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MATH 106 Finite Mathematics 2172-OL1-6380-V1

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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. The Benjamin Banneker Astronomics Company employs physicists and astronomers.

According to company data, a physicist does 2 observations and 3 calculations per day, whereas

an astronomer does 6 observations and 3 calculations per day. The company needs enough staff

on hand for at least 24 observations per day and at least 18 calculations per day. A physicist

makes $100 per day and an astronomer makes $90 per day. The company wants to minimize

daily labor costs in order to get a research grant. Let x represent number of physicists and y

represent number of astronomers.

1. Identify the daily production constraint for observations:

1. _______

A. 2𝑥 + 6𝑦 ≥ 24 C. 6𝑥 + 2𝑦 ≥ 24

B. 2𝑥 + 3𝑦 ≥ 18 D. 3𝑥 + 3𝑦 ≥ 18

2. State the objective function.

2. _______

A. 𝐶 = 18𝑥 + 24𝑦 C. 𝐶 = 90𝑥 + 100𝑦

B. 𝐶 = 24𝑥 + 18𝑦 D. 𝐶 = 100𝑥 + 90𝑦

3. Which of the following statements is NOT true:

3. ________

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 zero (0).

C. If events G and H are independent 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.

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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4. The Henderson family purchases a new home for $360,000, makes a down payment of 20%,

and finances the rest with a 30-year fixed mortgage at an annual interest rate of 3.9%

compounded monthly. What is the amount of their monthly loan payment?

4. _______

A. $1736.00 C. $2170.00

B. $1358.40 D. $1698.01

5. In a certain manufacturing process, the probability of having no type I defects is 0.90, the

probability of having no type II defects is 0.93, and probability of having neither defect is 0.89.

Find the probability that a part having both type I and type II defects occurs.

5. ______

A. 0.07

B. 0.04

C. 0.01

D. 0.06

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: 2, 1, 2, 5, 3, 5, 4, 5, 6, 5, 2, 5, 2, 2, 5 . Which

histogram below accurately reflects the frequency distribution of the 15 students’ responses?

6. ______

HISTOGRAM A HISTOGRAM C

HISTOGRAM B HISTOGRAM D

1 2 3 4 5 6

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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7. Determine which graph shows the correct solution region of the system of linear inequalities:

𝑥 + 𝑦 ≤ 2 𝑥 ≥ 0 𝑥 + 3𝑦 ≥ 3 𝑦 ≥ 0

7. _______

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

8. Find the equation of the line passing through (2, 6) and (– 3, – 1): 8. _______

A. 7x – 5y = – 16 B. 5x + y = – 16 C. x – y = – 4 D. x + y = 8

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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9. If $1,000 is invested at 6% compounded semiannually, the amount of money in the

investment account after 8 years can be determined using formula for:

9. _______

A. Single-payment, simple interest

B. Single-payment, compound interest

C. Sequence of payments: future value of an ordinary annuity

D. Sequence of payments: present value of an annuity / amortization

10. Which of the corner points for the system of linear inequalities graphed below maximizes

the objective function P = 5x + 6y ?

10. _______

A. (0, 3) C. (1, 2)

B. (0, 0) D. (2, 0)

11. The mean time from check-in to completion for a 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. 0.3413 C. 0.4772

B. 0.5000 D. 0.6826

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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12. Dwayne’s Digital Doctors is a small business specializing in personal information

technology (IT) device repair. The company has fixed costs of $618 a day and variable costs of

$8.50 per IT device repaired. The company charges $60 per IT device repaired. How many IT

devices must be brought in for repair each day for this company to break even? Round answer to

the nearest whole device.

