Mathematics

MATH 106 Finite Mathematics 2178-OL4-7981-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. Find the equation of the line passing through (5 , 3) and (– 4, – 1): 1. _______

A. 4x + 9y = – 25 B. 4x – 9y = – 7 C. 2x – y = – 7 D. 2x + y = 13

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

objective function P = 5x + 3y ?

2. _______

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

B. (1, 2) D. (2, 0)

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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3. As chief financial officer at Apocalyptic Fitness Supply, you track costs and revenue for the

daily manufacturing process for your company’s top-selling product, the SpineCrusher™

unstoppable elliptical trainer. Daily production costs are defined by 𝐶(𝑥) = 15𝑥 + 12000 where x = number of units made. Daily revenue coming is defined by 𝑅(𝑥) = 18𝑥 − 6000 where x = number of units sold. How many SpineCrusher™ unstoppable elliptical trainers must

be sold daily for the manufacturing process to break even ?

3. ________

A. 18000 B. 6000 C. 12000 D. 102000

4. If payments of $250 were made monthly for 30 years into an IRA (individual retirement

account) with 5.5% interest compounded monthly, the total amount in the account at the end of

30 years can be determined using formula for:

4. _______

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

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

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

5. ______

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

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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6. For $5 you can have a single chance to roll two fair 6-sided dice at the same time. If your roll

comes up “doubles” (same face is up on both dice) you win $30; if not, you win nothing. What

is the expected value of playing this game?

6. ________

A. − $5.00 C. 0

B. − $4.17 D. $0.83

7. Reggie buys a house for $295,000. He makes a 20% down payment and finances the balance

with a 30-year fixed loan at 4.26% interest compounded monthly. Reggie’s monthly payment is:

7. _______

A. $1169.80 C. $1170.67

B. $1154.08 D. $1162.36

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

8. _________

A. {Ø} C. { 7, 15 }

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

9. – 10. Sunnydale Farms has a total of 240 acres of cropland. The farm owner wants to plant

this acreage in corn and oats. An acre of corn brings $40 in profit, and an acre of oats gets $30

profit. A total of 320 labor-hours to raise the crops is available. Each acre of corn needs 2 labor-

hours, and each acre of oats needs 1 labor-hour. Let x represent acres of corn and y represent

acres of oats.

9. Identify the crop production constraint due to available cropland:

9. _______

A. 2𝑥 + 𝑦 ≤ 320 C. 2𝑥 + 𝑦 ≤ 240

B. 40𝑥 + 30𝑦 ≤ 320 D. 𝑥 + 𝑦 ≤ 240

10. State the objective profit function:

10. _______

A. 𝑃 = 30𝑥 + 40𝑦 C. 240 = 𝑥 + 𝑦

B. 𝑃 = 2𝑥 + 𝑦 D. 𝑃 = 40𝑥 + 30𝑦

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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11. The shaded “feasible region” graphed below satisfies which system of linear inequalities?

11. _______

A. 3𝑥 + 2𝑦 ≥ 18 𝑥 + 2𝑦 ≥ 10 𝑥 ≥ 0 𝑦 ≥ 0

B. 3𝑥 + 2𝑦 ≤ 18 𝑥 + 2𝑦 ≤ 10 𝑥 ≥ 0 𝑦 ≥ 0

C. 3𝑥 + 2𝑦 ≥ 18 𝑥 + 2𝑦 ≤ 10 𝑥 ≥ 0 𝑦 ≥ 0

D. 3𝑥 + 2𝑦 ≤ 18 𝑥 + 2𝑦 ≥ 10 𝑥 ≥ 0 𝑦 ≥ 0

12. The mean time from customer arrival to “service complete” for a customer at the Citysburg

office of the Department of Motor Vehicles is 93 minutes, with a standard deviation of 14

minutes. Assuming a normal distribution, what is the probability that a randomly chosen

customer experiences “arrival-to-service complete” time between 79 and 107 minutes?

12. ______

A. 0.5000 C. 0.3413

B. 0.6826 D. 0.4772

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

-1 0 1 2 3 4 5 6 7 8 9 10 11

(0,9)

(0,5) (4,3)

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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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 y – intercept:

_____________

c. State the equation algebraically in

slope – intercept form:

_____________________________

14. “Guilt and focusing on decision making” (Gangemi & Mancini, Journal of Behavioral

Decision Making, Vol 20, Jan 2007) reported on 171 volunteer students participating in an

experiment where each was randomly assigned to one of three groups. One group was made to

feel guilty, one group was made to feel angry, and the third group was not influenced (“neutral”).

