Sets and Relations Questions and Answers

Show only one step of the 4th order Runge Solution of the following initial value problem wit Ku 4x 0 2 1 x 10 dx y 0 0 375 2x dy 20y 0 dy 0 0

A survey of a random sample of 1280 student loan borrowers found that 218 had loans totaling more than 40 000 for their undergraduate education a Construct and interpret a 95 confidence interval for the true proportion of all student loan borrowers who have loans totaling more than 40 000 Make sure to follow the State Plan Do Conclude steps b Suppose you wanted to estimate the true proportion of all student loan borrowers who have loans totaling more than 40 000 with 95 confidence to within 1 Calculate the sample size you would need Use the sample proportion to estimate the population proportion

You are dealt one card from a standard deck of cards What is the probability of being dealt a heart or a eight Write your answer as a simplified fraction

Problem 4 2 points Is there a pair of STS 7 s defined on the same set S 1 2 3 4 5 6 7 that have exactly five triples in common If yes find such a pair otherwise explain why such a pair cannot exist

Shade B U D on the Venn diagram U B D

Sets B and Care subsets of the universal set U These sets are defined as follows U 3 5 6 7 9 B 3 6 C 3 7 9 Find the following sets Write your answer in roster form or as a B UC

For each statement choose if it is simple or compound If it is compound choose which type Statement a If the plane is late I ll miss my connection b The grass is green c The tree is an oak or the tree is an elm Type of statement O Simple Compound Choose one Conjunction O Disjunction Conditional O Biconditional Choose one O Simple O Compound Choose one

A college radio station surveyed 360 incoming freshmen to see how many like jazz music and how many like rap music The Venn diagram below shows the results Each number gives the number of freshmen who fall into that Venn diagram category All freshmen in the survey Like jazz 107 86 Like rap 99 68 a How many of the freshmen do not like rap music freshmen b How many of the freshmen like both jazz music and rap music freshmen c How many of the freshmen like jazz music or rap music or both freshmen

Construct a Venn diagram illustrating the sets below U a b c d e f g h y d e f h Z a c g a 6 b h U These buttons change the Venn diagram Z

Let the set A be defined as follows A 83 59 55 13 3 a Find the total number of subsets of A 0 b Find the total number of proper subsets of A 0

In the braces below list all subsets of the set 1 2 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 0 0 0 0

For each pair of sets choose the best description a A is the set of even numbers greater than 17 and less than 23 B is the set of integers greater than 1 and less than 5 b A is the set of integers greater than 20 and less than 24 B 21 22 23 c A g j k B q r t w Pair of sets d A 73 74 75 76 24 25 26 27 B Description equivalent but not equal O equal but not equivalent O both equivalent and equal O neither equivalent nor equal O equivalent but not equal equal but not equivalent O both equivalent and equal O neither equivalent nor equal O equivalent but not equal O equal but not equivalent O both equivalent and equal neither equivalent nor equal O O O O equivalent but not equal equal but not equivalent both equivalent and equal neither equivalent nor equal

Columbia was tragically destroyed during its return to Earth This was the result of a variety of engineering decisions that we can still learn from today Read the blog post by retired NASA Space Shuttle flight director and program manager Wayne Hale https waynehale wordpress com 2013 01 31 after ten years enduring lessons Write a personal reflection based on the blog post Consider the following prompts What can you learn from this tragic event that you can apply to your career as an engineer What actions by engineers could have potentially prevented the loss of Columbia In what ways are these lessons connected to this class Measurements Instrumentation Are there measurements that perhaps should have been made but weren t or measurements that were not made with sufficient

nd the GCF of 12x y z4 30x4y z 42x y4 5 2 3

Consider the linear program below and answer the following Min s t Min s t A B 20 a Write the problem in standard form 8A 58 24 182 11 1A 182 10 1854 S 8A 5B 2A 18 1A 18 0A 18 c What are the values of the slack and surplus variables 11 10 A B S S S70 b Solve the problem using the graphical solution procedure What is the value of the objective function at A B 4

