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MATH 106 Finite Mathematics 2152-OL2-6980-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. Which of the corner points for the system of linear inequalities graphed below maximizes the

objective function P = 7x + 8y ?

1. _______

A. (0, 4) C. (1, 2)

B. (3, 0) D. (2, 0)

2. Find the equation of the line passing through (1, 2) and (– 5, 4): 2. _______

A. – x – 3y = 7 B. x + 3y = 7 C. x – 3y = 7 D. x + 3y = – 7

MATH 106 Finite Mathematics 2152-OL2-6980-V1

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

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

3. ______

HISTOGRAM A HISTOGRAM C

HISTOGRAM B HISTOGRAM D

4. Identify the single row operation that transforms the matrix as shown: 4. ________

[ 10 −4 −5 2

| 9

−4.5 ] → [

0 0 −5 2

| 0

−4.5 ]

A. 0𝑅1 → 𝑅1 C. 0.5𝑅1 + 𝑅2 → 𝑅2

B. 𝑅2 ↔ 𝑅1 D. 2𝑅2 + 𝑅1 → 𝑅1

5. If payments of $1000 were made quarterly for 20 years into a “sinking fund” account with 8%

interest compounded quarterly, the amount in the account at the end of 20 years can be

determined using formula for:

5. _______

A. Sequence of payments; future value of an ordinary annuity

B. Sequence of payments; present value of an ordinary annuity

C. Single payment, compound interest

D. Single payment, simple annual interest

1 2 3 4 5 6

MATH 106 Finite Mathematics 2152-OL2-6980-V1

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6. A frequent gambler plays his favorite $1 slot machine at a local casino. He pays $1 for a

single chance to win $1000. The probability of hitting the $1000 jackpot in a single play is

0.001. The expected value of this game is:

6. ________

A. $999 C. $1.00

B. 0 D. − $1.00

7. Reggie buys a new car for $8500. He makes a 20% down payment and finances the balance

with a 48-month loan at 6.0% interest compounded monthly. Reggie’s monthly payment is:

7. _______

A. $175.67 C. $219.58

B. $159.70 D. $199.62

8. – 9. The Black Entertainment Television Company (BET) employs copy coordinators and

programming analysts. According to company data, a copy coordinator reviews 5 scripts and 3

show schedules per day, whereas a programming analyst reviews 2 scripts and 7 show schedules

per day. The company needs enough staff on hand to review at least 12 scripts per day and at

least 17 show schedules per day. A copy coordinator makes $230 per day and a programming

analyst makes $190 per day. The company wants to minimize daily labor costs. Let x represent

number of copy coordinators and y represent number of programming analysts.

8. Identify the daily production constraint for show schedules:

8. _______

A. 3𝑥 + 7𝑦 ≤ 12 C. 3𝑥 + 7𝑦 ≥ 17

B. 3𝑥 + 7𝑦 ≤ 17 D. 3𝑥 + 7𝑦 ≥ 12

9. State the objective function.

9. _______

A. 𝐶 = 230𝑥 + 190𝑦 C. 𝐶 = 12𝑥 + 17𝑦

B. 𝐶 = 190𝑥 + 230𝑦 D. 𝐶 = 17𝑥 + 12𝑦

10. If K = {3, 7, 11, 15} and M = {7, 12, 15, 18}, list {𝒙|𝒙 ∉ 𝑲 𝒂𝒏𝒅 𝒙 ∉ 𝑴}

10. _________

A. {Ø} C. { 7, 15 }

B. {3, 7, 11, 12, 15, 18} D. {3, 7, 11, 15, 7, 12, 15, 18}

MATH 106 Finite Mathematics 2152-OL2-6980-V1

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11. Determine which shaded region corresponds to the solution region of the system of linear inequalities

4𝑥 + 𝑦 ≥ 4 𝑥 ≥ 0 𝑥 + 2𝑦 ≤ 4 𝑦 ≥ 0

11. _______

GRAPH A.

GRAPH B.

GRAPH C.

GRAPH D.

12. The mean time from prescription drop-off to medicine pickup for a customer served at

Heisenberg’s Pharmacy is 39 minutes, with a standard deviation of 11 minutes. Assuming a

normal distribution, what is the probability that a randomly chosen customer experiences service

done between 28 and 40 minutes?

