MATH 106 Finite Mathematics Fall, 2013, 1.1 Page 1 of 10 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. 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. Rita purchases a car for $32,000, makes a down payment of 5%, and finances the rest with a 6-year car loan at an annual interest rate of 4.2% compounded monthly. What is the amount of her monthly loan payment? 1. _______ A. $556.44 B. $528.62 C. $503.57 D. $478.39 2. Find the result of performing the row operation (2)R1 + R2 → R2 2. _______ � 4 1 2 3 � −3 6 � A. � 4 1 10 3 � −3 6 � B. � 4 1 10 5 � −3 0 � C. � 8 12 2 3 � −6 6 � D. � 4 1 8 7 � −3 9 � MATH 106 Finite Mathematics Fall, 2013, 1.1 Page 2 of 10 3. Find the values of x and y that maximize the objective function 7x + 5y for the feasible region shown below. 3. _______ A. (x, y) = (5, 15) B. (x, y) = (8, 10) C. (x, y) = (0, 20) D. (x, y) = (10, 0) 4. Kindergarten children have normally distributed heights with a mean of 39 inches and a standard deviation of 2 inches. What is the probability that a randomly chosen kindergarten child will have a height between 37 and 41 inches? 4. ______ A. 0.5000 B. 0.6826 C. 0.7580 D. 0.9544 MATH 106 Finite Mathematics Fall, 2013, 1.1 Page 3 of 10 5. Determine which shaded region corresponds to the solution region of the system of linear inequalities 2x + y ≥ 4 x + y ≥ 3 x ≥ 0 y ≥ 0 5. _______ GRAPH A. GRAPH B. GRAPH C. GRAPH D. MATH 106 Finite Mathematics Fall, 2013, 1.1 Page 4 of 10 For #6 and #7: A merchant makes two raisin nut mixtures. Each box of mixture A contains 2 ounces of raisins and 9 ounces of peanuts, and sells for $2.80. Each box of mixture B contains 5 ounces of raisins and 12 ounces of peanuts, and sells for $4.00. The company has available 1,000 ounces of raisins and 3,500 ounces of peanuts. The merchant will try to sell the amount of each mixture that maximizes income. Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B. 6 ...

1. MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 1 of 10
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.
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. Rita purchases a car for $32,000, makes a down payment of
5%, and finances the rest with a
6-year car loan at an annual interest rate of 4.2% compounded
monthly. What is the amount of

2. her monthly loan payment?
1. _______
A. $556.44
B. $528.62
C. $503.57
D. $478.39
2. Find the result of performing the row operation (2)R1 + R2
→ R2 2. _______
� 4 1 2 3 �
−3
6
�
A. � 4 1 10 3 �
−3
6
� B. � 4 1 10 5 �
−3
0
�

3. C. � 8 12 2 3 �
−6
6
� D. � 4 1 8 7 �
−3
9
�
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 2 of 10
3. Find the values of x and y that maximize the objective
function 7x + 5y for the feasible
region shown below. 3. _______
A. (x, y) = (5, 15)
B. (x, y) = (8, 10)
C. (x, y) = (0, 20)
D. (x, y) = (10, 0)

4. 4. Kindergarten children have normally distributed heights with
a mean of 39 inches and a
standard deviation of 2 inches. What is the probability that a
randomly chosen kindergarten child
will have a height between 37 and 41 inches?
4. ______
A. 0.5000
B. 0.6826
C. 0.7580
D. 0.9544
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 3 of 10
5. Determine which shaded region corresponds to the solution
region of the system of linear
inequalities
2x + y ≥ 4

5. x + y ≥ 3
x ≥ 0
y ≥ 0
5. _______
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 4 of 10
For #6 and #7:
A merchant makes two raisin nut mixtures.
Each box of mixture A contains 2 ounces of raisins and 9
ounces of peanuts, and sells for $2.80.
Each box of mixture B contains 5 ounces of raisins and 12
ounces of peanuts, and sells for $4.00.
The company has available 1,000 ounces of raisins and 3,500
ounces of peanuts. The merchant
will try to sell the amount of each mixture that maximizes
income.
Let x be the number of boxes of mixture A and let y be the
number of boxes of mixture B.
6. Since the merchant has 1,000 ounces of raisins available, one

6. inequality that must be satisfied
is: 6. _______
A. 2.80x + 4y ≤ 1,000
B. 7x + 21y ≥ 1,000
C. 2x + 9y ≥ 1,000
D. 2x + 5y ≤ 1,000
7. State the objective function.
7. _______
A. 7x + 21y
B. 2.80x + 4y
C. 2x + 5y
D. 2x + 9y
8. A jar contains 12 red jelly beans, 8 yellow jelly beans, and 10
orange jelly beans.
Suppose that each jelly bean has an equal chance of being

7. picked from the jar.
If a jelly bean is selected at random from the jar, what is the
probability that it is not yellow?
8. _______
A.
15
4
B.
11
4
C.
11
7
D.
15
11
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 5 of 10

8. 9. When solving a system of linear equations with the unknowns
x1 and x2
the following reduced augmented matrix was obtained. 9.
_______
� 1 −5 0 0 �
−2
0
�
What can be concluded about the solution of the system?
A. The unique solution to the system is x1 = −5 and x2 = − 2.
B. There are infinitely many solutions. The solution is x1 = −
5t − 2 and x2 = t, for any real
number t.
C. There are infinitely many solutions. The solution is x1 = 5t
− 2 and x2 = t, for any real
number t.
D. There is no solution.
10. Which of the following statements is NOT true? 10.