Use the graph of y f x to answer the following 52 41 4 3 11 M 22 4

200 is what percent of 310 200 is of 310 Round answer to the nearest tenth of a percent

Prove for any sets A and B that AUB ANB HOME

Suppose the function g statisfies 32x 2x 127 g x x 16x 65 We want to use the Squeeze Theorem to evaluate lim g x 18 First evaluate lim H 8 32x2x2 127 Next evaluate lim x 16x 65 x 8 Therefore by the Squeeze Theorem lim a r

4 Prove or disprove the following issettion Let G H and K be groups If GXK H x K

Question 13 1 point 4 Listen How much more intense is an earthquake of magnitude 3 6 than an earthquake of magnitude 1 8 a twice as intense Ob 63 times more intense c 1 8 times more intense d 100 times more intense Question 14 1 point Saved 4 Listen A bacterial population doubles every 4 months If there were originally 2000 cells in the sample how many will there be in 2 months

Skipped Bookmarked Which of the following describes the composition of a frequency table O Can include 2 columns but no more than 5 Must include at least 4 columns O Can include from 1 to 4 columns Must include at least 2 columns but can include up to 4 columns 7 10 complete

One option in a roulette game is to bet 25 on red There are 18 red compartments 18 black compartments and two compartments that are neither red nor black If the ball land on red you get to keep the 25 you paid to play the game and you are awarded 25 If the ball lands elsewhere you are awarded nothing and the 25 that you bet is collected Fin the expected payback for this roulette game if you bet 25 on red The expected payback is Round to the nearest cent as needed

If A 3 7 9 15 16 28 and B 0 3 15 16 21 24 how many elements are there in the intersection of these two sets

1 Suppose you randomly guess the answer to each of 10 true or false questions What is the probability that you will get exactly half of the questions right Round your answer to the nearest thousandth 00 123 00 205 00 246

If not stated compounding frequency must be A Daily B Monthly C Weekly D Annual

You are planning to lend 7 000 to someone you know If you change him an annual interest rate of 3 4 compounded monthly how much will he owe you in 4 years Round to the nearest dollar

11 Consider the two triangles below with the congruences marked Are you given enough information to prove that these two triangles are congruent If so what reason would you give and what congruence statement would you write D C E

5 By using a single diagram illustrate a drawing to show the datum transformation From Coordinate System A to Coordinate System W at point P

Sequences and Functions Question 8 What is the closed form definition for the sequence below 4 12 36 108 81 Note that 4 is considered the 1st term Select one Ot n 4 3 1 t n 3 1 O t n 4 3 Ot n 4 3

Solve each inequality graph the solution and give interval notation Use U capital u as in umbrella for Union and oo two lower case o s as in octopus for infinity 4x 3 15 5 4 3 2 1 0 Clear All Draw Interval notation for the above graph and inequality is 2x 52 7 5 4 3 2 1 0 Clear All Draw 2 2 3 4 5 A

Portfolio A B C D Expected return 18 5 11 8 Standard deviation 12 7 14 20 Analyse the portfolios and make a conclusion on the portfolio that cannot lie on Markowitz efficient frontier Give reasons for your argument 9 marks

Sets L and D are defined as follows L 4 7 8 D 1 2 3 8 Answer each part below Write your answer in roster form or as a Find the intersection of L and D Ln D 0 b Find the union of L and D LU D 0 X 8 0 0

There are two bags containing only white and black marbles Bag A has 12 black marbles and 3 white marbles Bag B has 15 black marbles and 5 white marbles A marble is randomly chosen from each bag List these events from least likely to most likely Event 1 choosing a black marble from Bag B Event 2 choosing a black marble from Bag A Event 3 choosing a blue marble from Bag B Event 4 choosing a black or white marble from Bag A Least likely Most likely Event Event Event Event

A committee consisting of 6 people is to be selected from eight parents and four teachers Find the probability of selecting three parents and three teachers OA 2 33 ES OB 100 231 33 OD 10

