Math 106 Final Examination Version 2168-US1-4010 Fall, 2016

Prof. Moses Geek

math106fall2016-v1-4010_1.pdf

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MATH 106 Finite Mathematics 2168-US1-4010-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 following statements is NOT true:

1. ________

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

B. If events E and F are independent events, then 𝑃(𝐸 ∩ 𝐹) = ∅.

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(𝐵)

2. – 3. “A Place for Fido” is a business that manufactures and sells custom-built dog houses. A

small dog house requires 15 square feet (ft2) of plywood and 6 ft2 of insulation. A large dog

house requires 60 ft2 of plywood and 18 ft2 of insulation. The business currently has 900 ft2 of

plywood and 120 ft2 of insulation on hand. If a small dog house sells for $55 and a large dog

house sells for $100, what combination of small dog houses (“x”) and large dog houses (“y”)

should be built to maximize the revenue R while staying within constraints?

2. Identify the building material constraint for plywood:

2. _______

A. 15𝑥 + 60𝑦 ≥ 900 C. 6𝑥 + 18𝑦 ≤ 120

B. 15𝑥 + 60𝑦 ≤ 900 D. 6𝑥 + 18𝑦 ≥ 120

3. State the objective function.

3. _______

A. 𝑅 = 15𝑥 + 60𝑦 C. 𝑅 = 6𝑥 + 18𝑦

B. 𝑅 = 100𝑥 + 55𝑦 D. 𝑅 = 55𝑥 + 100𝑦

MATH 106 Finite Mathematics 2168-US1-4010-V1

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4. Two cards are drawn in succession from a standard 52-card deck, without replacement. What

is the probability that both cards drawn are queens?

4. _______

𝐴. 7

103 𝐵.

13 𝐶.

221 𝐷.

5. 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 most

closely depicts a unimodal frequency distribution with positive skew?

5. ______

HISTOGRAM A HISTOGRAM C

HISTOGRAM B HISTOGRAM D

6. The Harrison family buys a $295,000 home by putting a 20% down payment and financing

the balance with a 30-year fixed mortgage at 3.6%. What is the amount of their monthly loan payment to amortize the loan?

6. _______

A. $1363.56 C. $1072.96

B. $1072.92 D. $1341.20

1 2 3 4 5 6

MATH 106 Finite Mathematics 2168-US1-4010-V1

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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. 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 ?

8. ________

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

9. Find the equation of the line passing through (– 3, 3) and (2, – 3): 9. _______

A. y = – 3 B. 5x + 6y = 3 C. 6x + 5y = – 3 D. 6x – y = – 21

-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-US1-4010-V1

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10. At State University, there are 719 students taking Finite Mathematics or Statistics. 328 are taking Finite Mathematics, 476 are taking Statistics, and 85 are taking both Finite

Mathematics and Statistics. How many are taking Finite Mathematics but NOT Statistics?

10. ________

A. 243 C. 476

B. 391 D. 634

11. Which of the corner points for the system of linear inequalities graphed below maximizes the objective function P = 7x + 4y ?

11. _______

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

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

12. The mean time from check-in to completion for a customer served at the Townsburg branch of the Department of Motor Vehicles 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 completion between 94 and 112 minutes after check-in?

12. ______

A. 0.0228 C. 0.1587

B. 0.6826 D. 0.3413

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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.______________

equation 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 “guilt” emotional state : Answer: ______________

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

“guilt” 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 𝐶 ∩ 𝐵 : ___________________________________

b. Determine {𝒙|𝒙 ∈ 𝐴 𝒐𝒓 𝐶} : ___________________________________

c. Determine 𝐴′ ∩ 𝐵′: ___________________________________

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

16. A building construction team of 3 workers is forming from a department of 11 workers. 4

are electricians and 7 are builders.

(a) In how many ways can the 3 team members be randomly selected out of the 11 coworkers?

Show work.

(b) In how many ways can 3 team members be randomly selected from 11 coworkers if 1 must

be an electrician and 2 must be builders? Show work.

an electrician and 2 are builders? 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.

5𝑥 − 4𝑦 = −9

6𝑥 + 5𝑦 = −1

MATH 106 Finite Mathematics 2168-US1-4010-V1

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18. A freight-hauling firm estimates that it will need a new forklift in six years. The estimated

cost of the vehicle is $40,000. The company sets up a sinking fund that pays 8% compounded

semiannually, into which it will make semiannual payments to achieve the goal. Calculate the

size of the payments. Show work.

A. $2662.09 C. $1323.71

B. $2107.80 D. $1023.47

______________________________________________________________________________

19. According to Pricewaterhouse Coopers, "Global State of Information System Security

2015", there were 3.4 million “detected and reported information security incidents”

(cyberattacks, etc.) against computer networks in the USA in 2009. In 2014, that number had

risen to 42.8 million.

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

millions) of detected and reported information security incidents “y” in a given year “x”,

where x = 0 represents the year 2009? Explain/show work.

𝐴. 𝑦 = 0.13𝑥 + 2009 𝐶. 𝑦 = 7.88𝑥 + 2009

𝐵. 𝑦 = 0.13𝑥 + 3.4 𝐷. 𝑦 = 7.88𝑥 + 3.4

(b) Use the equation from part (a) to predict the number (in millions) of detected and

reported information security incidents in the year 2017. Round answer to nearest tenth

of a million. Show work.

and reported information security incidents against computer networks in the US with

respect to time is __________ 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 seed company claims that 80% of its bean seeds will germinate. If twenty of these seeds

are planted in warm, moist, soil, what is the probability that exactly 16 of them will germinate?

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-US1-4010-V1

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23. A recent UMUC criminal justice degree-earner now works for the State of Tennessota. She

is researching the length of time between defendants’ arrests and initial trial dates in six of

Tennessota’s counties to see if the counties need additional criminal justice resources. Recorded

lengths of time (in days) for each of the six counties are 41, 85, 44, 64, 44, and 52.

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

the mean? Show work/explanation.

(d) _______

A. 83.3% C. 50.0%

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 0.14 0.08 0.05 0.02 0.01

Find the expected number of overbooked passengers per flight.

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25. Mary McMath surveyed 122 students in a finite math class on what they most recently did

for fun. 67 went to the movies, 59 went to the big football game, and 13 went to the movies and

to the big football game.

(a) What is the probability that a randomly selected student went to either the movies or to

the big football game, but not both? 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