Sets and Relations Questions and Answers

Decide whether the statement is true or false. Ø∈{Ø} Choose the correct answer below. A. False because Ø contains 0 elements so the only element of {0} is 0. B. True because {Ø} is a subset of Ø. C. False because Ø contains no elements so nothing can belong to it. D. True because {Ø} represents a set with one element, Ø.

A number is selected from the set (1, 2, 3, 5, 15, 21, 29, 38, 500}. If equal elemental probabilities are assigned, what is the probability that the number chosen is either less than 29 or odd? 6/9 7/9 8/9

For the functions f(x) = -6x + 9 and g(x)= 3x + 9 find the following. (a) (fog)(x) and its domain (b) (gof)(x) and its domain

Express the given function has a composition of two functions f and g so that h(x) = (fog)(x), where one of the functions is x9 - 6. h(x)=√x9-6 f(x)=√x (Simplify your answer.) g(x)= (Simplify your answer.) .

5. Theresa decides to donate money to cancer research each year. Her brother, Tony, also decides to contribute. Together, they donate $1,000 per year to cancer research. If Tony is able to donate 1 times the amount that Theresa is able to donate, what is the amount in dollars that Tony will donate after 5 years, assuming the amount and proportions remain the same each year? A. $2,000 B. $2,100 C. $2,450 D. $3,000 E. $3,600

A person chooses a single number in a set containing the numbers from 1 to 50. Find the set representing the event E of choosing a number that that can be evenly divided by 6. Give your answer as a set, e.g. {1, 2, 3), and do not include E = in your answer.

Are the sets A and B finite or infinite? A = {x ∈ Z | -2 < x < 2}, B = {x∈R| - 2 < x <2}. Select the correct answer below: A is infinite and B is infinite A is finite and B is infinite A is infinite and B is finite A is finite and B is finite

Which of the following sets is a subset of B = {green, 66, 9, 70, love, 8}? Select the correct answer below: h = {green, 6, 9, 70, 8} g = {green, love, 8} f={70, love, 88} e = {green, 70, love, 81}

Consider V = {2, 3, 5, 7, 9, 11, 13, 15, 17, 19) as a universal set. Let PC be the set of those numbers that are either multiples of 3 or multiples of 5, excluding 3 and 5. Find the set P. Give your answer in proper set notation, for example {1, 2, 3, 4, 5).Do not include P = in your answer

Which of the following is the set M for all the letters that make up the word MATHEMATICS? Select the correct answer below: M= {M, T, H, C, S} M = {M, A, T, H, E, I, C, S} M = {M, A, T, H, E, M, A, T, I, C, S} M = {A, E, I}

In a class of 107 seniors, 37 students are taking the AP Calculus exam, 39 students are taking the AP Literature exam, and 38 students are taking the AP Biology exam. 9 students are taking the Calculus and Literature exam, 12 are taking the Literature and Biology exam, 14 are taking the Calculus and Biology exam, and 4 students are taking all 3 exams. Make a venn diagram to illustrate the data and then find the probability that a student selected at random will take: Only the Calculus Exam Calculus and Biology, but not Literature No AP exam

Consider the following sets: 1. The set containing all of the days in the month of December, 2. The set containing all of the days in the month of January, 3. The set of all integers between 210 and 242 exclusively. Are these three sets equivalent? Select the correct answer below: Yes No

Answer parts a and b. a. n(A ∪ B) = 16, n(A ∩ B)=3, and n(B) = 9, find n(A). b. If n(A) = 12, n(B) = 25, and n(A ∩ B)=8, find n(A ∪ B). a. n(A)= b. n(A ∪ B) =

Drag the expressions to the correct functions. Not all expressions will be used. Consider the functions fand g. f(x) = 4x² + 1 g(x)=x2-3 Perform the function compositions. - 24x2 +37 4x4 24024 36 1624 + 8x2 + 1 1624 + 8x22 4241112-3 (fog)(x) = (gof)(x) = 414 112-3

What is (Y∩X)c where X = {11, 14, 67, 5, 36,99), Y = (54, 11, 99, 5, 22, 808) and Universal Set= (2, 45, 90, 22, 11, 444, 14, 99, 808, 67, 8, 54, 36,5}? Select the correct answer below: (Y∩X)c = {2, 45, 90, 22, 444, 14, 808, 67, 8, 54, 36} (Y∩X)c = {11, 14, 67, 5, 36, 99, 54, 22, 808} (Y∩X)c = {2, 45, 90, 444, 8} (Y∩X)c = {54, 22, 808}

The event of you going to work is A and the event of you taking leave is B. If these events are mutually exclusive events, using P(A) = 0.55, and P(B) = 0.10, what is P(A/B)?

