Sets and Relations Questions and Answers

Scott is saving for a down payment to buy a house. The account earns 7.7% Interest compounded semi-annually, and he wants to have $10,000 in 5 years. What must his principal be? Round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.

Perform the indicated operations and designate the answer using the listing method. U=(g, h, i, j, k, l, m), X= {g, i, k, m), Y = {g, h, i), and Z = {h, i, j, k, l} X' - Y

For the following function, determine whether the function is one-to-one. {(4,6), (5,6), (-9,11), (6,-17)} Is the function one-to-one? No Yes

A passbook savings account has a rate of 7%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded 1000 times per year. Click the icon to view some finance formulas. The effective annual yield is%. (Round to the nearest tenth as needed.)

Solve the equation 2cos2x - 7cos x= 4 given that 0 < x < 2π. Provide your answer below: X=

Given a mean, standard deviation, and a raw score, find the corresponding z-score. Assume the distribution is normal. mean 70, standard deviation 10, x = 88 What is the corresponding z-score? Z=

You have $170. You start a part-time job that pays $8.50 per hour. a) Does the situation represent a function? If so, identify the independent and dependent variable b) You work no more than 4 hours. Find the domain.

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. In (x-5)+ In (x+4)= In (x-21) Rewrite the given equation without logarithms. Do not solve for x. (x - 5)(x+4)=(x-21) Solve the equation to find the solution set. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is {} (Simplify your answer. Use a comma to separate answers as needed.) OB. There are infinitely many solutions. OC. There is no solution.

In a survey of 75 pet owners, 24 said they own a dog, and 16 said they own a cat. 8 said they own both a dog and a cat? How many owned a dog but not a cat? Answer = Question Help: Video Submit Question owners

Let S be the universal set, where: S = {1, 2, 3, ..., 18, 19, 20} Let sets A and B be subsets of S, where: Set A = {1, 4, 6, 8, 13, 20} Set B = {7, 8, 10, 12, 14, 17, 20} Set C= {5, 7, 8, 11, 12, 14, 18, 19} LIST the elements in the set (AUBUC) (AUBUC)={\ } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set (An BnC) (An BnC)={ Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question. Question Help: Video 1 Video 2 Submit Question

In a loan database, there are 25 loans to clients with 19 years of business experience. Also, there are 14 loans made to clients with a High School education. In the database there are 31 loans to clients with 19 years of experience or who have a High School education. How many loans were made to clients with a High School education who also had 19 years of experience? Answer = Question Help: Video Submit Question loans K

In the last several weeks, 54 days saw rain and 29 days saw high winds. In that same time period, 15 days saw both rain and high winds. How many days saw either rain or high winds? days

The board of directors for Procter and Gamble is concerned that only 19% of the people who use toothpaste buy Crest toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will include advertisements and new labeling for the toothpaste. The research department conducts product trials in test markets for one month to determine if the market share increases with new labels. Write the company's alternative hypotheses. (Note that you'll need the null for the rest of the problem.)

It is false that cats are lazy or dogs are not friendly. (Hint: Use DeMorgan's laws.) A. Cats are not lazy or dogs are friendly. B. Cats are not lazy or dogs are not friendly. C. Cats are lazy and dogs are friendly. D. Cats are not lazy and dogs are friendly.

What is the image of (4, -8) after a dilation by a scale factor of 1/4 centered at the origin?

A system of linear inequalities is used to represent restrictions, or on a function that must be maximized or minimized.

Which of the following is the best definition of the domain of a relation? A. The set of all allowable output values, or x-values B. The set of all allowable input values, or y-values C. The set of all allowable output values, or y-values D. The set of all allowable input values, or x-values

A charity is hosting a benefit dinner. They are asking for $75 per table plus $35 per person. Martha is buying tickets for her friends and does not want to spend more than $300. a. Write an inequality to represent this situation, where x is the number of people. b. Solve the inequality. Show your work. c. What is the maximum number of friends Martha can invite? Explain your reasoning.

Let X = {a,b,c,13,14,15) and Y = {b,d,f, 13,15,17}. List the members of the set XUY, using set braces. XUY=

Let U = {a,b,c,d,e,f, 19,20,21,22,23,24}, X = {a,b,c,21,22,23), and Y = {b,d,f,20,22,24). List the members of the set X'nY', using set braces.

Find the number of subsets for the following set. {F,G,H,I,J} How many subsets does this set have? (Type a whole number.)

