Permutations and Combinations Questions and Answers

In the 2009-2010 school year in country A, there were 112,000 foreign students from country B. This number is 21% more than the number of students from country C. How many foreign students were from country C? There were about ______ students from country C. (Simplify your answer. Round to the nearest thousands as needed.)

What type of function is this ? f (x)= 2(1/7)ˣ 1. Exponential Growth because b>1 2. Exponential decay because b <1 3. Linear 4. None of the above

Solve the equation and check for extraneous solutions. 3x³ = 405 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution(s) is/are x= (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for a B. There is no solution.

Select the correct proof of the identity. cos x (tanx - sec (-x)) = sin x-1

Pamela's after-tax paycheck is $875, and she receives rent for her apartment, which she has leased to her friend for $300. Her fixed expenses amount to $535, and her variable expenses amount to $525. How much is her savings? 0 105 0 95 0 115

The legal downloading of music has been increasing at a constant rate since January 2014. The number of monthly downloads can be estimated by y=860x+3182, where x is the number of months after January 2014. a) Find the x-intercept as an ordered pair. _____ b) Write a sentence explaining the meaning of the answer to part (a). _______________________

A basket contains three apples, three peaches, and four pears. You randomly select a piece of fruit. What is the probability it is an apple or a peach?

There are 22 students in Mr. Elski's class. Thirteen of the students are female and nine students are male. Eighteen students are passing the class. Two of the students failing the class are female. Fill out the following chart. Female male total passing failing total Find the probability that if a student is chosen at random that they are male or passing.

Calculate the volume of liquid in the tank sketched below. Give your answer in liters, and round to the nearest 0.1 L.

Write the sum as a single logarithm. Assume that variables represent positive numbers. log5 (x)+ log5 (x+3)

Consider the following nonlinear system : 5x₁² = x₂² x₂ - 0.25(sin x₁ + cos x₂ ) = 0 Draw a sketch of the two functions on the same axes

"As the craft plopped her stern down again, the spray splashed past them. There was a long, loud swishing astern the boat." What musical device is emphasized in this sentence? A onomatopoeia (B) assonance syncope (D) apocope 3 Points E consonance

Suppose that the DE y""' (x) — 4y(x) =−32 x³ +72 has a solution of the form y = Aïx³ + B Find the values of A and B A = Number B = Number

A child is holding the end of a 48 meter string attached to a kit. The string has an angle of elevation of 80°. Determine the elevation of the kite. Give your answer rounded to the nearest whole number. The kite is meters high.

A 450-foot weather tower used to measure wind speed has a guy wire attached to it 375 feet above the ground. The angle between the wire and the vertical tower is 50°. Approximate the length of the guy wire (to the nearest foot).

Using the digits 0, 1, 2, 8, 9, determine how many 3-digit lock combinations are possible according to the following criteria One cannot be used for the first digit; digits may be repeated. The number of possible 3-digit lock combinations is

Two cards are drawn in succession from a standard 52-card deck. What is the probability that the first card is a heart and the second card is a club (A) If the cards are drawn without replacement? (B) If the cards are drawn with replacement? (A) What is the probability that the first card is a heart and the second card is a club if the cards are drawn without replacement? (Type an integer or decimal rounded to four decimal places as needed.)

Use the inner product <p.q> p(-3)q(-3) +p(0)q(0) + p(2)q(2) in Ps to find the orthogonal projection of p(x) proj, (p) 4x² 3x 3 onto the line L spanned by g(x)= 3²-42 +9.

X def b.c.0+ b.d.0 Y def X+ b.(c.0 + d.o) def Z W def a.Y a.Y + a.X (a) Draw a labelled transition system which includes the above states X, Y, Z and W. [5 marks] (b) Explain why Z2 W but Z 3 W. That is, argue that the second player has the winning strategy in the copy-cat (bisimulation) game which lasts for two rounds, but that the first player has the winning strategy in the game which lasts for three rounds. [3 marks] (c) Give a formula P of the modal logic M which is satisfied by Z but not by W. [2 marks]

(4 pts) Use Stokes' Theorem to evaluate the surface integral cu curl F-n dS where F(x, y, z) = (3x² - y³)i +3z²j+xyzk, G is the unit sphere G= {(x, y, z) | x² + y² +2²=1} and n is the outward-pointing unit normal vector to the surface. 00 O 3T -2T O E

You owe $302.87 on your credit card. Your average daily balance is $112.98, the billing cycle is 35 days, and the interest rate on the credit card is 16%. How much do you owe? (a)$316.44 (b)$306.40 (c)$304.60 (d)$303.66

How many ways can you give 5 different chocolates to 3 children so that each child gets at least one chocolate?

What type of slope does this line have? X = -2 A. Positive Slope B. Negative Slope C. o Slope D. Undefined Slope

You spin a spinner numbered from 1 to 4 and spin another spinner with the colors orange, violet, red, green, yellow and blue. Both spinners are divided into sections with the same area. How many possible outcomes are in the sample space? The sample space has________possible outcomes.

