(c)
Work for (a) and (b):
20
Answer:

22
Answer:
Work:
23
Answers:
(a)
(b)
(c)
(d)

Work for (b), (c), and (d):
24
Answer:
Work:

25
Answers:
(a)
(b) Region I:
Region II:
Region III:
Region IV:
Work:

MATH 106 Finite Mathematics 2148-OL4-7983-3D
Page 1 of 10
MATH 106 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and

other course materials as you work
on the exam, and you may use a calculator. You must complete
the exam individually.
Neither collaboration nor consultation with others is allowed.
Use of instructors’ solutions
manuals or online problem solving services in NOT allowed.
Record your answers and work on the separate answer sheet
provided.
There are 25 problems.
Problems #1–12 are Multiple Choice.
Problems #13–15 are Short Answer. (Work not required to be
shown)
Problems #16–25 are Short Answer with work required to be
shown.

MULTIPLE CHOICE
1. – 2. Amalgamated Furniture Company makes dining room
tables and chairs. A table requires
8 labor-hours for assembling and 2 labor-hours for finishing. A
chair requires 2 labor-hours for
assembly and 1 labor-hour for finishing. The maximum labor-
hours available per day for
assembling and finishing are 400 and 120, respectively.
Production costs are $600 per table and
$150 per chair. Let x represent number of tables and y
represent number of chairs made per day.
1. Identify the daily production constraint for finishing:
1. _______
A. 8� + 2� ≥ 400 C. 8� + 2� ≤ 400

B. 2� + � ≥ 120 D. 2� + � ≤ 120
2. State the objective function.
2. _______
A. � = 400� + 120� C. � = 8� + 2�
B. � = 600� + 150� D. � = 2� + �
3. Which of the following statements is NOT true:
2. ________
A. A probability must be less than or equal to 1.
B. If an event cannot possibly occur, then the probability of the
event is a negative number.
C. If events G and H are mutually exclusive events, then P (G
∩ H) = 0.

D. If only two outcomes are possible for an experiment, then the
sum of the probabilities of
the outcomes = 1.
Page 2 of 10
4. Raoul buys an Amalgamated dining room furniture set for
$10,000, makes a down payment
of 20%, and finances the rest with 60-month store financing at
an annual interest rate of 5.4%
compounded monthly. What is the amount of his monthly loan
payment to amortize the loan?
4. _______

A. $190.55 C. $152.44
B. $169.33 D. $211.67
5. In the dice game “Yahtzee”, five-of-a-kind gives the
maximum score for a single turn. What
is the probability of getting 5 “5”s in a single roll of 5 six-sided
dice?
5. ________
A. 1 7776 (0.000129) ⁄ C. 1 1296
(0.000772)⁄
B. 1 30⁄ (0.033333) D. 5 36⁄
(0.138889)
6. A survey of 15 randomly selected students responded to the
question “How many hours a day

do you work on MATH 106?” as follows: 3, 1, 3, 2, 5, 3, 4, 5,
6, 3, 2, 4, 3, 4, 3 . Which
histogram below accurately reflects the frequency distribution
of the 15 students’ responses?
6. ______
HISTOGRAM A HISTOGRAM C
HISTOGRAM B
HISTOGRAM D
0
2
4

6
1 2 3 4 5 6
0
2
4
6
1 2 3 4 5 6
0
2
4
6
8
1 2 3 4 5 6

0
2
4
6
8
1 2 3 4 5 6
Page 3 of 10
7. Determine which graph shows the correct solution region of
the system of linear inequalities:
� + � ≤ 2 � ≥ 0

� + 3� ≥ 3 � ≥ 0
7. _______
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
8. Find the equation of the line passing through (2, 3) and (– 3,
7): 8. _______
a. 5x – 4y = – 2 b. 5x + 4y = 22 c. 4x – 5y
= – 7 d. 4x + 5y = 23
Page 4 of 10

9. The amount of money you should deposit in an account
paying 8% compounded quarterly in
order to receive quarterly payments of $1000 for the next 4
years can be determined using
formula for:
9. _______
A. Sequence of payments: present value of an annuity /
amortization
B. Sequence of payments: future value of an ordinary annuity
C. Single-payment, compound interest
D. Single-payment, simple interest
10. Which of the corner points for the system of linear
inequalities graphed below minimizes the

objective function P = 5x + 6y ?
10. _______
A. (3, 0) C. (2, 0)
B. (1, 2) D. (0, 4)
11. The mean time from check-in to completion for a customer
service task at the Townsburg
branch of the DMV is 112 minutes, with a standard deviation of
18 minutes. Assuming a normal
distribution, what is the probability that a randomly chosen
customer experiences service done
between 94 and 130 minutes?

11. ______
A. 0.5000 C. 0.4772
B. 0.6826 D. 0.3413
Page 5 of 10
12. Identify the single row operation that transforms the matrix
as shown: 12. ________
[
−12 6
3 −1.5

|
−4
1
] → [
0 0
3 −1.5
|
0
1
]
A. 0.25�1 + �2 → �1 C. 4�2 + �1 → �1
B. 0�1 → �1 D. 4�1 + �2 → �2
* * * * * * * * * * * * *

Page 6 of 10
SHORT ANSWER (work NOT required to be shown)
13. For the linear equation −4� + 7� = 56:
a. Determine the slope: _______________________
b. Determine x – intercept if it exists:
_______________________
c. Determine y – intercept if it exists:

_______________________
d. Express equation in slope-intercept form:
_______________________
14. Let �(�) = 55, �(�) = 65, �(� ∪ �) = 85, and �(�)
= 100.
a. Determine �(�′) :
___________________________________
b. Determine �(� ∩ �) :
___________________________________
c. Determine �(�′ ∩ �′):
___________________________________
15. 1000 randomly-selected respondents to a TV marketing
survey were asked their age in years
(18 to 39 or 40+) and the kind of TV show most often watched.