Write the following compound statement in symbolic form and construct a truth table The tea is hot and the wine is not chilled p The tea is hot q The wine is chilled Determine the symbolic form of the compound statement and construct a truth table for the symbolic expression P T T www q T F

Determine whether A B ACB BCA ACB BCA or if none of these applies A x x is a type of food B pasta cheese apples eggs Which of the following are true statements Select all that apply ACB BCA A B ACB BCA None of the ob

A triangle of three numbers the product of their multiplication is 24750 where the product of adding one of the two numbers is equal to the square of the third number what is it Hint the number is multiples of 5

An object is dropped off a shelf and falls a distance "h" in one second. In the next second it will fall... A. h B. 2h C. 3h

Find the magnitude and direction angle of the vector v. v = 3(cos 50°i + sin 50°j) magnitude direction angle

A fair coin and an unbiased die are tossed. Let A be the event head appear on the coin and B be the event 3 on the die. Check whether A and B are independent events or not.

The government welfare program includes 1. Social Insurance Program II. Health Insurance Program III. Assistance Program O I only OI, II,& III together O I & II only

What is the best sentinel value if the data is all positive value, cannot be zero but can be a negative value (A) No answer (B) any positive value (C) any negative value (D) O (E) -1

An experiment involves tossing a pair of dice, one green and one red, and recording the numbers that come up. If x equals the outcome on the green die and y equals the outcome on the red die, describe the sample space S. Complete parts (a) and (b) below Describe the sample space S by listing the elements (XV) a. S=((1,1). (2.2), (3,3), (4,4), (5,5), (6,6)) b. S= ((1,1), (1,2), (1,3), (1.4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2.6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,0), (5,5), (5,6). (6.6)) c. S-((1,1), (12), (1,3), (1.4), (1,5), (1.6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6).(5,1), (5,2), (5,3), (5,4), (5,5), (5.0), (0,1), (6,2), (6,3), (6,4), (6,5), (6,6)) d. S=((1,2), (1.3), (1,4), (1.5), (1,6), (2.1), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,5), (4,6), (5, 1), (5,2), (5,3), (5,4),(5,6), (0.1), (6,2), (6,3), (6,4), (6,5))

Define an event that has as its elements the points (FFF, NFF, FFN, NEN). A. At least one river was safe for fishing. B. The second river was safe for fishing. C. The first river was not safe for fishing. D. This event is the same as the sample space.

Describe the sample space S by using the rule method. (A) S={(x,y) |1 ≤x≤6, 1≤y≤6, and x≠y} (B) S={(x,y) | 1≤x＜y≤6} (C) S={(x,y) | 1≤x≤6 and 1≤y≤6} (D) S={(x,y) | 1≤x≤6, 1≤y≤6, and x = y}

List the elements of 3 corresponding to event E that at least two of the rivers are safe for fishing. A.E=(FFN, FNF, NFF) B. E=(FF, FFF, FFN, FNF, NFF) C. E=(FFF, FFN) D. E=(FFF, FFN, FNF, NFF)

An engineering firm is hired to determine if certain waterways are safe for fishing. Samples are taken from three rivers. Complete parts (a) through (c) below. (a) List the elements of a sample space S, using the letters F for safe to fish and N for not safe to fish. A. S = (FFF, FFN, FNF, FNN, NFF, NFN, NNF, NNN} B. S = (FFF, NNN) C. S= (F, N. FF, FN, NF, NN, FFF, FFN, FNF, FNN, NFF, NFN, NNF, NNN) D. S=(FFF, FFN, FNN, NNN)

Two married couples have bought 4 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the men sit together to the right of all the women? (a) The 4 different people can sit in __ different ways. (b) There are __ different ways that each couple could sit together.

The lifespans of domesticated cats are normally distributed, with a mean of 15.7 years and a standard deviation of 1.6 years. What is the probability that a given cat will live at least 15.7 years? Select one: 50% 68% 0% 100%