Let U = {20, 21, 22, 23, 24, 25, 26}, A = { 23, 24, 25, 26}. Use the roster method to write the set A'. A' = { (Use a comma to separate answers as needed.)

Find the slope of the line. - 9x-8y = 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Simplify your answer.) B. The slope is undefined.

Which of the following is the inverse relation of the set below? {(-2,3), (7,-4), (3,7), (8,4)} {(3,-2), (-4,7), (7,3), (4,8)} {(7,-2), (-4,3), (2,3), (4,8)} {(-4,-2), (-4,3), (7,8), (4,3)} {(8,-2), (3,7), (7,-4), (4,-2)}

Write the contrapositive of the following conditional statement: "If the cat is running, he either spotted a mouse or he spotted a squirrel." The cat isn't running, and the cat didn't spot a mouse and he didn't spot a squirrel. If the cat didn't spot a mouse and he didn't spot a squirrel, then the cat isn't running. If the cat isn't running, then the cat spotted a mouse or a squirrel. If the cat spotted a mouse or a squirrel, then the cat isn't running. If the cat isn't running, then the cat didn't spot a mouse and he didn't spot a squirrel. If the cat didn't spot a mouse or he didn't spot a squirrel, then the cat isn't running.

Determine if the following function has an Inverse function. h(x) = |x|

- Consider three sets E₁ = {1,2,3}, F₁ = {1,3,4} and G₁ = {2,3,4,5). Two elements are chosen at random, without replacement, from the set E₁, and let S₁ denote the set of these chosen elements. Let E₂ = E₁ − S₁ and F₂ = F₁ U S₁. Now two elements are chosen at random, without replacement, from the set F₂ and let S₂ denote the set of these chosen elements. Let G₂ = G₁ U S₂. Finally, two elements are chosen at random, without replacement, from the set G₂ and let S3 denote the set of these chosen elements. Let E3 = E₂ US3. Given that E₁-E3, let p be the conditional probability of the event S₁ = {1,2}. Then the value of p is (A) / 3 (B)-- (C) 2/1/2 (D) ²/3 2|5

Consider the following functions f(x) = 2x and g(x) = 3√x Find the formula for (f/g) (x) and simplify your answer. Then find the domain for (f/g) (x)

A freelance computer consultant keeps a database of her clients, which contains the names S = {Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert). The following clients owe her money: A = {Acme, Crafts, Effigy, Global}. The following clients have done at least $10,000 worth of business with her: B = {Acme, Brothers, Crafts, Dion}. The following clients have employed her in the last year: C = {Acme, Crafts, Dion, Effigy, Global, Hilbert). A subset of clients is described that the consultant could find using her database. HINT [See Example 4.] The clients who have done at least $10,000 worth of business with her and have employed her in the last year. Write the subset in terms of A, B, and C. ANB BUA BNC BUC BNA List the clients in the subset. {Acme, Brothers, Crafts, Dion, Global, Hilbert} {Acme, Brothers, Crafts, Dion, Effigy, Global} {Acme, Crafts, Effigy, Global} {Acme, Crafts, Dion}

Which was not a response to the September 11 terrorist attacks on the United States? A. Iraq denounced the events and disassociated itself from al-Qaeda. B. World leaders pledged support to the United States during its recovery. C. Citizens all over the country came together to support each other and the president. D. The president requested and received congressional authorization for the use of military force.

Consider the following functions. f = [(-1.-2), (3, − 1), (1, 3)] and g = ((-1.–1), (3, 0), (1, − 3)} Find (gl)

Let A = {H, T}, B = {1, 2, 3, 4, 5, 6}, and C = {red}. Find the number indicated. n(A x CxC)

Use set notation to write the members of the following set, or state that the set has no members. Odd numbers between 14 and 56 that are multiples of 5. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. B. The set has no members. (Type whole numbers. Use a comma to separate answers as needed.)

What is the power set of the set (0,1,2)? (0. (0). (1), (2), (0, 1), (0.2), (1,2), (0.1.2)) (0.(0). (1), (2), (0, 1), (0.2), (1,2)) (10), (1), (2), (0.1), (0, 2), (1,2), (0.1,2)) ((0) (0) (1), (2), (0, 1), (0.2), (1,2), (0.1,2))

Let A be the set A=(1,2,3, 4) and let B be the set B=(5,6,7,8). What is an element in B*A? (6,4) (3,4) (4.7) (1,8)

Consider the following function on the given domain. Correct r(x) = (x+3)² - 5,x ≥-3 Step 1 of 2: Find a formula for the inverse of the function on the given domain, if possible.

