# Permutations and Combinations Questions and Answers

Algebra

Permutations and CombinationsConsider the following relation.
-4x8y = 4
Step 2 of 2: Determine if the relation is a function. If it is not, identify two ordered pairs as proof.

Algebra

Permutations and CombinationsHow many ounces of water must be added to 145 oz. of 55% sodium bicarbonate solution to produce a 30% solution? Round your answer to the nearest hundredth. OZ.

Algebra

Permutations and CombinationsWhen the number 1 is written as an exponential expression with a base of 4, what is the exponent?

Algebra

Permutations and CombinationsFind all zeros of the function.
f(x) = x^4 − 9x³ + 13x² + 45x − 50
Entry tip: Enter the zeros separated by commas.

Algebra

Permutations and CombinationsFor the given functions f and g, find the indicated composition.
f(x) =2/ (x+7) g(x)=7/6x
(fog)(x)

Algebra

Permutations and CombinationsGiven functions f and g, perform the indicated operations.
f(x) = 6x² - 7x, g(x) = x² - 2x - 35
Find f/g
(6-x)/35
(6x²-7x)/(x^2-2x-35)
(6x-7)/-2
6x/x+1

Algebra

Permutations and CombinationsSolve the equation 3x^3-28x^2+69x - 20 = 0 given that 4 is a zero of f(x) = 3x³-28x²+69x-20.

Algebra

Permutations and CombinationsFind the inverse of the one-to-one function.
f(x) = 3x-7/5
f⁻¹(x) =5/3x + 7
f⁻¹(x) =5x+7/3
f⁻¹(x) =5/3x-7
f⁻¹(x) =5x-7/3

Algebra

Permutations and CombinationsSimplify the inequality. Graph it, write it in interval notation, and then inequality notation. Write your answer in interval notation.
2x+2 ≤12 or 2x - 2≥0

Algebra

Permutations and CombinationsAre the following statements true or false?
1. If the set of vectors U spans a subspace S, then vectors can be added to U to create a basis for S
2. If the set of vectors U spans a subspace S, then vectors can be removed from U to create a basis for
3. If S₁ and S₂ are subspaces of R" of the same dimension, then S₁ = S₂.
4. If the set of vectors U is linearly independent in a subspace S then vectors can be added to U to create a basis for S
5. If the set of vectors U is linearly independent in a subspace S then vectors can be removed from U to create a basis for S.

Algebra

Permutations and CombinationsTo simplify the measurement of the acidity or basicity of a solution, the pH (hydrogen potential) measure was developed. The pH is given by the formula pH = -log [H+], where [H] is the concentration of hydrogen ions in moles per liter in the solution. Find the pH value of a solution for which [H*] =0.0000346.

Algebra

Permutations and CombinationsIt is found that the time (in minutes) required by a predator to find a prey is a random variable that is exponentially distributed with μ-20
A According to this distribution, what is the longest time within which the predator will be 90% certain of finding a prey?
B. What is the probability that the predator will have to spend more than 1 hour looking for a prey?

Algebra

Permutations and CombinationsUsing the equation, derive each of the values below. Make
sure you put an answer for each.
y = cos x
h=
b=
period =
a=
k=

Algebra

Permutations and CombinationsA commutative ring with unity element and without zero divisor is called a/an
a. field.
b. subfield.
c. subring.
d. integral domain.

Algebra

Permutations and CombinationsNightclub Management
You have just
opened a new nightclub, Russ' Techno
Pitstop, but are unsure of how high to set the
cover charge (entrance fee). One week you
charged $8 per guest and averaged 240
guests per night. The next week you charged
$10 per guest and averaged 200 guests per
night.
(a)
Find a linear demand equation showing the
number of guests q per night as a function of
the cover charge p.
q(p) =
(b)
Find the nightly revenue R as a function of the
cover charge p.
R(p) =
(c)
The club will provide two free non-alcoholic
drinks for each guest, costing the club $2 per
head. In addition, the nightly overheads (rent,
salaries, dancers, DJ, etc.) amount to $1,000.
Find the cost C as a function of the cover
charge p.
C(p) =
(d)
Now find the profit in terms of the cover
charge p.
P(p) =
Determine the entrance fee you should
charge for a maximum profit (in dollars).
p= $ per guest

Algebra

Permutations and CombinationsFind the general solution of the following equation. Express the solution explicitly as a function of the independent variable.
t^-4 y(t)=7

Algebra

Permutations and Combinations(a) Find the slope of the line through (-8, -3) and (-12, -19).
(b) Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
(a) Select the correct choice below and, if necessary, fill in the answer box to complete
your choice.
(Type an integer or a simplified fraction.)
A. The slope is
B. The slope is undefined.
(b) Choose the correct answer below.
A. The line is vertical.
B. The line through the points falls from left to right.
C. The line is horizontal.
D. The line through the points rises from left to right.

