Infinite Mathematics
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MATH106Summer2019-V1-6980_Final.pdf
MATH 106 Finite Mathematics 2195-OL2-6980
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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 graphing calculator/spreadsheet software. 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. Amalgamated Furniture Company makes dining room tables and chairs. A table requires 8
labor-hours for assembling and 2 labor-hours for finishing. A chair requires 2 labor-hours for
assembly and 1 labor-hour for finishing. The maximum labor-hours available per day for
assembling and finishing are 400 and 120, respectively. Production costs are $600 per table and
$150 per chair. Let x represent number of tables and y represent number of chairs made per day.
Identify the daily production constraint for assembly:
1. _______
A. 8𝑥 + 2𝑦 ≥ 400 C. 8𝑥 + 2𝑦 ≤ 400
B. 2𝑥 + 𝑦 ≥ 120 D. 2𝑥 + 𝑦 ≤ 120
2. Shonda buys an Amalgamated dining room furniture set for $10,000, makes a down payment
of 20%, and finances the rest with 60-month store financing at an annual interest rate of 5.4%
compounded monthly. What is the amount of her monthly loan payment to amortize the loan?
2. _______
A. $152.44 C. $169.33
B. $150.24 D. $154.66
3. Which of the following statements is TRUE:
3. ________
A. In describing data, a population is a subset of a sample
B. If 𝑥 ∈ 𝑀 𝑜𝑟 𝑥 ∈ 𝑁 then 𝑥 ∈ (𝑀 ∩ 𝑁)
C. In describing data, variance equals square root of standard deviation
D. None of the above statements are true.
MATH 106 Finite Mathematics 2195-OL2-6980
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4. Two balls are drawn in succession, without replacement, out of a box containing 2 red and 5
white balls. What is the probability that the first ball drawn is white and the second ball drawn is
also white?
4. _______
A. 5
21 B.
1
21 C.
10
21 D.
1
3
5. Which histogram below accurately reflects 15 survey responses presented in the following
frequency table?
Value Frequency
1 X
2 XX
3 XXXXXX
4 XXX
5 XX
6 X
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
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6. Determine which graph shows the correct solution region of the system of linear inequalities:
𝑥 + 𝑦 ≥ 2 𝑥 ≥ 0 𝑥 + 3𝑦 ≤ 3 𝑦 ≥ 0
6. _______
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
7. Find the equation of the line passing through (– 2, 1) and (5, 2): 7. _______
a. x – y = 3 b. 3x – 7y = 1 c. x – 7y = – 9 d. x + y = 7
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8. The total amount of money you should deposit in an account paying 8% compounded
quarterly in order to receive quarterly payments of $1000 for the next 4 years can be determined
using formula for:
8. _______
A. Sequence of payments: present value of an annuity / amortization
B. Sequence of payments: future value of an ordinary annuity
C. Single-payment, compound interest
D. Single-payment, simple interest
9. Which of the corner points for the system of linear inequalities graphed below minimizes the
objective function P = 7x + 6y ?
9. _______
A. (3, 0) C. (2, 0)
B. (0, 4) D. (1, 2)
10. The mean time from check-in to completion for a customer service task at the Townsburg
branch of the DMV 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 done in
more than 130 minutes?
10. ______
A. 0.3413 C. 0.9772
B. 0.1587 D. 0.8413
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11. Dwayne’s Digital Doctors is a small business specializing in personal information
technology (IT) device repair. The company has fixed costs of $618 a day and variable costs of
$8.50 per IT device repaired. The company charges $60 per IT device repaired. How many IT
devices must be brought in for repair each day for this company to break even? Round answer to
the nearest whole device.
11. _________
A. 73 C. 11
B. 12 D. 7
12. Which of the following statements is TRUE: 12. _________
A. Don’t round off any number in an amortization calculation unless it’s the final answer
B. If counting, sampling without replacement, & order doesn’t matter: use permutations
C. The graph of 3𝑥 − 2𝑦 < 5 is drawn as a solid line with solution set area shaded
D. The slope m of a horizontal line is always undefined
* * * * * * * * * * * * *
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SHORT ANSWER (work NOT required to be shown)
13. For the linear equation graphed at left:
a. Determine the slope:
_______________________
b. Determine y – intercept if it exists:
_______________________
c. Express equation in slope-intercept form:
_______________________
14. Let 𝑛(𝐴) = 92, 𝑛(𝐵) = 107, 𝑛(𝐴 ∩ 𝐵) = 67, and 𝑛(𝑈) = 140.
a. Determine 𝑛(𝐵′) : ___________________________________
b. Determine 𝑛(𝐴 ∪ 𝐵) : ___________________________________
c. Determine 𝑛(𝐴′ ∩ 𝐵′): ___________________________________
15. The following table showing political party affiliation of each of 67 US Senate members in
Jan 2019, and when they are up for re-election: (Source: www.senate.gov)
Up for Re-election Democrat Republican Other Total
Nov 2020 11 22 0 33
Nov 2022 12 21 1 34
Total 23 43 1 67
(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)
Find the probability that a single randomly-selected US Senator is:
(a) Up for re-election in 2022 and Republican: Answer: ______________
(b) Up for re-election in 2022 or Democrat: Answer: ______________
(c) Up for re-election in 2020 given that the selected Senator
is Republican: Answer: ______________
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SHORT ANSWER, with work required to be shown, as indicated.
