System of Equation – Mathematics Exam(Final)

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) = 

vertical asymptote(s) of the rational function - System of Equation

x = 0, x = 3, x = 5 – correct

x = -3, x = -5

x = 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.

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 = 

Matrix - Inverse
System of Equation - Mathematics Exam Final
Inverse Matrix
System of Equation - Mathematics Exam Final
Inverse Matrix
System of Equation - Mathematics Exam Final
Inverse Matrix
System of Equation - Mathematics Exam Final
Correct
Inverse Matrix
System of Equation - Mathematics Exam Final

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

log 64

log 25 – correct

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.

Simplex Tableau
System of Equation - Mathematics Exam Final
Simplex Tableau
System of Equation - Mathematics Exam Final
Simplex Tableau
System of Equation - Mathematics Exam Final
Simplex Tableau
System of Equation - Mathematics Exam Final
Simplex Tableau
System of Equation - Mathematics Exam Final
Correct

Solve the system of equations.
x – y + z = 0
x + y + z = -8
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


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.

System of Equation - Mathematics Exam Final
Pivot
System of Equation - Mathematics Exam Final
Correct
System of Equation - Mathematics Exam Final
System of Equation - Mathematics Exam Final
System of Equation - Mathematics Exam Final

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 / z10 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.

Simplex Tableau
System of Equation - Mathematics Exam Final

x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 4, z = 1

x1 = 0, x2 = 0, x3 = 3, x4 = 6, x5 = 0, z = 1

x1 = 3, x2 = 6, x3 = 3, x4 = 6, x5 = 0, z = 3

x1 = 3, x2 = 0, x3 = 0, x4 = 6, x5 = 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


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