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MATH 106 Finite Mathematics 2168-OL1-6382-1A

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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. An electronics firm manufactures two types of personal computers: a desktop model and

a laptop model. Producing a desktop computer costs $400 and 40 labor-hours. Producing a

desktop costs $250 and 30 labor-hours. The firm currently has $20,000 and 2160 labor-hours

available for desktop and laptop production. Each desktop sold brings the firm a $320 profit and

each laptop sold brings a $220 profit. Let x represent number of desktops and y represent

number of laptops made per week.

1. Identify the constraint for computer production labor-hours:

1. _______

A. 40𝑥 + 30𝑦 ≥ 2160 C. 400𝑥 + 250𝑦 ≤ 20000

B. 40𝑥 + 30𝑦 ≤ 2160 D. 400𝑥 + 250𝑦 ≥ 20000

2. State the objective function.

2. _______

A. 𝑃 = 320𝑥 + 220𝑦 C. 𝑃 = 400𝑥 + 250𝑦

B. 𝑃 = 220𝑥 + 320𝑦 D. 𝑃 = 250𝑥 + 400𝑦

3. Which of the following statements is NOT true:

3. ________

A. If an event cannot possibly occur, then the probability of the event is 0.

B. If events E and F are mutually exclusive events, then 𝑃(𝐸 ∩ 𝐹) = 0.

C. If only two outcomes are possible for an experiment, then the sum of the probabilities of the outcomes is equal to 1

D. Conditional probability is defined as

𝑃(𝐴|𝐵) = 𝑃(𝐴 ∩ 𝐵)

𝑃(𝐴)

MATH 106 Finite Mathematics 2168-OL1-6382-1A

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4. Students in four different MATH 106 class sections responded to the survey question “How

many hours a day do you work on MATH 106?” as shown below. Which histogram below

accurately reflects the section frequency distribution most likely described as bimodal?

4. ______

HISTOGRAM A HISTOGRAM C

HISTOGRAM B HISTOGRAM D

5. The Coolidge family buys a $330,000 home by putting a 20% down payment and financing

the balance with a 30-year fixed mortgage at 3.9%. What is the amount of their monthly loan payment to amortize the loan?

5. _______

A. $1245.14 C. $1245.20

B. $1245.18 D. $1556.51

6. A jar contains 15 red balls, 12 yellow balls, and 18 green balls. Suppose that each ball has an

equal chance of being picked from the jar. If a single ball is selected at random from the jar,

what is the probability that it is not red?

6. _______

𝐴. 2

3 𝐵.

15 𝐶.

5 𝐷.

1 2 3 4 5 6

MATH 106 Finite Mathematics 2168-OL1-6382-1A

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

7. ________

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

8. The Tralfaz appliance company manufactures small electric grills. The company has

production costs defined as 𝐶(𝑥) = 9.15𝑥 + 27200 where x is the number of grills made each month. Revenue is defined as 𝑅(𝑥) = 21.95𝑥 where x is the number of grills sold each month. How many grills must be sold each month for this manufacturing process to break even?

8. ________

A. 875 B. 1240 C. 2125 D. 2973

9. Find the equation of the line passing through (– 9, 3) and (6, – 3): 9. _______

A. 2x – 5y = – 33 B. 5x + 2y = – 39 C. 2x + 5y = – 3 D. 5x + 2y = 24

-10

-8

-6

-4

-2

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

(0,9)

(0,5) (4,3)

MATH 106 Finite Mathematics 2168-OL1-6382-1A

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10. A survey of 800 small businesses indicates that 250 own a videoconferencing system, 420 own projection equipment, and 180 own both videoconferencing and projection equipment.

How many own neither projection equipment nor a videoconferencing system?

10. ________

A. 310 C. 240

B. 70 D. 620

11. Which of the corner points for the system of linear inequalities graphed below maximizes the objective function P = 4x + 3y ?

11. _______

A. (0, 4) C. (0, 3)

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

12. The mean lifetime for a Zap™ car battery is 170 weeks, with a standard deviation of 10 weeks. Assuming a normal distribution, what is the probability that the measured lifetime of

a randomly chosen Zap™ car battery is greater than 180 weeks?

12. ______

A. 0.6826 C. 0.3413

B. 0.0228 D. 0.1587

MATH 106 Finite Mathematics 2168-OL1-6382-1A

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SHORT ANSWER (work NOT required to be shown)

13. Consider the graph (at left) of a line.

(a) Determine the slope. ______________

(b) State the y-intercept. ______________

of the line.

____________________

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.

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 “anger” emotional state : Answer: ______________

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

“anger” state:

Answer: ______________

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

U = {a, b, c, d, e, f, g, h, i, j,}; A = {a, c, e, g, i}; B = {b, d, f, h, j}; C = {a, b, d}

a. Determine 𝐴′ ∩ 𝐵 : ___________________________________

b. Determine (𝐴 ∪ 𝐶) − (𝐴 ∩ 𝐶) : ___________________________________

c. Determine 𝐵′ ∩ 𝐶′ : ___________________________________

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

16. Thirteen people work in an office. 8 are women and 5 are men. The flu virus is coming.

(a) In how many ways can the flu virus randomly select 5 workers out of the 13 to get sick?

Show work.

(b) In how many ways can the flu choose 5 workers, if 2 must be women and 3 must be men?

Show work.

that 3 are men and 2 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.

2𝑥 − 3𝑦 = 9

3𝑥 + 5𝑦 = 4

MATH 106 Finite Mathematics 2168-OL1-6382-1A

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18. The State of Texakota’s “child’s college education” annuity savings plan pays 7.6%

compounded quarterly. What equal quarterly deposit should be made into this annuity in order

to have $200,000 for college expenses in 19 years?. Show work.

A. $1194.97 C. $8839.00

B. $1023.47 D. $1194.75

______________________________________________________________________________

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 + 2002 C. y = – 2.33x – 30

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 2026. Round answer to nearest tenth of a billion dollars. Show work.

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

measurement.)

20. Bank A pays 5% compounded daily, while Bank B pays 5.12% compounded monthly.

Which bank pays more? Explain. Show work

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______________________________________________________________________________

21. A recent poll of Smallville voters showed that 60% of them support the mayor. What is the

probability that in a random sample of 20 Smallville voters, exactly 12 of them support the

mayor? Round answer to the nearest thousandth (three places after decimal). Show work.

______________________________________________________________________________

22. The feasible region shown below is bounded by lines 4x – y = 6, x + y = 3, and y = 0. Find the coordinates of corner point A. Show work.

MATH 106 Finite Mathematics 2168-OL1-6382-1A

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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 90, 82, 82, 100, 88, and 98.

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

the mean? Show work/explanation.

(d) _______

A. 50.0% C. 33.3%

B. 66.7% D. 68.3%

24. Air Weegotcha overbooks as many as five passengers per flight because some passengers with reservations do not show up for the flight. The airline's records indicate the following

probabilities that it will be overbooked at flight time.

Number overbooked at flight time 0 1 2 3 4 5

Probability of number overbooked 0.7 0.16 0.08 0.03 0.02 0.01

Find the expected number of overbooked passengers per flight.

MATH 106 Finite Mathematics 2168-OL1-6382-1A

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25. Mary McMath surveyed 120 students in a finite math class on what they most recently did

for fun. 50 went to the movies, 75 went to the big football game, and 10 went to the movies and

the big football game.

(a) What is the probability that a randomly selected student went to neither the movies nor

to the big football game? Show work.

(b) Let M = {students who went to movies} and G = {students who went to the “big game”}.

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

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

______________________________________________________________________________

G M

III I