Let U=(c, d, f, g, h, k, m), and A = {c, f). Determine if the statement below is true or false. A⊂U Choose the correct answer below. A. The statement is false because not every element of set A is contained in U. B. The statement is false because every element of set A is contained in U but A# U. C. The statement is true because every element of set A is contained in U and A=U. D. The statement is true because every element of set A is contained in U and A# U.

Fill the blank with either ∈ or to make the statement true. 4 _{2, 3, 6, 7) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The ∉ symbol should be used because (2, 3, 6, 7) is a set and none of the elements in 4 is a set. B. The ∈ symbol should be used because (2, 3, 6, 7) and 4 are equal sets. C. The ∈ symbol should be used because is an element of the set. D. The ∉ symbol should be used because is an element of the set. E. The ∉ symbol should be used because is not an element of the set. F. The ∈ symbol should be used because is not an element of the set.

On the first day of a song's release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day? Round to the nearest million. 27 million 35 million 37 million 38 million

Elmer has a job shoveling sidewalks that pays $22 per sidewalk shoveled and he plans to complete at most 10 sidewalks in a week. If x is the number of sidewalks he completes in a week and y is the money he earns in a week, write the domain and range of the function as compound inequalities.

Question If the function y = eis vertically compressed by a factor of 2, reflected across the y-axis, and then shifted down 3 units, cea + b. what is the resulting function? Write your answer in the form y = inswor below:

Suppose that the relation G is defined as follows. G={(8,-7), (-6, 7), (7,0), (2, 2)} Give the domain and range of G. Write your answers using set notation.

Given f(x) = (x + 2)² and g(z)=2-3z, find (ƒ+g) (z). You should not include (f+g) (z) = in your answer, and your answer should be fully simplified. Provide your answer below

28% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive. (a) P(2) = 0.255 (Round to the nearest thousandth as needed.) (b) P(x-2)= (Round to the nearest thousandth as needed.)

A veterinarian prescribed Alexandra, a 23-pound dog, an antibacterial medication in case an infection emerges after her teeth were cleaned. If the dosage is 7.75 mg for every pound, how much medicine was given?

To make a profit, a company's revenue must be greater than its operating costs. The company's revenue is modeled by the expression 7.5x - 100, where x represents the number of items sold. The company's operation costs are modeled by the expression 79.86 +5.8x. How many items does the company need to sell to make a profit? The inequality that will determine the number of items that need to be sold to make a profit is The solution to the inequality is The company must sell at least profit. items to make a

Determine the validity of the following argument using an Euler diagram: Statement: Every day I practice either piano or guitar. Statement: Yesterday I did not practice piano. Conclusion: Yesterday, I practiced guitar. Select the correct answer below: Yes, this is valid. No, this is not valid. There is no way to tell if this is valid from the information given.

A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 32 batteries of each type. (a) How many ways can a total inventory of 32 batteries be distributed among the eight different types? vertical bars and crosses, with the types Following the model of Example 9.6.2, represent each way of distributing the inventory as a string of batteries corresponding to the spaces around the vertical bars and the batteries corresponding to the crosses. It follows that the number of ways the total inventory can be distributed is (b) How many ways can a total inventory of 32 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries? (c) How many ways can a total inventory of 32 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?

Suppose that five microchips in a production run of fifty are defective. A sample of seven is to be selected to be checked for defects. (a) How many different samples of seven can be chosen from the production run of fifty? (b) How many samples will contain at least one defective chip? The set of samples that do not contain any defective chips and the set of samples that contain at least one defective chip ... are sets. So, the number of samples with at least one defective chip is (c) What is the probability (as a percent) that a randomly chosen sample of seven contains at least one defective chip? (Round your answer to one decimal place.)

Determine whether the statement is true or false, and explain why. Three sets divide the universal set into at most 6 regions. Choose the correct answer below. A. The statement is true. This statement applies to all Venn diagrams with three sets. B. The statement is false. Three sets divide the universal set into at most 8 regions. C. The statement is false. Three sets divide the universal set into at most 6 regions. D. The statement is false. Three sets divide the universal set into at most 4 regions.