Math-106-final

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MATH 106 Finite Mathematics Fall, 2013, 1.1

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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 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

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3. Find the values of
x and y that maximize the objective function 7
x + 5

y 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

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5. Determine which shaded region corresponds to the solution region of the system of linear

inequalities

2x + y ³ 4

x + y ³ 3

x ³ 0

y ³ 0

5. _______

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

MATH 106 Finite Mathematics Fall, 2013, 1.1

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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 inequality that must be satisfied

is: 6. _______

A. 2.80
x + 4

y £ 1,000

B. 7
x + 2
1

y ³ 1,000

C. 2

x + 9

y ³ 1,000

D. 2

x + 5y £ 1,000

7. State the objective function. 7. _______

A. 7
x + 21y

B. 2.80
x + 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 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.154B.114C.117D.1511MATH 106 Finite Mathematics Fall, 2013, 1.1

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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 = 5
t − 2 and x2 = t, for any real

number t.

D. There is no solution.

10. Which of the following statements is
NOT true? 10. ______

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.

D. If events
E and F are mutually exclusive events, then P(
E Ç F) = 0.

MATH 106 Finite Mathematics Fall, 2013, 1.1

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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 Ç 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: ______________

(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

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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.)

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 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

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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.

(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 = 2.5

x + 54.2

B. y = 0.10

x + 54.2

C. y = 0.10x − 144.3

D. y = 2.5x − 4908.3

(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

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21. The feasible region shown below is bounded by lines 4
x − y = 6,
x + y = 3, and
y = 0.

Find the coordinates of corner point
A. Show work.

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

T P

IIIV

I III

MATH 106 Finite Mathematics Fall, 2013, 1.1

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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.

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.