MATH 106 FINAL EXAMINATION | Complete Solution

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, and upload it into
the Final Exam folder in “Assignments”. DO NOT UPLOAD THIS EXAM!
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. A high school football team of 40 players includes 16 players who played on offense last
year, 17 who played defense, and 12 who weren’t on last year’s team. How many players from
last year played both offense and defense?
 1. _____
A. 7 B. 4 C. 11 D. 5
2. The McKinleys buy a $230,000 home by putting 20% down and financing the balance with a
30-year fixed-rate 4.2% mortgage, compounded monthly. What is the amount of their monthly
loan payment to amortize the loan?
 2. _____
A. $1124.74 B. $899.56 C. $1155.11 D. $899.79
3. During her four years at college, Niki received A's in 30% of her courses, B's in 50% of her
courses, and C's in the remaining 20%. If A = 4, B = 3, and C = 2, find her grade point average.
3. ______
A. 3.3 B. 3.1 C. 3.2 D. 3.0
4. A normal distribution of raw scores has a mean of 50 and a standard deviation of 7.
Approximately 95% of the distribution can be found between what two raw scores?
 4. ______
 A. 36 and 50 B. 50 and 64 C. 36 and 64 D. 43 and 57
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 2 of 10
5. Determine which region corresponds to the feasible region of the system of linear
inequalities:
3𝑥 + 7𝑦 ≥ 1
4𝑥 + 3𝑦 ≥ −5
A. Region I C. Region III
B. Region II D. Region IV 5. _______
6. Find the equation of the line passing through (– 2, 1) and (5, – 2): 6. _______
 A. 3x – 7y = – 13 B. 7x + 3y = – 11 C. x – 3y = – 5 D. 3x + 7y = 1
II
III IV
I
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 3 of 10
7. Which of the corner points for the system of linear inequalities graphed below minimizes the
objective function C = 7x + 6y ?
7. _______
 A. (0, 26) C. (4, 2)
B. (2, 6) D. (8, 0)
8. Identify the single row operation that transforms the matrix as shown: 8. ________
 [
1 2
0 1
|
15
7
] → [
1 0
0 1
|
1
7
]
A. 2𝑅2 + 𝑅1 → 𝑅1 C. 7𝑅1 + 𝑅2 → 𝑅2
B. −2𝑅2 + 𝑅1 → 𝑅1 D. 2𝑅1 + 𝑅2 → 𝑅2
9. – 10. A home healthcare agency employs registered nurses (RNs) and certified nurse’s
assistants (CNAs). An individual RN performs 100 medical care procedures and 40 patient
welfare tasks per month, and an individual CNA performs 15 medical care procedures and 280
patient welfare tasks per month. Enough RNs and CNAs are needed per month to perform at
least 500 medical procedures and at least 1500 patient welfare tasks. Monthly labor costs are
$16000 per RN and $3000 per CNA. The agency wants to minimize labor costs. Let x represent
number of RNs employed per month and y represent number of CNAs employed per month.
9. Identify constraint on monthly number of patient welfare tasks performed:
9. _______
A. 40𝑥 + 280𝑦 ≥ 500 C. 100𝑥 + 15𝑦 ≥ 500
B. 40𝑥 + 280𝑦 ≥ 1500 D. 100𝑥 + 15𝑦 ≥ 1500
10. State the objective function.
10. _______
A. 𝐶 = 16000𝑥 + 3000𝑦 C. 𝐶 = 500𝑥 + 1500𝑦
B. 𝐶 = 3000𝑥 + 16000𝑦 D. 𝐶 = 1500𝑥 + 500𝑦
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 4 of 10
11. The amount of money you should have in a retirement account paying 8% interest
compounded quarterly in order to be able to withdraw $10,000 a quarter for 15 years once you
retire can be determined using formula for:
11. _______
A. Periodic payments: present value of an annuity / installment payment on loan
B. Periodic payments: future value of an ordinary annuity
C. Single payment: compound interest
D. Single payment: simple annual interest
12. The following histogram correctly corresponds to which of the following frequency tables?
 12. ______
A B C D
Value Frequency Value Frequency Value Frequency Value Frequency
1 X 1 X 1 X 1 X
2 XXX 2 XX 2 XX 2 XX
3 XXXX 3 XXX 3 XXX 3 XXX
4 XXXXX 4 XXXX 4 XXXXX 4 XXXXX
5 XXXX 5 XXX 5 XXX 5 XX
6 X 6 X 6 X 6 X
0
1
2
3
4
5
6
1 2 3 4 5 6
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 5 of 10
SHORT ANSWER (work NOT required to be shown)
13. For the line graphed at left:
a. Determine the slope:
_______________________
b. Determine y – intercept if it exists:
_______________________
c. Express equation in slope-intercept form :
_______________________
d. Express equation in general (standard) form:
_______________________
14. The May 2016 makeup of the US House of Representatives by party affiliation and gender
follows:
Male (M) Female (F) Total
Democrat (D) 127 66 193
Republican (R) 225 22 247
Total 352 88 440
(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)
Find probability that a single randomly-selected member of the US House of Representatives is:
(a) Female and Democrat: Answer: ______________
(b) Female or Democrat: Answer: ______________
(c) Female given that the selected Representative is Democrat: Answer: ______________
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 6 of 10
15. Given the following Venn diagram:
List the members of the following sets:
a. (𝐴 ∪ 𝐶) Answer: ______________
b. (𝐴 ∩ 𝐵) ∩ 𝐶 Answer: ______________
c. 𝐴′ ∩ 𝐵′ ∩ 𝐶′ Answer: ______________
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 7 of 10
SHORT ANSWER, with work required to be shown, as indicated.
16. You’re at the library to do research for your statistics project. You need 5 sources. There
are 5 finite mathematics sources and 11 statistics sources to choose from. Order doesn’t matter.
(a) How many ways can 5 sources be randomly selected out of the 16 sources? Show work.
(b) How many ways can 5 sources be chosen, if 2 must be finite math and 3 must be statistics?
Show work.
(c) Using your answers to parts (a) and (b), if 5 sources are randomly selected from the 16
sources, what is the probability that 2 are finite math and 3 are statistics? 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.
4𝑥 + 3𝑦 = 14
 3𝑥 + 7𝑦 = 1
18. Lakesha needs $3,700 in two years for her college tuition. How much money should she
deposit lump sum in an account paying 8.4% compounded monthly to achieve that goal?
Round answer to nearest cent. Show work.
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 8 of 10
______________________________________________________________________________
19. The 2015 US Department of Justice, Bureau of Justice Statistics publication Probation and
Parole in the United States, 2014 (www.bjs.gov) states that 826 thousand US adult residents
were on parole in 2007, a figure which increased to 857 thousand in 2014.
a. Multiple choice: The linear regression model most closely fitting this data (where
p represents number [in thousands] of US adult residents on parole and t represents
years since 2007) is:
A. p = 0.23t + 2007 C. p = 4.43t + 2007
B. p = 4.43t + 826 D. p = 0.23t + 826
b. Use the model to predict the number US adult residents (in thousands) on parole in
2024 (round answer to one place after decimal) Show work!
c. Fill in the blanks to interpret the slope of the equation: The rate of change of US
adult residents (in thousands) on parole with respect to time is
____________________ per ______________. (Include units of measurement.)
20. A donut shop has a fixed operating cost of $124 per day and a variable operating cost of
$0.12 (12 cents) per donut produced. How many donuts can be made for a total daily cost of
$310? Show work
______________________________________________________________________________
21. There is a 0.73 probability that MATH 106 students will correctly follow all instructions on
the Final Exam. What is the probability that exactly 73 of the 100 students taking MATH 106 in
a particular term correctly follow all Final Exam instructions? Round answer to the nearest ten
thousandth (four places after decimal). Show work.
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 9 of 10
______________________________________________________________________________
22. The feasible region shown below is bounded by lines 2x – y = 4, x + 3y = 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 56, 80, 108, 76, 56, and 62.
 (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 19.91, what percentage of the data set falls within one standard deviation of
the mean? Show work/explanation.
(d) _______
A. 83.3% C. 66.7%
B. 68.3% D. 34.2%
MATH 106 Finite Mathematics 2162-OL4-7980-V1
Page 10 of 10
24. A local bicycle rental agency charted daily demand as shown in the following table:
Number of customers per day 14 16 18 20 22
Probability 0.3 0.2 0.3 0.1 0.1
Find the expected number of customers.
25. A survey of 200 consumers revealed the following movie rental preferences: 130 rented
from NetflixTM, 93 rented from RedboxTM, and 48 reported renting from both.
 (a) What is the probability that a randomly selected consumer rented from either NetflixTM
or RedboxTM ? Show work.
 (b) Let N = {consumers who rent from NetflixTM} and R = {consumers who rent from
RedboxTM}. Determine the number of consumers belonging to each of the regions I, II, III, IV.
Region I: ________ Region II: __________ Region III: _________ Region IV: __________