Finite Math Final
mbuden
final.pdf
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 1 of 9
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 + 6y ?
1. _______
A. (0, 0) C. (1, 2)
B. (0, 3) D. (2, 0)
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 2 of 9
2. Which of the following statements is NOT true:
2. ________
A. A probability must be less than or equal to 1.
B. If an event cannot possibly occur, then the probability of the event is 0.
C. If only two outcomes are possible for an experiment, then the sum of the probabilities of the outcomes = 1.
D. If events G and H are independent events, then P (G ∩ H) = 0.
3. Find the equation of the line passing through (4, – 1) and (3, 1):
3. _______
A. 5x – 4y = 11 B. 3x + 4y = 8 C. 2x + 5y = 3 D. 2x + y = 7
4. Sam purchases a new truck for $60,000, makes a down payment of 20%, and finances the rest
with 60-month dealer financing at an annual interest rate of 3.6% compounded monthly. What is
the amount of his monthly loan payment to amortize the loan?
4. _______
A. $875.36 C. $1,094.19
B. $944.00 D. $1,180.00
5. The mean time to get an oil change done at Leaky’s Garage is 61 minutes, with a standard
deviation of 15 minutes. Assuming normal distribution, what is the probability that a randomly
chosen customer experiences an oil change done between 46 and 76 minutes?
5. ______
A. 0.3413 C. 0.5000
B. 0.6826 D. 0.4772
6. One six-sided die is rolled once. What is the probability of rolling a number less than 3?
6. ________
A. 1
6 C.
1
2
B. 1
3 D.
2
3
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 3 of 9
7. Which of the following statements is FALSE? 7. ______
A. If all of the data values in a data set are identical, then the standard deviation is 0.
B. The variance is one of the measures of data dispersal relative to the mean.
C. The standard deviation is the square of the variance.
D. The variance can never be a negative number.
8. – 9. Leaky’s Garage employs supervisors and technicians. According to the union contract, a
supervisor does 3 brake jobs and 4 mufflers per day, whereas a technician does 7 brake jobs and
4 mufflers per day. The home office requires enough staff on hand for at least 24 brake jobs per
day and at least 18 mufflers per day. A supervisor makes $90 per day and a technician makes
$100 per day. The home office is looking to minimize daily labor costs. Let x represent number
of supervisors and y represent number of technicians.
8. Identify the daily production constraint for mufflers:
8. _______
A. 3𝑥 + 7𝑦 ≥ 24 C. 4𝑥 + 4𝑦 ≥ 18
B. 4𝑥 + 4𝑦 ≥ 24 D. 3𝑥 + 7𝑦 ≥ 18
9. State the objective function.
9. _______
A. 𝐶 = 90𝑥 + 100𝑦 C. 𝐶 = 24𝑥 + 18𝑦
B. 𝐶 = 100𝑥 + 90𝑦 D. 𝐶 = 18𝑥 + 24𝑦
10. Identify the row operation that produces the resulting matrix: 10. ________
[ 3 −2 −6 7
| −3 −4
] → [ 1
1
3
−6 7 |
− 13
3
−4 ]
A. 2𝑅1 + 𝑅2 → 𝑅2 C. − 1
3 𝑅2 + 𝑅1 → 𝑅1
B. 1
3 𝑅2 + 𝑅1 → 𝑅1 D.
1
3 𝑅1 → 𝑅1
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 4 of 9
11. Determine which region defines the solution region of the following system of linear
inequalities:
11. ________
2𝑥 − 5𝑦 ≤ −3 −3𝑥 + 𝑦 ≤ −2
A. Region I C. Region III
B. Region II D. Region IV
12. A Social Security number consists of 9 single digits. Order matters, and repetition of digits
is allowed. The total of possible Social Security numbers that could exist is found by evaluating:
12. ________
A. 10 × 9 C. C10,9
B. P10,9 D. 10 9
I
III
II
IV
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 5 of 9
SHORT ANSWER (work NOT required to be shown)
13. For the linear equation 7𝑥 − 6𝑦 = 42:
a. Determine the slope: _______________________
b. Determine x – intercept if it exists: _______________________
c. Determine y – intercept if it exists: _______________________
d. Express equation in slope-intercept form: _______________________
14. Let A = {1, 3, 5, 7, 9, 11, 13, 15}, let B = {– 1, – 3, 7, – 5, – 11, 9, – 13}, and let U = 𝐴 ∪ 𝐵.
a. List the elements of B’ : ___________________________________
b. List the elements of 𝐴 ∩ 𝐵: ___________________________________
c. How many elements comprise U ? ___________________________________
15. 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
Engineering 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 thousandth.)
