help with quiz 4

I would need you to show the work

MATH106 QUIZ 5 NAME: _____ _________________

Professor: Dr. Katiraie

INSTRUCTIONS

The quiz is worth 100 points. There are 10 problems (each worth 10 points).
This quiz is open book and open notes, unlimited time. This means that you may

refer to your textbook, notes, and online classroom materials, but you may not
consult anyone. You may take as much time as you wish, provided you turn in your
quiz no later than the due date posted in our course schedule of the syllabus.

You must show your work to receive full credit. If you do not show your work,

you may earn only partial or no credit at the discretion of the professor. Please
type your work in your copy of the quiz, or if you prefer, create a document containing
your work. Scanned work is acceptable also. Be sure to include your name in the
document.

Consult the Additional Information portion of the online Syllabus for options regarding
the submission of your quiz. If you have any questions, please contact me by e-mail
(farajollah.katiraie@faculty.umuc.edu ).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement
or answers the question.

1) Suppose P(C) = .05, P(M ∩ C) = .02, and P(M ∪ C) = .6.

Find the probability P(M ∩ C’) 1) _______

A) 0.956

B) 0.476

C) 0.55

D) 0.952

E) none of the above

2) Suppose P(C) = .048, P(M ∩ C) = .044, and P(M ∪ C) = .524.

Find the indicated probability P[(M ∩ C)’] 2) _______
A) 0.564

B) 0.568

C) 0.476

D) 0.956

E) None of the above

mailto:farajollah.katiraie@faculty.umuc.edu

Use a Venn diagram to find the desired probability.

3) A survey revealed that 35% of people are entertained by reading books, 28% by watching

TV, and 10% are entertained by both books and TV. What is the probability that a person will

be entertained through neither a book nor TV?
3) _________

A) 70%

B) 54%

C) 47%

D) 86%

E) None of the above

4) Of the coffee makers sold in an appliance store, 5% have either a faulty switch or a
defective cord, 1.9% have a faulty switch, and 1% have both defects. What is the probability

that a coffee maker will have a defective cord? 4) _________

A) 1%

B) 3.8%

C) 4%

D) 4.1%

E) None of the above

5) A survey of senior citizens at a doctor’s office shows that 60% of the seniors take blood

pressure lowering medication and 25% take cholesterol lowering medication. 15% take both

medications. What is the probability that a senior citizen takes either blood pressure or

cholesterol lowering medication? 5) _______

A) 70%

B) 89%

C) 61%

D) 75%

E) None of the above

Use the given table to find the probability of the indicated event.

Round your answer to the nearest thousandth.

6) College students were given three choices of pizza toppings and asked to choose one favorite.

The following table shows the results.

Toppings Freshman Sophomore Junior Senior Total

Cheese 15 12 16 27 70

Meat 25 26 16 12 79

Veggie 10 12 25 27 74

Total 50 50 57 66 223

Find the probability that a randomly selected student prefers a Veggie

topping. (Round your answer to three decimal places) 6) _______

A) 0.309

B) 0.332

C) 0.391

D) 0.345

E) None of the above

Solve the following problem.

7) A pair of standard fair dice is rolled, and the sum of the numbers showing on the upper faces

is noted. What is the probability that a sum greater than 9 is rolled?

Hint: Please see section 8.2, example 2 7) _______

A) 1/9

B) 0

C) 1/2

D) 1/6

E) None of the above

Solve the following problems.

8) If two cards are drawn without replacement from a deck, find the probability that the second

card is a spade, given that the first card was not a spade.

Hint: Please see section 8.3, example 4 8) _______

A) 11/12

B) 11/51

C) 4/17

D) 13/51

E) None of the above

9) If two fair dice are rolled, find the probability of a sum of 10 given that the roll is a “double”.

9) _______

A) 1/6

B) 1/5

C) 1/4

D) 1/3

E) None of the above

10) Two marbles are drawn without replacement from a box with 5 white, 2 green, 2 red, and 1

blue marble, Find the probability that both marbles are white.

Hint: Please see section 8.3, example 4 10) ______

A) 3/32

B) 3/28

C) 2/9

D) 9/56

E) None of the above

MATH106 QUIZ 4 NAME: _____ _________________

Professor: Dr. Katiraie

INSTRUCTIONS

The quiz is worth 100 points. There are 10 problems (each worth 10 points).