Algebra

Permutations and CombinationsA standard 52-card deck has four 13-card suits: diamonds, hearts, clubs, and spades. The diamonds and hearts are red, and the clubs and spades are black. Each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king, and an ace. An experiment consists of drawing 1 card from the standard deck. Find the probability of drawing a black five of hearts.

Algebra

Permutations and CombinationsHow many four letter passwords are possible if the first letter must be A or U, the second letter must be a vowel and repetition is not allowed?
4416
5520
- 4800
5200
6624

Algebra

Permutations and CombinationsThe notation X~ N(μ, o) is read as follows: X (represents a population distribution) has a normal distribution (represented by M) with mean μ and standard deviation o. This notation is a shorthand way to represent a distribution.
Sampling Distribution and Probability
Q1. If XN(42, 10) and X (represents sampling distribution of the mean) is computed from a random sample of size n 81, what is the distribution of X? In other words, what is X-N(?, ?)?

Algebra

Permutations and CombinationsOn your morning run you pass through a park where the paths are laid in hexagons. You always run left to right. How many possible routes are there through the park.
(A) 8
(B) 12
(C) 16
(D)20

Algebra

Permutations and CombinationsProve that if a subgroup N in G is normal then N is a disjoint union of conjugacy classes in G. Use this to find all normal subgroups in S4.

Algebra

Permutations and CombinationsFind all possible combinations of 20 coins of 5, 10 and 25 cents that add up to exactly 3 dollars.

Algebra

Permutations and CombinationsSuppose that $13,095 is invested at an interest rate of 5.2% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
a) The exponential growth function is P(t) =

Algebra

Permutations and CombinationsBilly and Jane are trying to determine how far they can travel in 8 hours if they travel at a rate of 86 km/h. Billy determines they could travel 688 km, while Jane determines they could travel 10.75 km. Who is correct? Use dimensional (unit) analysis to justify your answer.

Algebra

Permutations and CombinationsA rectangular swimming pool is 6 ft deep. One side of the pool is 2.5 times longer than the other. The amount of water needed to fill the swimming pool is 2160 cubic feet. Find the dimensions of the pool.

Algebra

Permutations and CombinationsThere are 7 women and 5 men in a department. A committee of five people is to be selected. How many different ways can the committee be selected if there must be 3 women and 2 men ?
A. 450
B. 4200
C. 4400
D. 210
E. 350

Algebra

Permutations and CombinationsSuppose a local symphony decides to raise money by raffling off a microwave oven worth $300, a dinner worth $100, and a book worth $20. A total of 1000 tickets are sold at $1 each. Find the expected value of winning for a person who buys 1 ticket.
A. -$0.58
B. -$0.38
C. $0.64
D. $0.83
E. $1.15

Algebra

Permutations and CombinationsMaximize the objective function 3x + 4y subject to the constraints.
x + 2y ≤ 20
3x + 2y ≥ 24
x≤6
x ≥ 0, y ≥ 0

Algebra

Permutations and CombinationsFind the equation of the line through the points (-5,7) and (1,-5)

Algebra

Permutations and CombinationsSolve the following system of equations using the method of elimination. Eliminate the variable x by multiplying both equations by numbers that will eliminate that variable when you add the equations together. What would you multiple each equation by to eliminate x? Finally, provide the solution to the system as a coordinate or indicate that there is No Solution or an Infinite number of solutions.
-7x+3y=-27
3x + 4y = 38
To eliminate x, multiply equation 1 by:
To eliminate x, multiply equation 2 by:

Algebra

Permutations and CombinationsFind the probability of obtaining exactly one tall when flipping ten coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth

Algebra

Permutations and CombinationsLet P represent the number of fish in a lake. Suppose this naturally changes over time t, abeying
dP/dz = P(1-P, 10-¹).
A. Find and classify the critical points (A.K.A equilibrium solutions to this.
B. Suppose some nearby people start eating the fish. They eat as much as they can, but the methods of 6shing will only successfully capture 3/4 of the fish at any given time. Create a new differential equation for
that models this new situation.
C. Suppose P(0) 500 in your answer to (8) What is lim P(t)

Algebra

Permutations and CombinationsMaricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks, bonds, and CDs. CDs pay 5.75 % interest, bonds pay 5.8 % interest, and stocks pay 9.9 % interest. Maricopa Success invests $ 35000 more in bonds than in CDs. If the annual income from the investments is $ 7475, how much was invested in each account?

