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Finite Math Final Exam

Directions:
This is a 25 question test covering material from chapters 1-8. Each question is worth 4 points. You should be able to complete the test within 90 minutes. You may continue taking the test after the timer has reached 0, but take note that on the real final you would have to turn the test in as is. Once you submit the test it will automatically be graded for you and an instructional video explaining how each problem is done in detail will be provided. Hit the start button when you are ready. Good luck.

Date: May 25, 2013

90:00

Start Test

One hundred people were interviewed after attending a modern opera theatre performance at the Musical Arts Center. 45 said the middle was tedious, 60 said the ending was beautiful, and 25 said both that the middle was tedious and that the ending was beautiful. How many people neither said that the ending was beautiful, nor said that the middle was tedious?

A) 20

B) 10

C) 15

D) 30

E) none of the others

A box contains 2 red, 1 white and 5 blue balls. Balls are drawn without replacement, noting the color of each, until a blue ball is drawn. Determine the number of elements in the sample space for this experiment. [Hint: Draw a tree diagram]

A) 7

B) 9

C) 8

D) 10

E) none of the others

A student marketing survey generated the following data:

35% like cycling
45% like jogging
25% like bowling
15% like both cycling and jogging
10% like both cycling and bowling
8% like both jogging and bowling
3% like all three

Find the percentage of those surveyed who like exaclty one sport.

A) .54

B) .48

C) .66

D) .3

E) none of the others

Events E and F are independent in a sample space with Pr[E] = .2 and Pr[F] = .4. Find Pr[E U F].

A) .08

B) .6

C) .16

D) .52

E) none of the others

Let A and B be events in a sample space with Pr[A|B] = .4, and Pr[A int B] = .2. Find Pr[B].

A) .6

B) .2

C) .5

D) .08

E) none of the others

A dorm committee is made up of 2 first-year students and 6 second-year students. A subcommittee of 3 is to be chosen so that there is at least one first-year student and at least one second-year student on the subcommittee. Find the number of ways the subcommittee can be chosen.

A) 30

B) 20

C) 48

D) 36

E) none of the others

There are 6 different versions of a final exam. The last row of an auditorium has only 4 students in it. Find the number of ways in which the exam can be passed out in the last row so that each student receives a different version of the exam.

A) 360

B) 15

C) 256

D) 1296

E) none of the others

A carton contains 3 red, and 5 green apples. Two apples are drawn without replacement, and the color of each is noted. Determine the probability that at least one of the apples drawn is green.

A) 12/28

B) 25/28

C) 3/28

D) 15/28

E) none of the others

In a large fleet of cars, 60% are Fords, and the rest Chevys. 30% of the Fords are equipped with antilock brakes, while only 20% of the Chevys have them. If you insist on a car with antilock brakes, and are given one at random, what is the probability that it will be a Ford?

A) 5/13

B) 7/13

C) 3/13

D) 9/13

E) none of the others

10.

Suppose an experiment has a sample space of outcomes S = {O1,O2,O3,O4,O5} with associated weights (probabilities) w1 = .20, w2 = .10, w3 = .35, w4 = .25, and w5 = .10. If E = {O1,O2,O3}, find Pr[E’].

A) .5

B) .3

C) .35

D) .25

E) none of the others

11.

Each day Debbie has a 15% chance of finding a legal parking spot on campus. Find the probability that she will find a spot exactly 4 out of 5 days one work week.

A) C(5,4)(.15)^1(.85)^4

B) (.15)^4(.85)^1

C) C(5,4)(.15)^4(.85)^1

D) C(5,1)(.15)^4(.85)^1

E) none of the others

12.

For $5 you can have a chance to roll a pair of fair six-sided dice. If you roll a double, i.e. both dice show the same number of dots on top, then you receive back $30; otherwise you get nothing. What is your expected gain or loss on each play?

A) 10

B) 0

C) -5

D) 2

E) none of the others

13.

A typical M118 student will show up at the correct room for the final exam with probability .9. Suppose that 1200 students take the exam and that afterward, you select 30 at random. Find the expected number of students selected who will have gone to the correct room.

A) 1080

B) 120

C) 30

D) 27

E) none of the others

14.

Find an equation for the straight line which goes through (1, 3) and is parallel to the line 10x+3y = 2.

A) y = -(10/3)x+19/3

B) y = -(10/3)x+10/3

C) y = -(10/3)x-10/3

D) y = (10/3)x+19/3

E) none of the others

15.

Suppose that the cost of a truck rental is related to the number of hours the truck is rented by a linear equation. Also, suppose the cost of a 2-hour rental is $55 and the cost of a 3-hour rental is $65. Find the cost of a 6-hour rental.

A) 75

B) 95

C) 110

D) 130

E) none of the others

16.

Michael’s Uptight Cafe makes both low-fat and high-fiber oatmeal cookies. Each low-fat cookie requires 1 ounce of oatmeal and 1/2 ounce of butter, while each high-fiber cookie requires 2 ounces of oatmeal and 2 ounce of butter. Damion, the absent-minded manager, forgets to order cookie ingredients and the cafe has only 20 ounces of oatmeal and 10 ounces of butter. Having fond memories of M118, however, he is able to calculate how many of each type of cookie should be made in order to use all the ingredients. Determine how many low-fat cookies Damion decides to make.