16. Eighteen people are summoned to jury duty. 11 are women and 7 are men.
(a) In how many ways can 12 jurists be randomly selected out of the 18 people? Show work.
(b) In how many ways can 12 jurists be chosen, if 7 must be women and 5 must be men? Show
work.
(c) If 12 jurists are randomly selected from the 18 people, what is the probability that 5 are men
and 7 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.
11𝑥 − 7𝑦 = 1
2𝑥 − 5𝑦 = −11
18. If mortgage lending institutions apply the “30% rule” (monthly mortgage payment of
combined principal and interest cannot exceed 30% of borrower’s monthly take-home pay) to a
borrower with monthly take-home pay of $4270, what is the maximum monthly payment this
borrower can handle? Show work.
A. $14,233.33 C. $2989.00
B. $1281.00 D. $1455.00
______________________________________________________________________________
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19. Python is a widely used high-level, general-purpose, interpreted, dynamic computer
programming language (https://www.python.org/). Python code runs on a wide variety of
systems, making the ability to program in Python a very desirable job skill. The percentage of
total permanent information technology (IT) jobs in both the US and the United Kingdom (UK)
requiring knowledge of Python programming language has changed significantly from 2006 to
2015. In 2006, 1.1% of permanent IT jobs required Python programming ability in the UK. By
2015, this percentage had risen to 7.2%. (Source: IT JobsWatch (UK), “Python Jobs Demand
Trend”, August 2016, www.itjobswatch.co.uk).
(a) Which of the following linear equations could be used to predict percentage of
permanent IT jobs in the UK requiring Python programming ability “y” in a given year
“x”, where x = 0 represents the year 2006? Explain/show work.
𝐴. 𝑦 = 6.545𝑥 + 1.1 𝐶. 𝑦 = 0.678𝑥 + 1.1
𝐵. 𝑦 = 0.922𝑥 + 1.1 𝐷. 𝑦 = 0.153𝑥 + 1.1
(b) Use the equation from part (a) to predict the percentage of permanent IT jobs in the
UK requiring Python programming ability in the year 2024. 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
percentage of permanent IT jobs in the UK requiring Python programming ability with
respect to time is _______________ per __________. (Include units of measurement.)
20. Amanda is selling an antique dining room furniture set through a broker. She wants to get
$3400 for herself, but the broker gets 15% of the selling price as commission. What should the
selling price be? Show work.
______________________________________________________________________________
21. There is a 0.78 probability that MATH 106 students will correctly follow all instructions on
the Final Exam. What is the probability that exactly 39 of 50 randomly selected students taking
MATH 106 Final Exam in a particular term correctly follow all instructions? Round answer to
the nearest ten thousandth (four places after decimal). Show work.
______________________________________________________________________________
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22. The feasible region shown below is bounded by lines – x + 2y = 4, 3x + y = 4, and y = 0. Find the coordinates of corner point A. Show work.
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 43, 86, 58, 46, 43, and 60.
(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 16.48, what percentage of the data set falls within one standard deviation of
the mean? Show work/explanation.
(d) _______
A. 34.2% C. 68.3%
B. 66.7% D. 83.3%
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24. A local car rental agency charted daily demand as shown in the following table:
Number of customers 6 8 10 12 14
Probability 0.15 0.20 0.25 0.30 0.10
Find the expected number of customers. Show work.
25. A marketing survey of 2000 randomly-selected convenience store customers found that 1415
of them bought a glazed donut yesterday. 1605 said they bought a frosted crème-filled donut
yesterday. 180 customers said they bought neither yesterday.
(a) What is the probability that a single randomly-selected customer bought a glazed donut
or a frosted crème-filled donut yesterday but not both? Show work.
(b) Let G = {customers who bought a glazed donut yesterday} and C = {customers who
bought a frosted crème-filled donut yesterday}. Determine the number of attendees belonging
to each of the regions I, II, III, IV.
Region I: ________ Region II: __________ Region III: _________ Region IV: __________
______________________________________________________________________________
U
C G
II
IV
III I
