Permutations and Combinations Questions and Answers

A 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.

There 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

Suppose 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

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

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

Solve 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:

Find 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

Let 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)

Maricopa'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?

6.1²66.7t + 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.

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

Jennifer 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?

Three 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?

Suppose 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?

Given 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

An 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.

Read 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?

Verne 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

To 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.

Which 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

All 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.

In 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

A 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

The 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.

Under the Emergency Solutions Grants (ESG) Program, activities eligible for funding include which of the following? A) Psychological counseling and supervision B) Renovation of buildings to be used as homeless shelters C) All of these D) Assistance in obtaining permanent housing

The main difference in qualifying standards for Freddie Mac from Fannie Mae is that Freddie Mac A) requires higher credit scores. B) uses only the total debt-to-income ratio. C) may require private mortgage insurance. D) only purchases conventional loans.

The FICO credit score range is A) 15-850. B) 250-550. C) 300-850. D) 300-550.

Find an equation for the plane that passes through the point (-1,6,0) perpendicular to the line x = -1+t, y = 6-2t, z = 3t, and then find the distance from the point (2,1,3) to that plane.

Real estate financial transactions that require the services of an appraiser and ones in which a federal financial institution, regulatory agency, or secondary market participant engages are called A) Security-Freeze Law transactions. B) Texas Appraiser Licensing and Certification Board (TALCB) transactions. C) federally related transactions. D) qualified mortgage (QM) transactions.

Under the Deceptive Trade Practices Act (DTPA), in order for treble damages to be awarded, a real estate professional must A) commit an act of omission. B) act knowingly. C) commit an unconscionable act. D) commit an act of commission.

Prove the identity. sin³x-cos²x=2sin2x-1

For the following data set, find the range and the sample standard deviation (round to the nearest tenth.) 101, 112, 124, 125, 131, 145, 155, 161, 179 Select one: a. range: 78, standard deviation: 25.0 b. range: 78. standard deviation: 34.2 c. range: 70, standard deviation: 29.2 d. range: 70, standard deviation: 18.3

A 200-pound male drinks in 2 hours. What is the maximum number of standard drinks the drinker can take to limit his BAC below 0.08? Explain how you got the number of standard drinks.

A machine to mill a brass plate has a setup cost of $700 and a unit cost of $4 for each plate manufactured. A bigger machine has a setup cost of $800 but a unit cost of only $1 for each plate manufactured. Find the break point. (Round your answer to the nearest whole unit.) Kyle estimates that it will take him 10 days to roof his house. A professional roofer estimates that it will take him 15 days to roof the same house. How long will it take if they work together? (Enter as improper fraction, not a mixed numeral)

Identify the amplitude. y = cos 4x Select one: a.π/2 b. 2π c. 4 d. 1

The graph below represents y = -3 cos (x + π) + 3.

Find the range of the function f(x) = -5 (3)x-1 Select one: a. (-∞,-1) b. (-∞,∞) c. (1.,∞) d. (-∞, 0)

What is the range of the function f(x)=2 x-2 Select one: a. [1.5] b. (-∞,0) c. (-∞,∞) d. (0,∞)

Use a calculator with ay key or a key to solve the following. The exponential function f(x) = 569(1.026)* models the population of a country, f(x), in millions, x years after 1968. Complete parts (a)-(e). a. Substitute 0 for x and, without using a calculator, find the country's population in 1968. The country's population in 1968 was million.

Say that you wish to estimate In(x) on [1.e] using a Chebyshev interpolating polynomial. How many data points would you need to guarantee that the error is less than 10-16.

In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from a random sample of 7 students who are physics majors exactly five belong to an ethnic minority. 0.147 0.068 0.037 0.049 0.015

There is a 30 people council. Find the number of making 5 people subcommittee.

The position of a weight attached to a spring is s(t)= -3 cos 4xt inches after t seconds. Complete parts a)-d) below. a) What is the maximum height that the weight rises above the equilibrium position? b) What are the frequency and period? The frequency of the oscillation is cycles per sec (Type an integer or a fraction. Type an exact answer, using a as needed.) The period of the oscillation is sec (Type an integer or a fraction. Type an exact answer, using x as needed.) c) When does the weight first reach its maximum height? after sec (Type an integer or a fraction Type an exact answer, using as needed.) d) Calculate and interpret s(1.3) s(1.3)= (Round to the nearest integer as needed.) Interpret s(1.3) Choose the correct answer below. OA After 1.3 sec, the weight is about 2 in above the equilibrium position OB. After 1:3 sec, the weight is about in above the equilibrium position Oc. After 2 sec, the weight is about 1.3 in above the equilibrium position. 27

Solve, graph on a number line, and write in interval notation. |2x - 3|-1 ≤6

Rationalize the denominator. Write in simplest terms. 32/√48 Select one: a. 8√3/3 b. 32√48/48 c. 12√3 d. 4√12/3

Ali, Bernard and Charlie shared some stamps. The ratio of Ali's stamps to Berard's stamps was 1:3. After Charlie received 1/3 of All's stamps and 1/2 of Bernard's stamps, the number of stamps he had doubled to 308 stamps. How many stamps did Ali, Bernard and Charlie have altogether?

Rewrite as sums or differences of logarithms. log(x8y8z)

Express as a product. log 10t-7

Pq Express log b p2q7/m33b8 in terms of sums and differences of logarithms.

Rewrite as sums or differences of logarithms. In (x7y3z)