12. _________

A. 11 C. 12

B. 73 D. 7

* * * * * * * * * * * * *

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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SHORT ANSWER (work NOT required to be shown)

13. For the linear equation −3𝑥 + 2𝑦 = 24:

a. Determine the slope: _______________________

b. Determine y – intercept if it exists: _______________________

c. Express equation in slope-intercept form: _______________________

14. Let 𝑛(𝐴) = 99, 𝑛(𝐵) = 90, 𝑛(𝐴 ∪ 𝐵) = 117, and 𝑛(𝑈) = 180.

a. Determine 𝑛(𝐵′) : ___________________________________

b. Determine 𝑛(𝐴 ∩ 𝐵) : ___________________________________

c. Determine 𝑛(𝐴′ ∩ 𝐵′): ___________________________________

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 sports and is age 18 – 39: Answer: ______________

(b) most often watches sports given that viewer is age 18 – 39: Answer: ______________

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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SHORT ANSWER, with work required to be shown, as indicated.

16. Nineteen people are summoned to jury duty. 11 are women and 8 are men.

(a) In how many ways can 12 jurists be randomly selected out of the 19 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.

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.

7𝑥 + 2𝑦 = 4

2𝑥 + 3𝑦 = −11

18. Cara knows she’ll need to buy a new car in 3 years. The car will cost $15,000 by then. How

much should she invest now at 12% compounded quarterly so that she will have enough to buy a

new car? Round answer to nearest cent. Show work.

A. $11,957.91 C. $10,520.70

B. $12,594.29 D. $9,532.77

______________________________________________________________________________

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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19. A 2012 report by the Animal Pet Products Association stated Americans spent $30 billion on

their pets in 2002. By 2011, that number measured $51 billion. Let y = amount (in $ billions)

Americans will spend on their pets in year x, where x = 0 represents the year 2002.

(a) Which of the following linear equations could be used to predict the amount y (in $ billions)

Americans spend on their pets in a given year x, where x = 0 represents the year 2002?

Explain/show work.

A. y = – 2.33x + 30 C. y = 2.33x + 51

B. y = – 2.33x + 2002 D. y = 2.33x + 30

(b) Use the equation from part (a) to predict the amount (in $ billions) Americans will spend on

their pets in the year 2018. Round answer to nearest tenth of a billion dollars. Show work.

with respect to time is ____________billion dollars per ________________. (Include units of

measurement.)

20. LaToya’s savings account has a current balance of $9200.00. Exactly 20 years from now,

how much interest will she have earned at 5% compounded annually? Show work

______________________________________________________________________________

21. According to the Canadian Journal of Information and Library Science (Vol 33, 2009), the

probability that workers in Canadian law libraries are satisfied with their job is 0.9. In a random

sample of 20 law librarians in Canada, what is the probability that exactly 15 of them are

satisfied with their job? Round answer to nearest ten-thousandth (4 places after decimal). Show

work

______________________________________________________________________________

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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22. The feasible region shown below is bounded by lines x + 3y = 4, 2x – 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 62, 39, 29, 33, 44, and 33.

(a) State the mode (if one exists).

(b) Find the median. Show work/explanation.

(d) Using the sample mean found in part (c), and given that the sample standard deviation of

the data set above is 12.0, 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%

MATH 106 Finite Mathematics 2172-OL1-6380-V1

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24. If the probability distribution for the random variable X is given in the table, what is the

expected value E(X) ? Show work.

xi – 30 10 20 60

pi 0.30 0.30 0.25 0.15

25. A marketing survey of 2000 randomly-selected convenience store customers found that 1415

of them bought a glazed donut yesterday. 1605 said they bought a frosted crème-filled donut

yesterday. 180 customers said they bought neither yesterday.

(a) What is the probability that a single randomly-selected customer bought only a glazed

donut and nothing else yesterday? Show work.

(b) Let G = {customers who bought a glazed donut yesterday} and C = {customers who

bought a frosted crème-filled donut yesterday}. Determine the number of attendees belonging

to each of the regions I, II, III, IV.

Region I: ________ Region II: __________ Region III: _________ Region IV: __________

______________________________________________________________________________

C G

III I