MATH 106 FINAL EXAMINATION 2015
MATH 106 Finite Mathematics
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MATH 106 FINAL EXAMINATION
This is an openbook 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.
Collaboration or consultation with others is NOT allowed. Use of instructors’ solutions
manuals and/or online problem solving services is 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. Sheila purchases a car for $24,000, makes a down payment of 25%, and finances the rest with
a 60month car loan at an annual interest rate of 5.4% compounded monthly. What is the amount
of her monthly loan payment?
1. _______
A. $457.32 C. $508.00
B. $381.00 D. $342.99
2. Find result of performing row operation 0.5?1 + ?2 ? ?2 on matrix K:
2. _______
? = [ 8 ?2
?6 5  10
?9 ]
A. [ 8 ?2
?2 4  10
?4 ] B. [ 4 ?1
?2 4  5
?4 ]
C. [ 4 ?1
?6 5  5
?9 ] D. [ ?2 4
?6 5  ?4
?9 ]
3. Customers shopping at a particular supermarket spend a mean time shopping of 47 minutes,
with a standard deviation of 11 minutes. Assuming a normal distribution, what is the probability
that a randomly chosen customer will spend between 36 and 58 minutes shopping in the
supermarket?
3. ______
A. 0.3413 C. 0.6826
B. 0.9544 D. 0.7580
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4. Find the values of x and y that maximize the objective function P = 7x + 5y for the feasible
region shown below. 4. _______
A. (x, y) = (10, 0)
B. (x, y) = (8, 10)
C. (x, y) = (5, 15)
D. (x, y) = (0, 20)
5. Two balls are drawn in succession out of a box containing 2 red and 5 white balls. The balls
are drawn without replacement. What is the probability that both balls drawn are red?
5. _______
A. 19
42 B. 1
21 C. 13
42 D. 2
7
6. Which of the following statements is NOT true? 6. ______
A. If all of the data values in a data set are identical, then the standard deviation is 0.
B. The variance can be a negative number.
C. The standard deviation is the square root of the variance.
D. The variance is a measure of the dispersion or spread of a distribution about its mean.
7. If K = {3, 7, 11, 15} and M = {7, 12, 15, 18}, list {?? ? ? ?? ? ? ?}
7. ______
A. { 3, 7, 11, 12, 15, 18 } C. { ? }
B. { 3, 7, 7, 11, 12, 15, 15, 18 } D. { 7, 15 }
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8. Determine which shaded region corresponds to the solution region of the system of linear
inequalities
x + y t 2
x + 3y ? 3
x t 0
y t 0 8. ____
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
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9 – 10. At Burger Heaven a “double” contains 2 meat patties and 6 pickles, whereas a “triple”
contains (wait for it!) 3 meat patties and 3 pickles. Near closing time one day, only 24 meat
patties and 48 pickles are available. If a “double” sells for $1.50 and a “triple” sells for $2.00,
then how many of each should be made in order to maximize profit? Let x represent number of
“double” burgers and y represent number of “triple” burgers.
9. Identify the production constraint for pickles:
9. _______
A. 6? + 3? ? 24 C. 6? + 3? ? 24
B. 6? + 3? ? 48 D. 6? + 3? ? 48
10. State the objective function.
10. _______
A. ? = 24? + 48? C. ? = 1.5? + 2?
B. ? = 48? + 24? D. ? = 2? + 1.5?
11. You can win Transylkota’s “Deep6” lottery jackpot if you correctly choose 6 nonrepeating
integer numbers between 1 and 30 (in any order) and those numbers are drawn. You buy one
ticket. What is the probability that it’s the jackpot winner?
11. ______
A. ?(?) = 1??30,6 C. ?(?) = 1 306 ?
B. ?(?) = 1/?30,6 D. ?(?) = 6 306 ?
12. Find the equation of the line passing through (7, 5) and ( – 1 , – 1): 12. ______
A. 2x – 3y = – 1 B. 3x – 4y = 1 C. 3x + 4y = 41 D. 2x + 3y = – 5
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______________________________________________________________________________
SHORT ANSWER (Work not required to be shown)
13. Consider the following graph of a line.
(a) State the xintercept. ______________
(b) State the yintercept. ______________
Answer: ______________
(c) Determine the slope. ______________ Answer: ______________
(d) Find the slopeintercept form of the equation
of the line.