A) 5

B) 10

C) 15

D) 20

E) none of the others

17.

Which of the following is true about this system of linear equations?

A) the system has no solution.

B) the system has exactly one solution.

C) the system has exactly two solutions.

D) the system has infinitely many solutions.

E) none of the others

18.

Which of the following is defined?

A) AB

B) AC

C) BC

D) CD

E) none of the others

19.

Refer to the matrices in number 18. If BD were defined, what size will the result matrix be?

A) 1x1

B) 2x3

C) 3x2

D) 3x3

E) none of the others

20.

Find the value of x for the solution to the system of equations:
x + 1y + 3z = 6
2y + 4z = 2
x + 3y + z = 2

A) 2

B) 3

C) 4

D) 5

E) none of the others

21.

Find the (1,2) entry of the inverse of A.

A) Option 1

B) Option 2

C) Option 3

D) Option 4

E) none of the others

22.

An economy has two goods: steel and grain. One needs .28 units of steel to produce 1 unit of steel, and .29 units of grain to produce 1 unit of grain. In addition, one needs .3 units of grain to make 1 unit of steel, and .4 units of steel to make one unit of grain. Let x1 be the number of units of steel produced and x2 be the number of units of grain produced. Find the technology matrix associated with the corresponding Leontief economic model.

A) Option 1

B) Option 2

C) Option 3

D) Option 4

E) none of the others

23.

Let the following be the techonology matrix, demand vector, and production schedule for a Leontief Economic Model. Find x1.

a as the techonology matrix, b as the demand vector, and c as the production schedule

A) -5

B) 5

C) 30/4

D) -30/4

E) none of the others

24.

Find the minimum of x + 2y on the feasible set shown below.

A) 4

B) 3

C) 1

D) 0

E) none of the others

25.

Consider the following transition matrix for a Markov chain. Find the probability of being in state 2 in the long run.

transition matrix P, r1c1 = 1/2, r1c2 = 1/3, r2c1 = 1/8, r2c2 = 7/8

A) 1/5

B) 4/5

C) 2/5

D) 1

E) none of the others

Finite Math Final Exam

A box contains 2 red, 1 white and 5 blue balls. Balls are drawn without replacement, noting the color of each, until a blue ball is drawn. Determine the number of elements in the sample space for this experiment. [Hint: Draw a tree diagram]

A student marketing survey generated the following data:

Events E and F are independent in a sample space with Pr[E] = .2 and Pr[F] = .4. Find Pr[E U F].

Let A and B be events in a sample space with Pr[A|B] = .4, and Pr[A int B] = .2. Find Pr[B].

A dorm committee is made up of 2 first-year students and 6 second-year students. A subcommittee of 3 is to be chosen so that there is at least one first-year student and at least one second-year student on the subcommittee. Find the number of ways the subcommittee can be chosen.

There are 6 different versions of a final exam. The last row of an auditorium has only 4 students in it. Find the number of ways in which the exam can be passed out in the last row so that each student receives a different version of the exam.

A carton contains 3 red, and 5 green apples. Two apples are drawn without replacement, and the color of each is noted. Determine the probability that at least one of the apples drawn is green.

In a large fleet of cars, 60% are Fords, and the rest Chevys. 30% of the Fords are equipped with antilock brakes, while only 20% of the Chevys have them. If you insist on a car with antilock brakes, and are given one at random, what is the probability that it will be a Ford?

Suppose an experiment has a sample space of outcomes S = {O1,O2,O3,O4,O5} with associated weights (probabilities) w1 = .20, w2 = .10, w3 = .35, w4 = .25, and w5 = .10. If E = {O1,O2,O3}, find Pr[E’].

Each day Debbie has a 15% chance of finding a legal parking spot on campus. Find the probability that she will find a spot exactly 4 out of 5 days one work week.

For $5 you can have a chance to roll a pair of fair six-sided dice. If you roll a double, i.e. both dice show the same number of dots on top, then you receive back $30; otherwise you get nothing. What is your expected gain or loss on each play?

A typical M118 student will show up at the correct room for the final exam with probability .9. Suppose that 1200 students take the exam and that afterward, you select 30 at random. Find the expected number of students selected who will have gone to the correct room.

Find an equation for the straight line which goes through (1, 3) and is parallel to the line 10x+3y = 2.

Suppose that the cost of a truck rental is related to the number of hours the truck is rented by a linear equation. Also, suppose the cost of a 2-hour rental is $55 and the cost of a 3-hour rental is $65. Find the cost of a 6-hour rental.

Which of the following is true about this system of linear equations?

Which of the following is defined?

Refer to the matrices in number 18. If BD were defined, what size will the result matrix be?

Find the value of x for the solution to the system of equations: x + 1y + 3z = 6 2y + 4z = 2 x + 3y + z = 2

Find the (1,2) entry of the inverse of A.

Let the following be the techonology matrix, demand vector, and production schedule for a Leontief Economic Model. Find x1.

Find the minimum of x + 2y on the feasible set shown below.

Consider the following transition matrix for a Markov chain. Find the probability of being in state 2 in the long run.

Find the value of x for the solution to the system of equations:
x + 1y + 3z = 6
2y + 4z = 2
x + 3y + z = 2