Sets and Relations Questions and Answers

For f(x) = 5x -2 and g(x) = 3x^2 - 4. find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(-2); d. (gof)(-2) a. (fog)(x) = (Simplify your answer.) b. (gof)(x) = (Simplify your answer.) c. (fog)(-2) = (Simplify your answer.) d. (gof)(-2) = (Simplify your answer.)

If set A contains four distinct numbers and set B contains seven distinct letters, how many elements are in (A ∪ B)? Enter

The function f(x) = x + 19 is one-to-one. Find an equation for f1(x), the inverse function.

Solve the equation x³ + 2x² - 5x-6=0 given that 2 is a zero of f(x) = x³ + 2x² - 5x - 6.

Solve the equation x3-13x² +47x-35= 0 given that 1 is a zero of f(x) = x3 - 13x² + 47x - 35.

For the given data: 1; 9; 15; 22; 23; 24; 24; 25; 25; 26; 27; 28; 29; 37; 45; 50 Determine the Quartiles, Q1, Q2 and Q3 of the data: Q1: Q2: Q3:

If A = {even numbers) and B = {odd numbers), which of the following is true? Enter a, b, c, d, or e. a. 39 € A c. 48 € B b. An B=0 d. AUB=A e. none of the above

Which of the following equations demonstrate that the set of polynomials is not closed under the certain operations? A. Multiplication: (x² - 5x+3)(x - 5) = x² - 10x² +28x-15 B. Division: (x²+x)+(x+1)=x C. Division: (x² - 5x+3)+(x-5) = x+= D. Subtraction: (3x² + x³)-(-2x4+x³) = 5x*

Name the kind or kinds of symmetry the following figure has: point, line, plane, or none. (Select all that apply.) O plane line none point

Set A and the universal set U are defined as follows. U = {h, p, q, r, x, y) A = {p, r, x} Find the following sets. Write your answer in roster form or as Ø. (a) 4nØ = (b) AU A' =

How many solutions are there to the equation below? 8(x-3) = 8x-24 A. Infinitely many solutions B. No solution C. One solution

Set D and the universal set U are defined as follows. U = {2, 3, 4, 5, 6, 7, 8} D=(5, 6, 8} Find the following sets. Write your answer in roster form or as Ø.

Express the following interval in set-builder notation and graph the interval on a number line. [0, 8) What is the interval in set-builder notation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. All real numbers. C. There is no solution.

- Which of the following rules describes the translation of point P(-5, -4) to point P'(-8, -7) a. (x,y) → (x-3, y + 3) b. (x, y) → (x-3, y-3) c. (x,y) → (x+3, y− 3) d. (x,y) → (x+3, y + 3)

Julia can make a key chain in 2 minute(s) 54 seconds. At this rate, which is closest to the amount of time she will need to make 9 key chains? Choose the correct answer below. A. 2 minutes B. 18 minutes C. 27 minutes D. 3 minutes

Unit 09 Learning Target #1: I can describe subsets of a sample space in terms of outcomes, unions, intersections, and complements. Given the following sets C={1, 4, 7, 9} D={3, 4, 5, 7, 8} Determine if the following are true or false CCD [Select] DCC [Select] Cn D=Ø [Select]

Learning Target #1: I can describe subsets of a sample space in terms of outcomes, unions, intersections, and complements. Given the following sets A-(1, 5, 7, 8) B-(1, 5, 7, 9) Find AUB [Select] Find A B [Select] Find A [Select ]

Which of the numbers listed below are solutions to the equation? Check all that apply. x²=-25 A. -5 B. 5 C. 625 D. 12.5 E. 50 F. none of these

Bill is trying to plan a meal to meet specific nutritional goals. He wants to prepare a meal containing rice, tofu, and peanuts that will provide 159 grams of carbohydrates, 320 grams of fat, and 184 grams of protein. He knows that each cup of rice provides 41 grams of carbohydrates, 0 grams of fat, and 2 grams of protein. Each cup of tofu provides 6 grams of carbohydrates, 8 grams of fat, and 22 grams of protein. Finally, each cup of peanuts provides 25 grams of carbohydrates, 74 grams of fat, and 29 grams of protein. How many cups of rice, tofu, and peanuts should he eat?