Find the probability that a randomly selected student:
(a) majors in engineering and is part-time. Answer: ______________
(b) majors in engineering or is part-time. Answer: ______________
(c) majors in engineering, given that the student is part-time. Answer: ______________
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 6 of 9
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 6 workers out of the 13 to get sick?
Show work.
(b) In how many ways can the flu choose 6 workers, if 3 must be women and 3 must be men?
Show work.
(c) If the flu virus randomly selects 6 workers from the 13 in the office, what is the probability
that 3 are men and 3 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.
−5𝑥 + 2𝑦 = 13
2𝑥 − 7𝑦 = 1
18. If $300,000 is to be saved over 25 years, how much should be deposited monthly if the
investment earns 8% compounded monthly? Show work.
A. $315.45 C. $216.62
B. $260.87 D. $180.48
______________________________________________________________________________
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 7 of 9
19. According to the US Department of Justice’s Bureau of Justice Statistics, 2.4% of US
firearms purchase/transfer applications submitted in 1999 were rejected due to background check
information. In 2009, the rejection rate of applications submitted due to background check
information was 1.4%.
(a) Which of the following linear equations could be used to predict application rejection
rate y in a given year x, where x = 0 represents the year 1999? Explain/show work.
A. y = – 10x + 1999 C. y = – 10x + 2.4
B. y = – 0.1x + 1999 D. y = – 0.1x + 2.4
(b) Use the equation from part (a) to predict the firearms application rejection rate (%) in
the year 2019. Round answer to nearest hundredth of a percent. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The rate of change of
application rejection rate with respect to time is
______________________ per ________________. (Include units of measurement.)
20. Tamika’s savings account has a balance of $4069. If she makes no deposits or withdrawals
for 4 years, and the account accrues interest at 5% compounded quarterly, what will be the total
amount of money in her savings account at the end of the 4-year period? Show work
______________________________________________________________________________
21. According to a recent Pew Research Center report, 0.8 is the probability that a randomly
selected American adult knows what Twitter™ is. Eight American adults are randomly selected.
Find the probability that exactly 6 of the 8 American adults randomly selected knows what
Twitter™ is. Round answer to nearest ten-thousandth (4 places after decimal). Show work
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 8 of 9
______________________________________________________________________________
22. The feasible region shown below is bounded by lines – x + 3y = 3, x + y = 4, and y = 0. Find the coordinates of corner point A. Show work.
23. A developmental psychologist studies the number of words that six children have learned at
a particular age. The numbers are 8, 15, 7, 10, 15, and 5.
(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 4.2, 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. 68.3% D. 34.2%
MATH 106 Finite Mathematics Spring, 2015 2152 – OL1 – 6382 – V1
Page 9 of 9
24. The probability distribution for the random variable x is displayed in the following table:
xi 13 8 – 5 9 10
pi 0.20 0.25 0.30 0.10 0.15
Find the expected value E(X) . Show work.
25. An instructor surveyed her class of 45 students and found that most of them watched TV
and/or got on the Internet last night. 10 students said they watched TV but did not get on the
Internet. 16 students said they got on the Web but did not watch TV last night. 43 of the
students watched TV or got on the Internet (or both) last night.
(a) How many of the students got on the Internet last night? Show work.
(b) Let T = {students who watched TV} and W = {students who got on the Internet}.
Determine the number of attendees belonging to each of the regions I, II, III, IV.
Region I: ________ Region II: __________ Region III: _________ Region IV: __________
______________________________________________________________________________
U
W T
II
IV
III I