9. ______
A. The variance is a measure of the dispersion or spread of a
distribution about its mean.
B. If all of the data values in a data set are identical, then the
standard deviation is 0.
C. The variance is the square root of the standard deviation.
D. The variance must be a nonnegative number.
11. In a certain manufacturing process, the probability of a type
I defect is 0.06, the probability
of a type II defect is 0.07, and the probability of having both
types of defects is 0.02.
Find the probability that neither defect occurs. 11. ______
A. 0.85
B. 0.87
C. 0.89
D. 0.98
12. Which of the following is NOT true? 12. ______
A. If an event cannot possibly occur, then the probability
of the event is a negative number.
B. A probability must be less than or equal to 1.
C. If only two outcomes are possible for an experiment, then the
sum of the probabilities of
the outcomes is equal to 1.

10. D. If events E and F are mutually exclusive events, then P(E ∩
F) = 0.
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 6 of 10
SHORT ANSWER:
13. Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8}. Let A = {1,
2, 3, 8} and B = {1, 3, 5}.
Determine the set A ∩ B'. Answer: ______________
(Be sure to notice the complement symbol applied to B.)
14. Consider the following graph of a line.
(a) State the x-intercept. Answer: ______________
(b) State the y-intercept. Answer: ______________

11. (c) Determine the slope. Answer: ______________
(d) Find the slope-intercept form of the equation of the line.
Answer: ____________________
(e) Write the equation of the line in the form Ax + By = C
where A, B, and C are integers.
Answer: ____________________
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 7 of 10
15. A company compiled information about the gender and
working status of its 420 employees,
as shown below.
Full-time Part-time Totals
Male 210 40 250
Female 90 80 170
Totals 300 120 420
(Report your answers as fractions or as decimal values rounded
to the nearest hundredth.)

12. Find the probability that a randomly selected employee is:
(a) a male part-time employee. Answer: ______________
(b) a male employee or a part-time employee. Answer:
______________
(c) male, given that the employee is part-time. Answer:
______________
SHORT ANSWER, with work required to be shown, as
indicated.
16. For a five year period, Brad deposited $600 each quarter
into an account paying 3.6% annual
interest compounded quarterly. (Round your answers to the
nearest cent.)
(a) How much money was in the account at the end of 5
years? Show work.
(b) How much interest was earned during the 5 year period?
Show work.
Brad then made no more deposits or withdrawals, and the
money in the account continued to
earn 3.6% annual interest compounded quarterly, for 4 more

13. years.
(c) How much money was in the account after the 4 year
period? Show work.
(d) How much interest was earned during the 4 year period?
Show work.
17. Three flags are arranged vertically on a flagpole, with one
flag at the top, one flag in the
middle, and one flag at the bottom. To create the flagpole
arrangement, 13 flags are available,
each flag a different color. How many different flagpole
arrangements of 3 flags are possible?
Show work.
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 8 of 10
18. A recreational club has 15 members. 10 of the club members
are men and 5 are women.
(a) In how many ways can the club choose 6 members to form a
volleyball team? Show work.

14. (b) In how many ways can the club choose 6 members to form
the volleyball team, if 3 team
members must be men and 3 team members must be women?
Show work.
(c) If a 6-person volleyball team is selected at random from the
15 club members, what is the
probability the team consists of 3 men and 3 women? Show
work.
19. The average temperature in Metropolis in 1985 was 54.2
degrees. In 2010, the average
temperature in Metropolis was 56.7 degrees. Let y be the
average temperature in Metropolis in
year x, where x = 0 represents the year 1985.
(a) Which of the following linear equations could be used to
predict the average Metropolis
temperature y in a given year x, where x = 0 represents the
year 1985? Explain/show work.
A. y = 2.5x + 54.2
B. y = 0.10x + 54.2
C. y = 0.10x − 144.3
D. y = 2.5x − 4908.3

15. (b) Use the equation from part (a) to predict the average
temperature in Metropolis in the year
2030. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The
rate of change of temperature with
respect to time is ______________________ per
________________. (Include units of
measurement.)
20. Solve the system of equations using elimination by addition
or by augmented matrix methods
(your choice). Show work.
x + 2y = 3
5x + 4y = 21
MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 9 of 10
21. The feasible region shown below is bounded by lines 4x − y
= 6, x + y = 3, and y = 0.
Find the coordinates of corner point A. Show work.

16. 22. A survey of 120 gardeners found the following: 80
gardeners grow tomatoes. 30 gardeners
grow peppers. 92 gardeners grow tomatoes or peppers (or
both).
(a) How many of the surveyed gardeners grow both
tomatoes and peppers? Show work.
(b) Let T = {tomato growers} and P = {pepper growers}.
Determine the number of gardeners
belonging to each of the regions I, II, III, IV.
U
P T
II
IV
III I

17. MATH 106 Finite Mathematics Fall, 2013, 1.1
Page 10 of 10
23. Consider the sample data 50, 69, 43, 35, 20, 50, 48.
(a) State the mode.
(b) Find the median. Show work/explanation.
(c) State the mean.
(d) The sample standard deviation is 15.1. What percentage
of the data fall within one
standard deviation of the mean? Show work/explanation.
(d) _______
A. 57%
B. 68%
C. 71%
D. 75%
24. If the probability distribution for the random variable X is
given in the table, what is the
expected value of X? Show work.

18. xi – 20 10 30 40
pi 0.25 0.20 0.40 0.15
25. The probability that a U.S. adult has a cell phone is 0.83.
Five U.S. adults are randomly
selected. Find the probability that exactly 2 of the 5 adults has a
cell phone. Show work.
Show work.