Given: Universal Set U = {1, 2, 3, 4, 6, 8} Subset B = {1, 2, 3, 4) What is the complement of Set B in Set U? a) {1, 2, 3, 8} b) {6, 8} c) {1, 2, 3, 4) d) {1, 2, 3, 4, 6, 8}

Given the following equation what are the two important points used for graphing? y = 2.3x+1 (-1, 2) and (0, 6) (0, 2) and (1, 6) (0, 3) and (1, 5) (1, 2) and (2, 6)

In a class of 40 students, 34 like bananas, 22 like pineapple, and 2 dislike both fruits. A student is randomly selected. Find the probability the student: a) Likes both fruits b) Likes at least one fruit c) Likes bananas given that he or she likes pineapples d) Dislikes pineapple given that he or she likes bananas e) Are the events independent?

A bear is an animal and a zoo contains many animals, including bears. Three classes Animal, Bear, and zoo are declared to represent animal, bear, and zoo objects. Which of the following is the most appropriate set of declarations?

Kylie is ordering a taxi from an online taxi service. She has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far she travels. She wrote an equation to represent her total cost, y = 3.5+2.3x, where y represents the total cost in dollars and cents, and a represents the number of miles she travels. What could the number 3.5 represent in the equation? How much the taxi costs per mile. The flat charge to order the taxi. The total charge for 1 mile. How far Kylie can ride for $1.

Solve the system algebraically. 5x + 3y = -3 x = 3y - 15

Which set of ordered pairs represents y as a function of x? A {(0, 0), (-1, 2), (-1, -2), (-2, 4), (-2,-4)} B {(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)} C {(0, 0), (0, 1), (0, 2), (0, -1), (0, -2)} D {(0, 0), (-1,-0.5), (-2,-1), (-3,-1.5), (-4,-2)}

The volume of a gas varies directly with its temperature and inversely with its pressure. When the temperature is 125 Kelvin and the pressure is 15 lb/cm², the volume is 100 m³. What is the volume when the temperature is 275 Kelvin and the pressure is 25 lb/cm²? A. 118 m³ B. 125 m³ C. 132 m³ D. 148 m³

Which of the following is the contrapositive and negation of the following conditional statement? "If I don't have a mask then I cannot go into the store." Contrapositive: If I can go into the store then I have a mask. Negation: I don't have a mask and I can go into the store. Contrapositive: If I can go into the store then I don't have a mask. Negation: I have a mask and I can go into the store. Contrapositive: If I have a mask then I can go into the store. Negation: I have a mask and I cannot go into the store. Contrapositive: If I cannot go into the store, then I don't have a mask Negation: If I don't have a mask, then I can go into the store.

Let E represent the set of all of the prime numbers that are less than 20. Let T represent the set of the factors of six. If x represents the amount of elements that are in ur, find the value of -3x+11. -22 -31 -19 -13 -28

Ricardo and Kim rowed their canoes from their base camp to a fishing camp. They rowed a distance of x miles upstream on one river, (3x² - 9) miles downstream on another river, and (2x + 9) miles across a calm lake. Which expression is equivalent to the total distance, in miles, Ricardo and Kim rowed their canoes? 5x² 6x² 3x²+2x 3x² + 3x

For the 250 students asked, 96 enjoy Korean Dramas, 125 adore Western TV Series, and 148 love Anime Shows. Also, 52 enjoy both K-Dramas and Western TV Series, 56 adore both Anime and Western TV Series, and 64 love both K-Dramas and Anime Shows. Moreover, 45 loves to watch all three types of shows. How many students do not watch Anime or K- Dramas? a. 62 students b. 70 students c. 81 students d. 83 students

A pet store keeps track of the purchases of customers over a four-hour period. The store manager classifies purchases as containing a dog product, a cat product, a fish product, or a product for a different kind of pet. The data to the right was recorded. Complete parts (a) through (d) below. (a) How many purchases were for a dog product only? purchases (Type a whole number.) (b) How many purchases were for a cat product only? 87 customers purchased a dog product, 98 customers purchased a cat product, 27 customers purchased a fish product; 24 customers purchased a dog and a cat product; 7 customers purchased a dog and a fish product, 11 customers purchased a cat and a fish product, 3 customers purchased a dog, a cat, and a fish product; 36 customers purchased a product for a pet other than a dog, a cat, or a fish. purchases (Type a whole number.) (c) How many purchases were for a dog or fish product? purchases (Type a whole number.) (d) How many purchases were there in total? purchases (Type a whole number.)