Among the 30 students registered for a course in discrete mathematics, 15 people know the JAVA programming language, 12 know HTML, and 5 know both of these languages. (a) How many students know at least one of JAVA or HTML? (b) How many students know only JAVA? (c) How many know only HTML? (d) How many know exactly one of the languages JAVA and HTML? (e) How many students know neither JAVA nor HTML?

Given the universal set U consisting of all integers between and including 1 and 20, and let the set A consist of all of the powers of 2 (integers of the form 2^n where n is a whole number) within the universal set. Find the complement of the set A. Write your answer in proper set notation, for example {1, 2, 3, 4, 5, 6}.

What is a set? Describe the use of braces for listing the members of a set.

In the braces below, list all subsets of the set {g, f, e). Write each subset in your list in roster form. If there is more than one subset in your list, separate them with commas. If you need the empty set in your list, use the symbol Ø.

Sets G and I are defined as follows. G= {0, 4, 7, 8) I=(-1, 0, 3, 5, 8} Answer each part below. Write your answer in roster form or as Ø. (a) Find the intersection of G and I. (b) Find the union of G and I.

You and your friend are arguing on whether or not the SPOTTY News graph that was on TV last night was correct. . Your friend stated: I don't believe the graph because they did not start the graph at 0. . You stated: I believe the graph because it clearly shows that one bar is higher than the other, where the graph starts does not matter. Who is correct and why? You are correct, it does not matter where the graph starts. Your friend is correct. You can easily exaggerate data when the graph does not start at 0. Your friend is correct. Everything that they post on the news is gathered through reliable data. You are correct. Everything that they post on the news is gathered through reliable data.

Write each set in the indicated form. If you need to use 11 ." to indicate a pattern, make sure to list at least four elements of the set. As you answer below, remember that the natural numbers are just the counting numbers. This means that 0 is not a natural number, and negative numbers are not natural numbers either. (a) Roster form: (1, 3, 5, 7, ...} Descriptive form: (Choose one) (b) Descriptive form: The set of natural numbers greater than or equal to 5 and less than or equal to 7. Roster form:

In the braces below, list all subsets of the set {e, d). Write each subset in your list in roster form. If there is more than one subset in your list, separate them with commas. If you need the empty set in your list, use the symbol Ø. ({0} Ø X S 0.0.... ?

At the north campus of a performing arts school, 20% of the students are music majors. At the south campus, 30% of the students are music majors. The campuses are merged into one east campus. If 24% of the 1000 students at the east campus are music majors, how many students did each of the north and south campuses have before the merger? The north campus had students.

Read the scenarios below. Determine which scenario can be represented by an inequality, an equation, or a system of equations. Use the drop-down menu to the left of each scenario to select your answer. Choose each option only once. Your parents saved $3000 for a family vacation! Due to reduced travel (caused by COVID-19), each airplane ticket is now only $150! Determine how many airplane tickets you can purchase without exceeding the $3000 budget. When you arrived to your destination for vacation, you took a taxi to the hotel. The taxi fare was $2.14 per mile and you gave the driver a $8 tip. You paid a total of $52.03. How many miles was the airport from the hotel? Once you arrived at the hotel, you and your family ordered in some Chinese food. You spent a total of $80 for 6 meals to buy dinner for your family. The sweet-and-sour chicken meal costs you $12 each and the beef-and-brocolli meal costs you $14 each. How many of each meal did you buy? a. System of Equations b. Equation c. Inequality

Find the payment necessary to amortize the following loan. $7900; 8.4% compounded semiannually; 24 semiannual payments The payment is $ (Round to the nearest cent as needed.)

Identify the property of real numbers illustrated in the following equation. Answer (3-5) (7-5)= [(3-5)-7](5) Commutative Property of Addition O Associative Property of Addition O Distributive Property O Multiplicative Identity Property O Multiplicative Inverse Property O Commutative Property of Multiplication O Associative Property of Multiplication O Additive Identity Property O Additive Inverse Property O Zero Factor Law

A jet plane has 160,000 pounds of fuel after the first hour of flight. The four engines consume a total of 14,000 pounds per hour at its cruising altitude. How many pounds of fuel remain after the 9th hour? 126,000 pounds 272,000 pounds 34,000 pounds 048,000 pounds

The implication operation, i.e. xRy is defined as x implies y, on the set (0,1). Is the relation reflexive? Yes No Is the relation irreflexive? Yes No Is the relation transitive? Yes No Is the relation symmetric? Yes No Is the relation antisymmetric? Yes No Is the relation a poset? Yes No Is the relation an equivalence relation? Yes No O No

A concert hall has 14 seats in the first row, 16 seats in the second row, 18 seats in the third row, and so on. If the pattern continues, how many seats are in the first 10 rows? 140 seats 144 seats 230 seats 320 seats

state the domain for the function below. f(x)=(2x - 6)/(x² + 2x + 5) all real numbers except o and 3 all real numbers of x all real numbers except o all real numbers except 3

Jerome will be buying a used car for $7,000 in 3 years. How much money should he ask his parents for now so that, if he invests it at 7% compounded continuously, he will have enough to buy the car? Jerome should ask for $ (Round to the nearest cent as needed.)