Immediately after reaching these emotional states, the students were asked to decide whether or

not to spend lots of money to repair a very old car (not a “historic”/antique). The “stated” option

was “spend the money to repair the car”. The following raw data was recorded:

Emotional State Choose stated option C Don’t choose stated option C’ Totals

Guilt 45 12 57

Anger 8 50 58

Neutral 7 49 56

Totals 60 111 171

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

Find the probability that a randomly-selected student:

(a) is in the “neutral” emotional state : Answer: ______________

(b) chooses the stated option, given that the student is in the

“neutral” state:

Answer: ______________

(c) chooses the stated option and is in the “neutral” state? Answer: ______________

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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15. Use the following information to answer parts a-c.

a. List elements of 𝐴′ ∩ 𝐵 : ___________________________________

b. List elements of (𝐴 ∪ 𝐶) − (𝐵 ∩ 𝐶) : ___________________________________

c. List elements of 𝐴 ∩ 𝐶′ : ___________________________________

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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______________________________________________________________________________

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

16. You are a restaurant manager. You must pick 17 entrees for your menu. There are 14 meat

offerings and 11 poultry offerings to choose from.

(a) In how many ways can 17 entrees be randomly selected out of the 25 meat and poultry

offerings? Show work.

(b) In how many ways can 17 entrees be chosen, if 11 must be beef and 6 must be chicken?

Show work.

(c) If 17 entrees are randomly selected from the 25 offerings, what is the probability that 6 are

chicken and 11 are beef? 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.

3𝑥 + 2𝑦 = −10

2𝑥 − 3𝑦 = 2

18. Christina is selling an antique dining room furniture set through a broker. She wants to get

$1500 for herself, but the broker gets 15% of the selling price as commission. What should the

selling price be? Show work.

A. $1650.00 C. $1725.00

B. $1764.71 D. $1783.52

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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______________________________________________________________________________

19. According to the US Center for Disease Control and Prevention National Center for Health

Statistics, 10.0 percent of adolescent (ages 12 – 19) Americans were obese in 1995; an amount

which climbed to 18.0 percent in 2008.

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

Americans who are obese “y” in a given year “x”, where x = 0 represents the year 1995?

Explain/show work.

𝐴. 𝑦 = 13

8 𝑥 + 1995 𝐶. 𝑦 =

8

13 𝑥 + 1995

𝐵. 𝑦 = 13

8 𝑥 + 10 𝐷. 𝑦 =

8

13 𝑥 + 10

(b) Use the equation from part (a) to predict the percent of adolescent Americans who are

obese in the year 2027. Round answer to nearest tenth of a percent. Show work.

(c) Fill in the blanks to interpret the slope of the equation: The rate of change of number

of Americans age 65 or older with respect to time is

______________________ per ________________. (Include units of measurement.)

20. If $460,000 is to be saved over 15 years, how much should be deposited semi-annually if

the investment earns 15% compounded semi-annually? Round answer to nearest cent. Show

work.

A. $4435.77 C. $17612.13

B. $4790.74 D. $4448.77

______________________________________________________________________________

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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21. The feasible region shown below is bounded by lines x + y = 3, 4x – y = 6, 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

six randomly-selected network users receive in a day. Numbers are 64, 110, 112, 110, 98, and

100.

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

the mean? Show work/explanation.

(d) _______

A. 66.7% C. 83.3%

B. 34.1% D. 68.3%

MATH 106 Finite Mathematics 2178-OL4-7981-V1

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23. There is a 0.95 probability that MATH 106 students will correctly follow all instructions on

the Final Exam. What is the probability that exactly 19 of the 20 students taking MATH 106 in a

particular section correctly follow all Final Exam instructions? 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 mall developer surveyed 500 customers yesterday to learn what they go shopping for at

the mall. 280 customers said they shopped for clothes. 355 customers said they went shopping

for electronics. 200 customers said they shopped for both clothes and electronics.

(a) What is the probability that a single randomly-selected shopped for neither clothing nor

electronics yesterday? Show work.

(b) Let C = {customers shopping for clothes} and E = {customers shopping for electronics}.

Determine the number of customers belonging to each of the regions I, II, III, IV.

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

______________________________________________________________________________

U

E C

II

IV

III I

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