12. ______

A. 0.5000 C. 0.6826

B. 0.4772 D. 0.3413

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______________________________________________________________________________

SHORT ANSWER (work NOT required to be shown)

13. For the equation graphed below:

a. Determine the slope m:

m = _____________

b. Determine the x – intercept:

_____________

c. Determine the y – intercept:

_____________

d. State the equation algebraically in slope –

intercept form:

_____________________________

14. 1000 students at a particular college were asked their status (full-time or part-time) and their

chosen undergraduate degree field of study. The following table was obtained.

Undergraduate

Major

Full-time Part-time Total

Business 192 14 206

Education 32 104 136

Health Sciences 210 116 326

Social Sciences 178 154 332

Total 612 388 1000

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)

Find the probability that a randomly selected student:

(a) majors in social sciences and is part-time. Answer: ______________

(b) majors in social sciences or is part-time. Answer: ______________

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15. Let 𝑛(𝐴) = 60, 𝑛(𝐵) = 75, 𝑛(𝐴 ∩ 𝐵) = 15, and 𝑛(𝑈) = 150.

a. Determine 𝑛(𝐵′) : ___________________________________

b. Determine 𝑛(𝐴 ∪ 𝐵) : ___________________________________

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

______________________________________________________________________________

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

16. Eighteen people are summoned to jury duty. 11 are women and 7 are men.

(a) In how many ways can 12 jurists be randomly selected out of the 18 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. Christina is selling an antique dining room furniture set through a broker. She wants to get

$2000 for herself, but the broker gets 15% of the selling price as commission. What should the

selling price be? Show work.

A. $2300.00 C. $2150.00

B. $2279.83 D. $2352.94

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18. Solve the system of equations using substitution, elimination by addition, or augmented

matrix methods (your choice). Show work.

3𝑥 − 2𝑦 = 18

−2𝑥 + 5𝑦 = −1

______________________________________________________________________________

19. According to the US Census Bureau, "United States Census 2010", 33 million Americans

were age 65 or older in 1995; an amount which climbed to 40 million in 2010.

(a) Which of the following linear equations could be used to predict number of

Americans age 65 or older (in millions) “y” in a given year “x”, where x = 0 represents

the year 1995? Explain/show work.

𝐴. 𝑦 = 15

7 𝑥 + 1995 𝐶. 𝑦 =

15 𝑥 + 1995

𝐵. 𝑦 = 15

7 𝑥 + 33 𝐷. 𝑦 =

15 𝑥 + 33

(b) Use the equation from part (a) to predict the number of Americans age 65 or older (in

millions) in the year 2055. Round answer to nearest tenth of a million people. Show

work.

of Americans age 65 or older with respect to time is

______________________ per ________________. (Include units of measurement.)

20. A local car rental agency charted daily demand as shown in the following table:

Number of customers 14 16 18 20 22

Probability 0.15 0.20 0.25 0.30 0.10

Find the expected number of customers. Show work

MATH 106 Finite Mathematics 2152-OL2-6980-V1

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______________________________________________________________________________

21. 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.

22. A network security specialist records the number of incoming e-mails containing links that

eight randomly-selected network users receive in a day. Numbers are 50, 10, 30, 74, 56, 26, 50,

and 40.

(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 19.9, what percentage of the data set falls within one standard deviation of

the mean? Show work/explanation.

(d) _______

A. 34.2% C. 87.5%

B. 75.0% D. 68.3%

MATH 106 Finite Mathematics 2152-OL2-6980-V1

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23. Each day Evelyn has a 0.12 probability of finding a legal parking spot in front of the

company where she works. What is the probability that she will find a spot on exactly 3 of the 5

days of her work week? Round answer to the nearest thousandth (three places after decimal).

Show work.

24. You have $5000 to invest in a single payment. Which is the better investment: 9.0%

compounded annually or 8.7% compounded monthly? Show work

25. A dietitian surveyed her group of 100 patients and found that most of them ate fast food

yesterday. 55 patients said they ate at “Greasies” yesterday. 45 patients said they ate at

“Pluckies” yesterday. 15 patients said they ate at both “Greasies” and “Pluckies” yesterday.

(a) What is the probability that a single randomly-selected patient ate at neither “Greasies”

or at “Pluckies” 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: __________

______________________________________________________________________________

P G

III I