Permutations and Combinations Questions and Answers

What is the probability of rolling 6 on a fair number cube and flipping a coin and getting tails? Write your answer as a percent rounded to the tenths place. Do not include the percent symbol.

If A and B are mutually exclusive, and if P(A) = 32% and P(B) = 35%, what is P(A or B)? P(A or B)=

S and T are mutually exclusive events. Find P(S or T). P(S)=5/8 P(T) = 1/8 P(S or T) =d to three decimal places as needed)

Telephone numbers are preceded by a 3-digit area code (e.g. 437). In the following questions, any digit from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9) can be used unless otherwise stated. How many area codes are possible if: a. the first digit must be 1? b. the third digit must not be 4? c. the second and third digits must be the same? d. neither 1 nor 2 must be used?

S and T are mutually exclusive events. Find P(S or T). Write your answer as a fraction in simplest form (a/b). P(S) = 3/5, P(T) = 1/3

In a group of 11 students, there are 6 females and 5 males How many different 4-member committees are possible if there are no restrictions? How many different 4-member committees are possible there must be exactly 2 girls? How many different 4-member committees are possible there must be at least 1 girl? Determine the probability that a 4-member committee chosen at random from this group will consist of at least 1 females. Write your answer as a percent.___%

A ski resort has 3 chair lifts, each with access to 6 ski trails. Explain how you can find the number of possible outcomes when choosing a chair lift and a ski trail without making a list, a tree diagram, or table.

Find an equation of the line having the given slope and containing the given point. Slope 3/4 through (-4,4)

Find the domain of the rational function. f(x) = 7x /11-x

A class rolled number cubes. Their results are shown in the table. What is the experimental probability of rolling each number?

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 150. What is the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots?

Baby Ethan wants to arrange 9 blocks in a row. How many different arrangements can he make?

Assume that 3 customers arrive and order different appetizers to share from a choice of 12 appetizers. a. Does this problem involve permutations or combinations? b. Why? c. In how many possible ways can this be done?

A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You pick one marble from the jar at random. Find the theoretical probability. a. P(red) b. P(not white)

A monk crossbred plants, which can have purple or white flowers, and obtained 502 plants with white flowers and 351 plants with purple flowers. Find the experimental probability that a plant had each type of flower.

To create an entry code, you must first choose 3 letters and then, 4 single-digit numbers. How many different entry codes can you create?

explain in words why three forces must lie in the same plane when they are acting on an object in equilibrium

You want to be able to withdraw $40,000 each year for 30 years. Your account earns 6% interest. a) How much do you need in your account at the beginning? b) How much total money will you pull out of the account? c) How much of that money is interest?

Mr. Anderson put $1000 into an account that earns 4.5% annual interest. The interest is compounded annually and there are no withdrawals. How much money will be in the account at the end of 30 years? Round to the nearest cent.

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=x4 + 4x³ + 3x²-3x-7; f(6)

Suppose Alice encrypted an existing English word using Hill cipher with a 4 x 4 permutation matrix as the key. The obtained ciphertext is THMA. Find the matrix that was used as the key.

Prove that the triangles on the grid below are congruent by using the following methods: 1) SSS 2) SAS

A population has the following characteristics. (a) A total of 75% of the population survives the first year. Of that 75%, 25% survives the second year. The maximum life span is 3 years. (b) The average number of offspring for each member of the population is 2 the first year, 4 the second year, and 2 the third year. The population now consists of 176 members in each of the three age classes. How many members will there be in each age class in 1 year?

Suppose you deposit your graduation cash gifts into an account that pays 4% annual interest compounded continuously. If you are 18 when you graduate, get $1000 in cash gifts and leave the money in the account until you are 30, how much money will you have? Round to the nearest dollar.

Consider the following function and point. F(x) = (x + 2)/(x-2)₁ (3,5) (a) Find the derivative of the function. f'(x) = Find f'(x) when x = 3. f'(3) = Give the slope of the graph of the function at the given point (3, 5). slope Find an equation of the tangent line to the graph of f at the given point y =

How many people must be chosen from 17 couples to be sure atleast one couple is included? a. 18 b. 17 c. 2 d. 3 e. 34

From a deck of 52 cards, how many 5 cards tobe formed to be formed to have two pairs of the same numbers example(two"l0s", and two"Qs or "2s" and two "S"s a.109824 b.6864 C.247104 d.123552 e.27456

Consider the following random sample of data: 2, -9, 3, -10, 5, -7, 9, 1, 4, 87 a) What is the mean of the sample data? b) If the outlier is removed, what is the mean of the remaining sample data?

