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MATH 106 Finite Mathematics 2185-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. Eclat State University is establishing a 24-hour online academic dishonesty detection and

prevention center to attack the problem of online cheating by its students. The center employs

certified network administrators and newly graduated students from the university’s

cybersecurity program. A minimum of 190 labor hours per week is needed to perform detection

of academic dishonesty. Prevention of academic dishonesty once detected requires a minimum

of 162 labor hours per week. A certified network administrator can perform 30 labor hours of

detection and 9 labor hours of prevention in a week at $7800 per person. A newly graduated

student can perform 10 labor hours of detection and 18 labor hours of prevention per week at

$4200 per person. Let x represent number of certified network administrators needed and y

represent number of newly graduated students needed.

1. Identify the labor-hour constraint associated with dishonesty prevention:

1. _______

A. 9𝑥 + 18𝑦 ≤ 162 C. 30𝑥 + 10𝑦 ≥ 190

B. 9𝑥 + 18𝑦 ≥ 162 D. 30𝑥 + 10𝑦 ≤ 190

2. State the objective labor cost function:

2. _______

A. 𝐶 = 190𝑥 + 162𝑦 C. 𝐶 = 9𝑥 + 18𝑦

B. 𝐶 = 30𝑥 + 10𝑦 D. 𝐶 = 7800𝑥 + 4200𝑦

3. Find the equation of the line passing through (– 4, 1) and (11, – 5): 3. _______

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

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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4. Which of the following statements is NOT true:

4. ________

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)

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

accurately reflects the section frequency distribution most likely described as positively skewed?

5. ______

HISTOGRAM A HISTOGRAM C

HISTOGRAM B HISTOGRAM D

6. The Wilson family buys a $325,000 home by putting a 20% down payment and financing the

balance with a 30-year fixed mortgage at 4.35%. What is the amount of their monthly loan payment to amortize the loan?

6. _______

A. $1295.23 C. $1294.31

B. $1293.39 D. $1289.72

1 2 3 4 5 6

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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7. 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 green?

7. _______

𝐴. 2

3 𝐵.

15 𝐶.

5 𝐷.

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

8. ________

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

-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 2185-OL1-6382-1A

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

production costs defined as 𝐶(𝑥) = 4.5𝑥 + 27200 where x is the number of grills made each month. Revenue is defined as 𝑅(𝑥) = 21.5𝑥 where x is the number of grills sold each month. How many grills (nearest whole number) must be sold each month for this manufacturing

process to break even?

9. ________

A. 875 B. 1600 C. 2125 D. 1266

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 either projection equipment or a videoconferencing system?

10. ________

A. 620 C. 70

B. 490 D. 310

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

the objective function P = 3x + 4y ?

11. _______

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

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

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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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 less than 160 weeks?

12. ______

A. 0.1587 C. 0.3413

B. 0.0228 D. 0.6826

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.

____________________

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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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

“neutral” state:

Answer: ______________

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′ : ___________________________________

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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

16. Sixteen people work in an office. 10 are women and 6 are men. The flu virus is coming.

(a) In how many ways can the flu virus randomly select 5 workers out of the 16 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 = 13

3𝑥 + 5𝑦 = 10

18. The State of Texakota’s “child’s college education” annuity savings plan pays 7.2%

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

to have $300,000 for college expenses in 15 years?. Show work.

A. $8217.59 C. $8576.00

B. $2817.59 D. $2144.00

______________________________________________________________________________

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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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 + 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 2023. 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

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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______________________________________________________________________________

21. A recent poll of Smallville voters showed that 55% of them support the mayor. What is the

probability that in a random sample of 20 Smallville voters, exactly 11 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 as shown. Find coordinates of corner point A. Show work.

0 0.5 1 1.5 2 2.5 3 3.5 4

Feasible Region

A y = 6

MATH 106 Finite Mathematics 2185-OL1-6382-1A

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23. A network security specialist records numbers of incoming e-mails containing links that six

randomly-selected network users receive in a day. Numbers are 221, 296, 235, 243, 239, 296.

(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 32.61, 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 2185-OL1-6382-1A

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25. Rutgers University researcher Donald McCabe surveyed 71,300 undergraduate students

between Fall 2002 and Spring 2011 semesters to study the extent of student-admitted academic

integrity and dishonesty in completing requirements for coursework. Some of his survey results

are found on International Center for Academic Integrity website https://academicintegrity.org/ .

Of the 71300 students who responded to the survey:

• 12121 respondents said they had deliberately cheated on at least one test

• 28520 respondents said they had deliberately cheated on at least one written assignment or

project

• 9982 respondents said they had deliberately cheated on at least one test and on at least one

written assignment or project

(a) What is the probability that a single randomly-selected student who responded to the

survey said she/he had deliberately cheated on at least one written assignment or project but not

on a test? Show work.

(b) Let T = {students reported cheating on test} and A = {students reported cheating on

assignment/project}. Determine the number of surveyed students belonging to each of the

regions I, II, III, IV.

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

______________________________________________________________________________

T A

III I

https://academicintegrity.org/