______________________
14. 980 randomlyselected respondents to a marketing survey were asked their age in years
(18 to 39 or 40+) and the choice of vacation destination they liked best. Following data
obtained:
Preferred Vacation
Destination
Age 1839 Age 40 + Total
Theme Park 245 17 262
Seashore 135 183 318
Mountains 151 85 236
Spa Resort 51 113 164
Total 582 398 980
(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)
Find the probability that a randomlyselected respondent:
(a) prefers the mountains or is age 18 – 39: Answer: ______________
(b) prefers the mountains given that the respondent is age 18 – 39: Answer: ______________
(c) prefers the mountains and is age 18 – 39: Answer: ______________
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15. Let U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, B = {1,3,4,6}, and C = {2,4,6}.
List the members of the following sets:
a. ? ? ? Answer: ______________
b. ? ? ? Answer: ______________
c. ?? ? ?? Answer: ______________
SHORT ANSWER, with work required to be shown, as directed.
16. There is a collection of 13 books. 9 of the books are fiction and 4 of the books are nonfiction.
As an assignment, a student must read 6 of the books over the summer.
(a) In how many ways can 6 of the 13 books be chosen? Show work.
(b) In how many ways can the 6 books be chosen, if 4 of the books must be fiction and 2 of the
books must be nonfiction? Show work.
(c) If 6 books are selected at random from the collection of 13 books, what is the probability that
4 are fiction and 2 are nonfiction? Give answer as a fraction or as a decimal rounded to nearest
tenthousandth (4 places after decimal) Show work.
______________________________________________________________________________
17. Solve the system of equations using elimination by addition, substitution, or augmented
matrix methods (your choice). Show work.
7? ? 4? = 6
2? + 3? = 10
______________________________________________________________________________
18. Cara needs $9,000 in 11 years. What amount can she deposit at the end of each quarter at
8% annual interest compounded quarterly so she will have her $9,000? Show work.
A. $125.19 C. $134.01
B. $129.49 D. $540.69
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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 2022. 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. The feasible region shown below is bounded by lines x + y = 1, 2x + y = 3, and y = 0.
Find the coordinates of corner point A. Show work.
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21. If the probability distribution for the random variable X is given in the table, what is the
expected value of X? Show work.
xi – 30 10 20 60
pi 0.30 0.30 0.25 0.15
______________________________________________________________________________
22. There is a 0.91 probability that MATH 106 students will correctly follow all instructions
on the Final Exam. What is the probability that exactly 91 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.
23. A psychologist studied the number of words spoken by a sample of 8 threeyearolds. The
numbers of words recorded per each 3yearold were 20, 19, 30, 22, 50, 36, 44, and 19.
(a) State the mode (if one exists. If not, indicate “none”).
(b) Find the median. Show work/explanation.
(c) State the mean. Show work/explanation.
(d) The sample standard deviation is 12.2. What percentage of the data fall within one
standard deviation of the mean? Show work/explanation.
(d) _______
A. 34%
B. 88%
C. 68%
D. 75%
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24. Christina is selling an antique dining room furniture set through a broker. She wants to get
$1500 for herself, but the broker gets 15% of the selling price as commission. What should the
selling price be? Show work.
A. $1650.00 C. $1725.00
B. $1764.71 D. $1783.52
25. A mall developer surveyed 500 customers yesterday to learn what they go shopping for at
the mall. 345 customers said they shopped for clothes. 290 customers said they went shopping
for electronics. 200 customers said they shopped for both clothes and electronics.
(a) What is the probability that a single randomlyselected shopped for either clothing or
electronics yesterday, but not both? Show work.
(b) Let C = {customers shopping for clothes} and E = {customers shopping for electronics}.
Determine the number of customers belonging to each of the regions I, II, III, IV.
Region I: ________ Region II: __________ Region III: _________ Region IV: __________
______________________________________________________________________________
U
C E
II
IV
I III

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Solution: MATH 106 FINAL EXAMINATION 2015 SOLUTION