Which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression 5 + 3 (3.8)? 3 (8.3)+5 3 (3.8) +5 (3.3) 8+5 5+3 (24)

Consider the interval [2/9,16/9] (a) Find the length of the interval. (b) If we partition [2/9,16/9] into 7 subintervals of equal length, then (i)the length of each subinterval is (ii)the first subinterval is . (Enter your answer using interval notation.) (iii)the midpoint of the first subinterval is (iv)the midpoint of the second subinterval is

Promenade Limousine Rental You and your friends are planning to go to prom. To rent a limo, it will cost $200 and an additional $25 for refreshments for each passenger. You've already confirmed that you and your best friend will be going. However, your other three friends haven't gotten back to you yet. Each friend (including yourself) will bring along their prom date so the possible number of guests is 4 through 10 (in groups of 2). You need to make a quick budget to split up the potential costs, so you utilize some of your mathematics know-how. For this Performance Task, use these definitions to make sense of the problem and to calculate your final answers. Promenade Dance - A promenade dance (or prom) is a semi-formal (black tie) dance that is typically held near the end of the senior year. Limousine - A limousine (or limo) is a luxury sedan vehicle generally driven by a chauffeur and with a partition between the driver and the passenger compartment. Cost Equation - The formula used to calculate costs is: Total Cost Variable Costs + Fixed Costs Variable costs, as opposed to fixed costs, are those that change based on the amount of some variable. 1. Write a function for the cost where x is the number of passengers. (1 point) 2. Cost Identify the domain of this function. (1 point) Domain: { _______ , _______ , _______, _______ }

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.01.

Let P be the set of integers that are multiples of 3 between 1 and 10 and Q be the set of positive integers that are multiples of 4 and are less than 15. Which of the following list of elements does not belong to the union of P and Q? Select the correct answer below: 05 03 06 04

Consider the set U of all natural numbers and let A be the set consisting of multiples of 6. Which of the following numbers is not part of the complement of A? Select the correct answer below: 17 99 37 24

Which data set has the greatest spread? Set A-{84, 91, 87, 77, 94, 89, 74} Set B-{89, 73, 84, 91, 87, 77,94} Set C-73, 84, 89, 88, 77, 91, 87, 90} Set D-{84, 89, 88, 82, 91, 87, 99} O A. OB. Set B O. C. Set C OD. Set D Set A

Suppose that the function y = f(x) is increasing on the interval [5,9]. Complete parts a through d below. (a) Over what interval is the graph of y = f(x + 2) increasing? The graph of y=f(x+2) is increasing over the interval (Type your answer in interval notation.)

Use the addition property of inequality to solve the inequality and graph the solution on a number line. x-3<2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation.) B. The solution set is Ø, the empty set.

(1 point) UNL has decided to gradually transition from one online gradebook system to another. The percentage of professors still using the old system / years after Fall 2015 is given by a) Evaluate B(0) and B(4). B(0)=| B(4)= B(t) = 100 - 16t. b) Find the slope, the horizontal intercept, and the vertical intercept. Enter the horizontal and vertical intercepts as points (a, b), including the parentheses. Slope: Horizontal Intercept: Vertical Intercept: ⠀⠀ c) What is a reasonable domain for B(r)? What is the range of B(t) on this domain? Be sure to write your answers as intervals. Domain: Range:

7. Tara is solving an equation. Her first step is shown below. Solve 4y - 8(y - 2) = 6 Step 1: 4y - 8y + 16 = 6 Which property justifies Tara's first step? Distributive Property Subtraction Property of Equality Identity Property Associative Property of Multiplication

Determine whether the relation is a function. {(-4,-5), (-2, -9), (2, -8), (2, 8)} Function Not a function

Solve the compound inequality. Graph the solution set. 2x-4>4 and 2x+1 <11 Select the correct choice below and, if necessary, fill the answer box to complete your choice. A. The solution set is (Type your answer in interval notation.) B. The solution set is Ø.

In the following example, an everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe the inverse activity. entering a room Choose the correct answer below. OA. leaving a room OB. not entering a room ...

Sets M and B are defined as follows. M=(3, 5, 7) B=(-2, 2, 3, 5, 6, 8} Answer each part below. Write your answer in roster form or as Ø (a) Find the union of M and B. MUB= (b) Find the intersection of M and B.

A basketball team has two substitute players: Smith and Jordan. The coach can choose to use one, neither, or both of these substitute players in a game. In the braces below, list all the possible sets of substitute players that the coach can use. Write each set in your list in roster form. If there is more than one set in your list, separate them with commas. If you need the empty set in your list, use the symbol Ø.