Determine which symbol belongs in the blank to make the statement true. {-1,0,7} _{0,8,- 1,6,7}

Let U= {a,b,c,d,e,f,6,7,8,9,10,11), X = {a,b,c,7,8,9), and Y = {b,d,f,6,8,10}. List the members of the set X'nY', using set braces. X'nY' = {} (Use a comma to separate answers as needed.)

Socialist feminism argues that dismantling the capitalist heirarchical system is sufficient to eradicate gender inequalities True False

Let U = { 14, 15, 16, 17, 18, 19, 20}, A={17, 18, 19, 20). Use the roster method to write the set A'. A'= (Use a comma to separate answers as needed.)

If h(x) = {(0, -9), (5,2), (8, -3), (10, 11)}, which set of ordered pairs represents the inverse of h(x)? A. ((0, 9), (-5,-2), (-8, 3), (-10, -11)} B. ((-9,0), (2, 5), (-3, 8), (11, 10)} C. {(9, 0), (-2,-5), (3, -8), (-11, -10)} D. ((0.-9), (5,2), (8, -3), (10, 11)}

Let U ={a,b,c,d,e,f,8,9,10,11,12,13), X = {a,b,c,9,10,11), and Y = {b,d,f,8,10,12). List the members of the set X'nY', using set braces. X'∩y' = (Use a comma to separate answers as needed.)

Let U = { 6, 7, 8, 9, 10, 11, 12), A = {8, 10, 11, 12). Use the roster method to write the set A'. (Use a comma to separate answers as needed.)

Suppose S={-2, -1, 0, 1, 2} and T={0, 1, 2, 3, 4). Which set represents S∩T? {3,4} {0, 1, 2} {-2, -1} {-2, -1, 0, 1, 2, 3, 4}

Identify the Domain and Range for the following set of coordinates: (-4,2), (3,-5), (4,-2), (9,-7) Select one: a. D = {4, -3, -4, -9} and R = (-2, 5, 2, 7}. b. D = (-2, 5, 2, 7) and R = {4, -3, -4, -9}. c. D = {2, -5, -2, -7} and R = {-4, 3, 4, 9}. d. D={-4, 3, 4, 9) and R = {2, -5, -2, -7}.

Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function? Select all correct answers. Select all that apply: {(2, 10), (8,8), (-4,7), (3, 10)} {(8,6), (-2,-1), (-4,-2), (-2, 8)} ((-3,4), (7,6), (0, 1), (0,8)} ((9,6), (6,0), (1,-5), (0,6)} {(2,1), (2,0), (9, 14), (-3,8)}

In 2003, the population of an African country was about 7.6 million people, which is 3 million more than 2 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950.

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

Let U = {1,3,5,6,8,9,14,17,18). Determine the complement of the set (1,3,5,8,9,14,17,18). The complement is. (Use a comma to separate answers as needed. Use ascending order.)

Explain why the empty set is a subset of every set. A. If there is at least one element of set A that is not an element of set B, then A is not a subset of B. If A is the empty set, which contains no elements, then there can never be any elements in A, much less elements in A that do not belong to B. B. If all elements in set A are also elements of set B and all elements in set B are also elements in set A, then A and B are subsets. If A is the empty set, then there can never be any elements in A, much less elements in A that belong to B. C. If there is at least one element of set A which is also an element of set B, then A is a subset of B. If A is the empty set, which contains no elements, then there can never be any elements in A, much less elements in A that belong to B.

Express the given set using the roster method. The set of natural numbers less than 6. Express the set of natural numbers less than 6 in roster form. (Use a comma to separate answers as needed. Use ascending order.)

In an international food festival, Scott can try foods from Greece, Japan, and Korea. He can choose to try foods from some, none, or all of these countries. In the braces below, list all the possible sets of countries whose food Scott can try. 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.

Sets A, B, and C are subsets of the universal set U. These sets are defined as follows. U = { f, g, h, p, q, r, x, y, z } A = { f, g, p, q } B = { g, h, q, x, y } C = { p, q, x, y, z} Find A' ∩ (C∪B). Write your answer in roster form or as Ø. A' ∩ (C∪B) =

Select ⊆ or ⊈ for the blank so that the resulting statement is true. {Sunday, Thursday} {Friday, Saturday, Sunday, Monday, Tuesday} Choose the correct answer below. A. ⊆ B. ⊈