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.
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
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 / 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.
- x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 4, z = 1
2. x1 = 0, x2 = 0, x3 = 3, x4 = 6, x5 = 0, z = 1
3. x1 = 3, x2 = 6, x3 = 3, x4 = 6, x5 = 0, z = 3
4. 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