Following table was obtained.
Show Most
Watched on TV
Viewer Age
18 - 39
Viewer Age
40 +
Total
Comedy 208 88 296
Drama 150 74 224
News 32 140 172
Sports 228 80 308

Total 618 382 1000
(Report your answers as fractions or as decimal values rounded
to the nearest hundredth.)
Find the probability that a randomly-selected respondent:
(a) most often watches news and is age 18 – 39: Answer:
______________
(b) most often watches news given that viewer is age 18 – 39:
Answer: ______________
(c) most often watches news or is age 18 – 39: Answer:
______________

Page 7 of 10
SHORT ANSWER, with work required to be shown, as
indicated.
16. Sixteen people are summoned to jury duty. 11 are women
and 5 are men.
(a) In how many ways can 12 jurists be randomly selected out
of the 16 people? Show work.
(b) In how many ways can 12 jurists be chosen, if 9 must be
women and 3 must be men? Show
work.

(c) If 12 jurists are randomly selected from the 16 people, what
is the probability that 3 are men
and 9 are women? Round answer to nearest ten-thousandth (4
places after decimal). Show
work.
_____________________________________________________
_________________________
17. Solve the system of equations using substitution,
elimination by addition, or augmented
matrix methods (your choice). Show work.
2� + 3� = −5

3� − 2� = 12
18. Cara needs $9,000 in 11 years. What amount can she
deposit at the end of each quarter at
8% annual interest compounded quarterly so she will have her
$9,000? Show work.
A. $540.69 C. $129.49
B. $134.01 D. $125.19
_____________________________________________________
_________________________

Page 8 of 10
19. According to the IMS Institute for Healthcare Informatics,
"Use of Medicines in the United
States: Review of 2011", Americans spent $8.5 billion on
antipsychotic drugs in 2004; an
amount which climbed to $18.3 billion in 2011.
(a) Which of the following linear equations could be used to
predict annual American
expenditure (in US $ billions) on antipsychotic drugs “y” in a
given year “x”, where x = 0
represents the year 2004? Explain/show work.
�. � =
5

7
� + 8.5 �. � = 1.4� + 2004
�. � =
5
7
� + 2004 �. � = 1.4� + 8.5
(b) Use the equation from part (a) to predict the amount (in US
$ billions) that Americans
will spend on antipsychotic drugs in the year 2034. Round
answer to nearest tenth of a
billion dollars. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The
rate of change of annual

spending on antipsychotic drugs in the US with respect to time
is
______________________ per ________________. (Include
units of measurement.)
20. Tamika’s savings account has a balance of $4069. If she
makes no deposits or withdrawals
for 4 years, and the account accrues interest at 5% compounded
quarterly, what will be the total
amount of money in her savings account at the end of the 4-year
period? Show work
_____________________________________________________
_________________________
21. According to a recent Pew Research Center report, 0.8 is
the probability that a randomly

selected American adult knows what Twitter™ is. Ten
American adults are randomly selected.
Find the probability that exactly 7 of the 10 American adults
randomly selected know what
Twitter™ is. Round answer to nearest ten-thousandth (4 places
after decimal). Show work
_____________________________________________________
_________________________
Page 9 of 10

22. The feasible region shown below is bounded by lines – x +
2y = 4, 3x + y = 4, and y = 0.
Find the coordinates of corner point A. Show work.
23. A network security specialist records the number of
incoming e-mails containing links that
six randomly-selected network users receive in a day. Numbers
are 15, 36, 15, 45, 43, and 38.
(a) State the mode (if one exists).
(b) Find the median. Show work/explanation.
(c) Determine the sample mean. Show work

(d) Using the sample mean found in part (c), and given that
the sample standard deviation of
the data set above is 13.6, what percentage of the data set falls
within one standard deviation of
the mean? Show work/explanation.
(d) _______
A. 34.2% C. 68.3%
B. 66.7% D. 83.3%

of 10
24. A local car rental agency charted daily demand as shown in
the following table:
Number of customers 6 8 10 12 14
Probability 0.15 0.20 0.25 0.30 0.10
Find the expected number of customers. Show work.
25. A dietitian surveyed her group of 100 patients and found
that most of them ate fast food
yesterday. 15 patients said they at neither “Greasies” nor
“Pluckies” yesterday, 55 patients said
they ate at “Pluckies” yesterday, and 15 patients said they at
both “Greasies” and “Pluckies”

yesterday.
(a) How many of the patients ate only at “Greasies”
yesterday? Show work.
(b) Let G = {patients who ate at “Greasies”} and P =
{patients who ate at “Pluckies”}.
Determine the number of attendees belonging to each of the
regions I, II, III, IV.

Region I: ________ Region II: __________ Region III:
_________ Region IV: __________
_____________________________________________________
_________________________
U
P G
II
IV
III I

Instructions This is an open-book exam. You may refer to you.docx

Instructions This is an open-book exam. You may refer to you.docx

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