A university polls 200 students. 80 students drink tea, 140 drink coffee, and 30 drink neither. What is the probability that you choose a random student that they drink both?

You take out a 50-day single-payment loan for $910 with an interest rate of 19%. Find the amount of the maturity value.

Il takes Ron 12 hours to paint a house and it takes Rita 6 hours. How long should it take if they worked together? (A) 9 hours (B) 18 hours (C) None of the choices are correct (D) 4 hours (E) 3 hours

Suppose the number of students in a class for the Business Statistics program at a University has a mean of 23 with a standard deviation of 4.3. If 15 classes are selected randomly, find the probability that the mean number of students is between 20 and 30. (A) 0.9699 (B) 0.6824 (C) 0.8412 (D) 0.9966

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 94 inches, and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49 randomly picked years will exceed 96.8 inches? 0.0026 0.4192 0.5808 0.0808

Why are unbiased estimators preferred over biased estimators? Unbiased estimators follow the normal distribution, where as biased estimators follow the original distribution Unbiased estimators require a greater sample size which gives greater accuracy over biased estimators. Unbiased estimators behave with reliable results, where as biased estimators are inconsistent. Unbiased estimators retain the original distribution of the sample, where as biased estimators follow a normal distribution.

Janet bought a used car for $9,000. She has a simple interest loan with 14% interest for 24 months. Janet decided to pay off the loan early, and has an unpaid balance of $1,920. Find the amount of the final payment.

Prove the following vector identities using index notation (a) (axb) (cx d) = (a. c) (b. d) - (a.d) (b. c) (b) ax (bx c) + bx (cx a) + cx (axb) = 0 (c) (a. ∇)a= 1/2∇(a.a) - ax (∇ xa)

Given the quadratic function f(x)=-6x² -2x Compute f(a+ h)-f(a)= Assuming h≠0, compute f(a+ h)-f(a)/(h)=

The box-and-whisker plot shown below represents the number of magazine subscriptions sold by members of a club. Which statistical measures do points B, D, and E represent, respectively? 1) minimum, median, maximum 2) first quartile, median, third quartile 3) first quartile, third quartile, maximum 4) median, third quartile, maximum In the box-and-whisker plot below, which is the median (2nd quartile)? 1) 25 2) 30 3) 45 4) 50 3. a. Determine the least value for Box plot A and B. b. Which set contains the greatest value, and what is it? c. What is the interquartile range of Box plot B? d. Which box plot has the greater range?

Given the one-to-one function f(x)=x³ + 4 find the following. Hint: You do not need to find the equation for f(x). a. f(-4) b. f¯¹ (-60)

The cost of a classified ad is determined by its length. Hammond plans to sell his car and places a 5-line ad. The newspaper charges $15 for the first two lines and $5 per extra line to run the ad for one week. What will Hammond's ad cost to run for two weeks? A $60 B $30 C $15 D $7.50

Suppose a city with population 400,000 has been growing at a rate of 8% per year. If this rate continues, find the population of this city in 20 years. The population in 20 years will be approximately (Round to the nearest whole number as needed.)

Solve the equation for x. Give an exact answer and a four-decimal-place approximation. log (2x-3)= -0.9 The exact answer is x =

Nemo's annual premium is $1,644. If he pays quarterly, there is a $2 per payment surcharge. What is his quarterly payment? A $388 B $411 C $413 D $412

Victoria is going to invest into an account that pays 9% compounded daily. How much would Victoria need to invest, to the nearest dollar, for the value to account to reach $580 in 6 years? (a)$338.02 (b)$3 (c)$338 (d)$2.64

Write as a single logarithm. Assume that variables represent positive numbers. 2log 8(x)-1/4(log8 (x)) + 4log 8(x)

A binomial experiment has 4 trials in which p = 0.75. What is the probability of 1 success? (a) 0.0469 (b) 0.0639 (c) 0.3945 (d) 0.4394

In how many ways can 3 pizza toppings be chosen from 12 available toppings?

How many 4-digit numbers can be made by using digits 1 to 7 (repetition is not allowed), if the digit 4 will always be there in the number? a) 272 b) 480 c) 289 d) 270

(x-6)/(x² - 49) < 0. Solve the following rational inequality Give your answer using interval notation.

Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair. (a) How many ways can this be done, if the order of the choices is taken into consideration? (b) How many ways can this be done, if the order of the choices is not taken into consideration?

Solve each equation for 0 ≤ θ < 2π. 3) -3 = -3tan θ A) {0,π/4,π,5π/4} B) {π/4} C) {π/4,π,5π/4} D) {π/4,5π/4}

A spinner has 10 equally sized slices numbered from 1 to 10. Some are white and some are grey, as shown below. Answer the following questions. Write each answer as a fraction. The wheel will be spun and will stop on a slice at random. (a) What is the probability that the wheel stops on a grey slice? (b) What is the probability that the wheel stops on a grey slice, given that the wheel stops on a number less than 9?

A wooden artifact from an ancient tomb contains 50 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)

Solve the logarithmic equation algebraically, Round the result to three decimal places. Verify your answer using a graphing utility. log ₂x +log₂(x-3)=2. X=