This quiz is open book and open notes, unlimited time. This means that you may

refer to your textbook, notes, and online classroom materials, but you may not

consult anyone. You may take as much time as you wish, provided you turn in your

quiz no later than the due date posted in our course schedule of the syllabus.

You must show your work to receive full credit. If you do not show your work,

you may earn only partial or no credit at the discretion of the professor. Please

type your work in your copy of the quiz, or if you prefer, create a document containing

your work. Scanned work is acceptable also. Be sure to include your name in the

document.

Consult the Additional Information portion of the online Syllabus for options regarding

the submission of your quiz. If you have any questions, please contact me by e-mail
(farajollah.katiraie@faculty.umuc.edu ).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement

or answers the question.

1) Find the maximum value of the function, if it exists, on the given feasible region.

Find the maximum of z = 22x + 2y 1) _______

A) 154

B) 120

C) 162

D) 142

E) none of the above

mailto:farajollah.katiraie@faculty.umuc.edu

2) Find the minimum value of the function, if it exists, on the given feasible region.

Find the minimum of z = 9x – 2y 2) _______

A) 11

B) 7

C) 55

D) 32

E) None of the above

3) Use graphical methods to solve the linear programming problem.
3) _________

Maximize z = 10x + 2y

Subject to: 2x + 3y ≤ 12
2x + y ≤ 8
x ≥ 0
y ≥ 0

A) Maximum of 49 when x = 3 and y = 2

B) Maximum of 32 when x = 2 and y = 3

C) Maximum of 40 when x = 4 and y = 0

D) Maximum of 52 when x = 4 and y = 4

E) None of the above

4) A college student can spend no more than 8 hours a week tutoring. She charges $15

an hour to tutor finite math and $12 to tutor algebra. She limits herself to no more than

3 hours per week to tutor algebra and spends at least 1 hour a week tutoring each

subject. How many hours per week should she spend tutoring each subject to maximize

her income? What is her maximum weekly income?

4) _________

Hint: Let x = number of hours per week to tutor finite math and

y = number of hours per week to tutor algebra

Then use graphical methods to solve the following linear programming problem:

Maximize z = 15x + 12y
Subject to: x + y ≤ 8
y ≤ 3
x ≥ 1
y ≥ 1

A) 4 hours of finite math and 4 hours of algebra; maximum income is $108 per week

B) 7 hours of finite math and 1 hour of algebra; maximum income is $117 per week

C) 5 hours of finite math and 3 hours of algebra; maximum income is $111 per week

D) 9 hours of finite math and 5 hours of algebra; maximum income is $195 per week

E) None of the above

5) Let U = {q, r, s, t, u, v, w, x, y, z}, A = {q, s, u, w, y}, B = {q, s, y, z}, and

C = {v, w, x, y, z}.

Find the elements in the set A ∩ C’ 5) _______

A) {t, v, x}

B) {u, w}

C) {r, s, t, u, v, w, x, z}

D) {q, s, u}

E) None of the above

6) Use the counting formula to solve the following problem.

If n(B) = 24, n(A ∩ B) = 5, and n(A ∪ B) = 28, find n(A). 6) _______

A) 12

B) 14

C) 9

D) 10

E) None of the above

7) If n(A) = 35, n(B) = 90 and n(A ∪ B) = 110, what is n(A ∩ B)? 7) _______

A) 15

B) 18

C) 28

D) 16

E) None of the above

Solve the following problems.

8) At East Zone University (EZU), 980 students are taking College Algebra or Philosophy. 550

are taking Philosophy, 500 are taking College Algebra, and 70 are taking both College Algebra

and Philosophy. How many are taking College Algebra but not Philosophy?

8) _______

A) 824

B) 430

C) 377

D) 447

E) None of the above

9) A restaurant offered salads with 8 types of dressings and 6 different toppings. How many

different types of salads could be offered? 9) _______

A) 32 types

B) 16 types

C) 12 types

D) 48 types

E) None of the above

10) How many ways can a committee of 4 be selected from a club with 13 members?

10) ______

A) 30,240

B) 17,160

C) 715

D) 100,000

E) None of the above