If light travels at a speed of 3 x 10⁸ m/s, and remembering the formula distance = speed x time. (or d = v*t), calculate the distance traveled by light in 2 milliseconds (i.e. in t = 2 x 10-³ seconds)

What happens to the input when you plug it in? Find expressions for the composite functions (MG) (t) and (Go M)(r). Explain in words what happens to your input when you plug it in to these composite functions. We call G and M inverses.

Give the version of the Parallel Postulate as used in Euclidean geometry, beginning the statement with, "Given a line and a point P not on,..." Now show how to change this statement in two different ways, giving rise to two different forms of non-Euclidean geometry.

A chemist has three different acid solutions. The first acid solution contains 20 % acid, the second contains 40% and the third contains 60%. He wants to use all three solutions to obtain a mixture of 112 liters containing 35 % acid, using 3 times as much of the 60% solution as the 40 % solution. How many liters of each solution should be used?

Describe the transformation of the parent function y = 2*.

Find a basis for the orthogonal complement of the subspace of Rª spanned by the vectors. V₁ = (1, 4, -4,3), V₂ = (3, 11, 3, 5), V3 = (1, 3, 11, -1) The basis for the row space is W₁ = ( W₂ = ( M. i " i i 1 1 0 ) 0 1 ) .

Find all solutions to sin (x + 4) + sin(x-4)=0 on [0, 2π). Enter the answer in terms of , as needed. Do not enter a decimal approximation.

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. Find sin B when b = 5 and c = = 6.

If2-√3 is a root of a polynomial with integer coefficients, which of the following is another root? 2√3 3-√2 2+√3 √3-2

A garden has width /13 and length 7/13. What is the perimeter of the garden in simplest radical form? Select one: O a. 16√13 O b. 91 O c. 8√13 Od. 14v13

When x⁴ - 16 is factored completely, one of the factors will be

Write a rate in simplest form for earning $171 in 18 hours.

2. Use the Law of Cosines to determine the indicated angle O. (Assume a = 136.5, b = 59.2, and c = 160.5. Round your answer to the nearest degree.) 0 =

Express the proposition as an English sentence and determine whether it is true or false, where p and q are the propositions p: "9.9=81" q: "8.10<7.11 The contrapositive of p →q A. If 8.10 is not less than 7. 11, then 9.9 is not equal to 81; false B. If 8.10 is not less than 7. 11, then 9.9 is equal to 81; false C. If 8.10 is less than 7.11, then 9.9 is equal to 81; false D. If 8.10 is less than 7.11, then 9.9 is not equal to 81; false

We distribute 30 indistinguishable toy cars to 3 people (say, A, B, and C). How distinguishable many ways can we do this so that no people get precisely 10 toy cars?

Dylan has 7 soccer trophies. He can only fit 4 trophies in a row on his display shelf. In how many different ways can Dylan arrange the trophies on the shelf? Select on O 28 O 840 O 35 O 210

Samantha is arranging the letters in the word "MUSICAL." How many different 7-letter arrangements can she make if she must use all seven letters each time? Select one: O 5040 O 7 O823,543 O28

(a) How many black playing cards must be drawn from a single deck of cards to be sure that at least two are the same suit? (b) How many black playing cards must be drawn from a single deck of cards to be sure that at least twelve are spades or at least twelve are clubs? (a) There must be at least _____ black playing cards drawn from a single deck of cards to ensure there are at least 2 of the same suit. (b) There must be at least ________ black playing cards drawn from a single deck of cards to ensure there are at least twelve spades or twelve clubs.

A hole is cut through the center of a thick sheet of metal. The metal is 8.5mm thick,10cm long and 13cm wide. The hole was 4cm wide. Find the weight of the metal. (in grams)

Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to bedrawn at random and monetary prizes awarded as follows: 1 prize of $500, 3 prizes of $200, 5 prizes of $30, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket? Let X be the random variable for the amount won on a single raffle ticket. E(X)=dollars (Round to the nearest cent as needed.)

On three rolls of a single die, you will lose $14 if a 3 turns up at least once, and you will win $8 otherwise. What is the expected value of the game? Let X be the random variable for the amount won on a single play of this game. E(X)= dollars (Type an integer or a decimal rounded to the nearest cent as needed.)

Which of the following situations can be modeled with a periodic function? the height of a football after it has been thrown the height of a person riding on an escalator the height of a building after it has been constructed the height of a pebble stuck in the tread of a tire