Permutations and Combinations Questions and Answers

Find the solution region (ie, the graph) of each system of linear inequality (inequalities). (Hint: Ex in P. 2-5 of Ch 3.1 in LN). a. 3x + 4y ≤7. b. 3x-2y ≤10. c. 3x + 4y ≤7. 3x-2y ≤10. d. 3x + 4y ≤7. 3x-2y ≤10, x,y≥20.

Bob chooses the secret primes p = 5 and q = 11. Bob chooses the encryption exponent e = 3. Bob publishes N = 55 and e = 3. If Bob receivers the ciphertext c = 24 from Alice, what is the plaintext m that Bob obtains by deciphering c?

4. Elena bikes 20 minutes each day for exercise. Write an equation to describe the relationship between her distance in miles, D, and her biking speed, in miles per hour, when she bikes: a. at a constant speed of 13 miles per hour for the entire 20 minutes

Solve the system of equations. 2x-6y=6 8x-24y=27 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. There is one solution. The solution of the system is (Simplify your answer. Type an ordered pair.) B. The solution set of the system is {(x,y)| 2x-6y=6}. C. The solution set is Ø.

Write an expression having only two terms that is equivalent to 2x-3. Explain how you wrote the expression and how you can check that it is equivalent.

Find the LCD of the following. Do not combine fractions. 6/5x-35 5/ 6x-42 The LCD is

Let R³ have the Euclidean inner product. For which values of k are u and v orthogonal? u=(6,7,4) and v=(8, 2, k)

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for 20 hours per week. His goal is to make $300 per week. Let m = the number of hours spent mowing and g = the number of hours spent gardening. Select the two equations below that create the system of equations which will model this scenario. m+g=300 15m +20g = 20 m+g=15 m + g = 20 15m +20g = 300

Algebra Q2. If y = cle 3x + c2e-3x is a solution of the ODE y" - 9y = 0, find a solution of the IVP y" - 9y = 0 Subject to IC: y(0) = 2, y '(0) = 4

9) Use a probability tree: 85% of Americans have dental insurance. Of those that have dental insurance, 68% see the dentist for regular check-ups, but 46% of those without dental insurance go in for regular check-ups. What percent of Americans overall will go in for a regular check-up?

3. Verify the identity. Show the steps or no credit will be earned. secθ sinθ cotθ = 1

Functions that repeat over time are common in every day life. The English language has many words that stand for common periods of time. State the period of time from which each term derives. a. annual b. quarterly c. circadian

Olsen Outfitters Inc. believes that its optimal capital structure consists of 60% of equity and 40% of debt, and its tax rate is 30%. Olsen must raise additional capital to fund it upcoming expansion. The firm will have $5 million of retained earnings with a cost of r, 12%. New common stock in an amount up to 10 million would have a cost of re-14.5%. Furthermore, Olsen can raise up to $6 million of debt at an interest rate of rd=8% and an additional $7 million of debt at rd=11%. The CFO estimates that a proposed expansion would require an investment of $11 million. What is the WACC for the last dollar raised to complete the expansion? 9.44% 10.40% 11.90% 10.94%

The traffic-control monitor on the freeway shows 200 vehicles per minute passing the camera in 5 minutes. Of those vehicles, on average, 125 have one passenger, 60 have four or fewer passengers, and 15 have more than four passengers. P(vehicle with more than four people) P(vehicle with four or fewer people

Determine whether to use a permutation or combination to solve the problem. How many different orders can you choose to read six of the nine books on your summer reading list? How many ways are there to choose 5 shirts out of 7 to take to camp? How many different ways can 8 swimmers earn first, second, or third place? How many ways can you choose 2 out of 4 kinds of flowers for a bouquet?

A fair number cube is tossed. Find P(even or more than 1). Write your answer as a fraction in simplest form (a/b).

Mrs. Jackson is a history teacher. To choose two students at random, she decides to choose the tallest and the shortest students in the class. Mrs. Jackson's strategy resulted in a fair decision. Select one: True False

Draw the following 15) Irregular 16-gon 16) vertical angles 17) Rectangle

A 55# child has an order for Dilantin (phenytoin) 7 mg/kg/day to be given in divided doses q12h. The medication available is Dilantin Suspension 125 mg/5 mL in an fl oz viii container. 1. How many mL are in this container? 2. How many mg will the child receive in 24 hours? 3. How many mg will the child receive per dose? 4. How many milliliters of medication should be administered to the child per dose? 5. How many full doses of medication are in one stock bottle? 6. What utensil should be provided for accuracy of administration?

You have been asked to interpret this symbolic logic. In x≤5Ax>3, what value of x will this be false? 3 4 5 6

If /theta= 60 degrees, find the exact value of the following. Sin^2(/theta)

In a survey at a university 56% of students say that they got less than the recommended eight hours of sleep per night. In a group of 4800 students, how many would you expect get eight or more hours of sleep per night?

You should rotate tires on a car at regular intervals. In how many ways can four tires be arranged on a car?

You and your friends are picking up videos at a video store. You have selected 7 videos but will only have time to watch 3. How many different ways can you select 3 videos to watch?

A class tossed coins and recorded 161 heads and 179 tails. What is the experimental probability of heads? Write the answer as a fraction in form a/b.

A manufacturing company performs a quality- control analysis on the ceramic tile it produces. Suppose a batch of 15 tiles has 4 defective tiles. If 3 tiles are sampled at random, what is the probability that exactly 1 of the sampled tiles is defective? How many ways can 3 tiles be selected from 15 tiles?

Use the formula for Pr to solve the following question. At a benefit concert, eight bands have volunteered to perform but there is only enough time for six of the bands to play. How many lineups are possible?

Out of four games, team A has won one game and team B has won three games in a championship series. What is the experimental probability that team A wins the next game? Write your answer as a fraction in simplest form in the form a/b.

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 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?

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.

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.

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