Algebra

Permutations and Combinations6.1²66.7t + 3000
t² +573
=
The function p(t) = 6.1t²-66.7t+3000/t²+573 models the pH level p(t) of a mouth t minutes after eating food containing sugar.
a) Find, to the nearest tenth, the pH of a mouth 30 minutes after eating a food containing sugar.
b) Find the equation of the horizontal asymptote.
c) What happens to the pH level of a mouth as the time since eating the sugary food increases?
The mouth returns to its normal pH of 6.1.
The mouth returns to its normal pH of 5.24.
The sugar keeps the pH of the mouth at abnormal levels until the end of time.
The pH of the mouth approaches 0.

Algebra

Permutations and CombinationsSolve the system using any method. Write your answer as an ordered pair.
(2x + 3y = 6
(3x + 5y = 8

Algebra

Permutations and CombinationsJennifer took a survey about the pets the students in her class have. Of the 27 students, 14 had cats, 12 had dogs, and 4 had both a cat and a dog. How many students did not have a dog or a cat?

Algebra

Permutations and CombinationsThree coworkers work for the same employer. Their jobs are warehouse manager, office manager, and truck driver. The sum of the annual salaries of the warehouse manager and office manager is $61000. The sum of the annual salary of the office manager and the truck driver is $62000. The annual salaries of the warehouse manager and the truck driver total $59000. What is the annual salary of each of the co-workers?

Algebra

Permutations and CombinationsSuppose there are 4 trains connecting town X to town Y and 6 roads connecting town Y to town Z. In how many ways can a person travel from X to Z via Y?

Algebra

Permutations and CombinationsGiven cos 30 = √3/2 use the trigonometric identities to find the exact value of each of the following.
(a) sin 60°
(b) sin² 230°
(c) sec π/6
(d) csc π/6

Algebra

Permutations and CombinationsAn arch is in the shape of a parabola with its vertex at the top. It has a span of 100 feet and a maximum height of 40 feet. Find the equation of the parabola, and determine the height of the arch 10 feet from the center of the base of the arch.

Algebra

Permutations and CombinationsRead the problem in the box below. Make a list to help you find the correct answer.
Ana wants to paint her dog's doghouse. She has 4 colors: Green, Maroon, Blue and Wheat. One color will cover the walls and another color will be used for the trim. (For example, green walls with wheat trim GW). Which one of these answers shows all of the possible color combinations?

Algebra

Permutations and CombinationsVerne has 6 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more ways can Verne line up his books than Jenny?
Select one:
a. 696
b. 720
c. 14
d. 24

Algebra

Permutations and CombinationsTo modify who pays for what in paragraph 12, the parties may define their agreement in the
A) Modifying Addendum.
B) Modification language.
C) Special Provisions Addendum.
D) Special Provisions paragraph.

Algebra

Permutations and CombinationsWhich of the following is NOT addressed by a TREC-promulgated form?
A) A lease with an option to purchase
B) A purchase using seller financing
C) Assumption of an FHA-insured loan
D) The purchase of a fee-simple town house

Algebra

Permutations and CombinationsAll of the following are listed as a farm and ranch improvement in Paragraph 2 the TREC Farm and Ranch Contract EXCEPT
A) pens.
B) irrigation equipment.
C) fences.
D) barns.

Algebra

Permutations and CombinationsIn a Texas nonjudicial foreclosure, the property must be posted with a notice of sale at LEAST how many days before the auction?
A) 21
B) 30
C) 20
D) 10

Algebra

Permutations and CombinationsA buyer is purchasing a property with a loan from a mortgage broker, who is charging an origination fee of 1%. If the loan requires a 90% LTV and the purchase price is
$200,000, how much is the origination fee?
A) $3,500
B) $9,000
C) $1,800
D) $2,000

Algebra

Permutations and CombinationsThe discount rate is the rate
A) mortgage brokers will pay to the secondary market.
B) charged to member banks borrowing from the Federal Reserve Bank.
C) mortgage bankers will pay to the secondary market.
D) at which borrowers will be charged one point.