### System of Equation – Mathematics Final Exam

These chapters discuss matrix, probability and system of equation – Mathematics Final Exam is based on these chapters.

Give the equation of the vertical asymptote(s) of the rational function.

g(x) =

**x = 0, x = 3, x = 5 – correct**

x = -3, x = -5

2x = 1, x = -3, x = -5

x = 3, x = 5

A survey of 300 families showed that

115 had a dog;

88 had a cat;

40 had a dog and a cat;

112 had neither a cat nor a dog, and in addition did not have a parakeet;

10 had a cat, a dog, and a parakeet.

How many had a dog only?

35

**25 – correct**

30

40

State the linear programming problem in mathematical terms, identifying the objective function and the constraints.

A firm makes products A and B. Product A takes 2 hours each on machine L and machine M; product B takes 4 hours on L and 2 hours on M. Machine L can be used for 8 hours and M for 6 hours. Profit on product A is $9 and $10 on B. Maximize profit.

Maximize9A + 10B

Subject to: 2A + 2B ≥ 8

2A + 4B ≥ 6

A, B ≤ 0.

**Maximize9A + 10B**

Subject to: 2A + 4B ≤ 8 – correct

2A + 2B ≤ 6

A, B ≥ 0.

Subject to: 2A + 4B ≤ 8 – correct

2A + 2B ≤ 6

A, B ≥ 0.

Maximize9A + 10B

Subject to: 2A + 2B ≤ 8

2A + 4B ≤ 6

A, B ≥ 0.

Maximize10A + 9B

Subject to: 2A + 2B ≤ 8

2A + 4B ≤ 6

A, B ≥ 0.

Find the inverse, if it exists, of the given matrix.

A =

If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a double.

1/5

1/3

**1/6 – correct**

1/4

One card is selected from a deck of cards. Find the probability of selecting a black card or a king.

1/26

27/52

**7/13 – correct**

15/26

Write as a single logarithm. log 5 + log 40 – log 8

- log 15

2. log 64

3. **log 25 – correct**

4. log 39

A bakery makes sweet rolls and donuts. A batch of sweet rolls requires of flour, eggs, and of sugar. A batch of donuts requires of flour, eggs, and of sugar. Set up an initial simplex tableau to maximize profit

The bakery has 660 lb of flour, 780 dozen eggs, of sugar. The profit on a batch of sweet rolls is %76 and on a batch of donuts is $66.00.

Solve the system of equations.

1. x – y + z = 0

2. x + y + z = -8

3. x + y – z = -10

(-5, 1, -4)

**(-5, -4, 1) – correct**

No solution

(1, -5, -4)

Solve the system.

1/3x + 1/3 y = 1

x – y = -13

(-6, 9)

(5, 9)

**(-5, 8) – correct**

No solution

Find an equation of the the line through (8, 2), and perpendicular to 4x – 5y = 52.

-5x + 4y = 52

-5x + 4y = -48

4x + 5y = -48

**-5x – 4y = -48 – correct**

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a given week. Use the table to find the system of inequalities that describes the manufacturer’s weekly production.

Use x for the number of chairs and y for the number of tables made per week. The number of work-hours available for construction and finishing is fixed.

2x + 3y ≥ 36

2x + 2y ≥ 28

x ≥ 0

y ≥ 0

2x + 3y ≥ 28

2x + 2y ≥ 36

x ≥ 0

y ≥ 0

2x + 3y ≤ 28

2x + 2y ≤ 36

x ≥ 0

y ≥ 0

**2x + 3y ≤ 36**

2x + 2y ≤ 28 – correct

x ≥ 0

y ≥ 0

2x + 2y ≤ 28 – correct

x ≥ 0

y ≥ 0

If Bob deposits $5000 at the end of each year for 2 years in an account paying 5% interest compounded annually, find the amount he will have on deposit.

$15,762.50

$5250.00

**$10,250.00 – correct**

$5000.00

Use the indicated entry as the pivot and perform the pivoting once.

Find the probability of the given event. A card drawn from a well-shuffled deck of 52 cards is an ace or a 9.

13/2

5/13

10

**2/13 – correct**

Allan borrowed $4700 from his father to buy a car. He repaid him after 11 months with interest of 11%. Find the total amount he repaid.

$5173.92

$5130.83

$5217.00

$473.92

A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls?

4410 ways

5170 ways

**4620 ways – correct**

5665 ways

Write the expression ln √fz / z^{10} as a sum and/or a difference of logarithms with all variables to the first degree.

1/2ln fz – 10 ln z

ln f – 10 ln z

** 1/2ln f – 19/2ln z – correct**

ln f – 19/2ln z

Write the basic solution for the simplex tableau determined by setting the nonbasic variables equal to 0.

- x
_{1}= 0, x_{2}= 0, x_{3}= 0, x_{4}= 0, x_{5}= 4, z = 1

2. x_{1} = 0, x_{2} = 0, x_{3} = 3, x_{4} = 6, x_{5} = 0, z = 1

3. x_{1} = 3, x_{2} = 6, x_{3} = 3, x_{4} = 6, x_{5} = 0, z = 3

4. x_{1} = 3, x_{2} = 0, x_{3} = 0, x_{4} = 6, x_{5} = 0, z = 3

Find the number of subsets of the set. {math, English, history, science, art}

**32** **– correct**

28

24

16

There are 6 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

**120** **– correct**

216

720

20

The number of bacteria growing in an incubation culture increases with time according to B(x) = 1800(2)^{x} , where x is time in days. Find the number of bacteria when x = 0 and x = 5

1800, 7200

3600, 57,600

**1800, 57,600** **– correct**

1800, 18,000

Find the probability of the event.

The probability that a radish seed will germinate is .7. The gardener plants 20 seeds and she harvests 16 radishes.

.068

.075

**.130** **– correct**

.571

John owns a hotdog stand. He has found that his profit is represented by the equation , with P being profits and x the number of hotdogs. How many hotdogs must he sell to earn the most profit?

23 hotdogs

29 hotdogs

**28 hotdogs – correct**

46 hotdogs

$4774 is deposited into a savings account at 8% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $1,000,000?

94 years

47 years

**67 years – correct**

61 years