Functions Questions and Answers

K Consider the universal set U ice cream hat sofa potato chip flat screen TV apple strawberry chicken cell phone computer muffin pencil Let M x x is human made Let E y y is edible Determine M N E Determine all elements of Mn E Select all that apply A C flat screen TV E potato chip G ice cream 1 sofa K strawberry M MnE is the empty set hat GOOD B apple D pencil F muffin H cell phone J chicken L computer

The number of elements in each region are shown in the Venn diagram to the right Find n B n B Points 0 of 1

Consider the universal set U potato chip fish TV hat hammer radio cell phone pineapple muffin coconut shoe pizza Let E y y is edible Determine E Determine all elements of E Select all that apply 00 A fish C radio E cell phone G potato chip I coconut K muffin M E is the empty set B hat D hammer F pineapple H shoe J TV L pizza

K Let U a b c d e f g h i j k Let A c d f g i j Let B c e g i j Let C a c d f h Determine ANC Choose the correct answer below and if necessary fill in the answer box in your choice OA ANC 1 Use a comma to separate answers as needed B An C is the empty set

Draw a scatter diagram and find r for the data shown in the table Round r to three decimal places OD No Solution 25 24 23 22 21 20 X 0 1 2 19 18 17 16 15 14 13 12 44 3 4 10 9 8 y 24 18 15 13 10 Fill

Use the table to answer the question Consider the set V GPA below 3 0 Which set is equivalent to but not equal to V Choose the set equivalent to V but not equal to V This que OA Carmen Gina Brenda OB Dana Elston Carmen Gina Brenda Frank OC Dana Carmen OD Elston Carmen Gina point s possible Class Rank GPA Acti 3 3 Bane 2 6 Year 2 2 Base 2 5 Soc 3 2 Ten 3 2 Cho Major Dana History Junior Elston Physics Senior Carmen Business Freshmen Gina History Senior Brenda History Junior Frank Business Junior

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places z 1 5 D

A normal distribution has a mean of 85 7 and a standard deviation of 4 87 Find the data value corresponding to the value of z given Enter your answer to four decimal places z 0 85

K List all the two element subsets of the following set 4 8 12 16 Choose the correct answer below OA 4 8 4 12 4 16 8 12 8 16 12 16 OB 4 8 8 12 12 16 OC 4 8 4 12 4 16 8 12 8 16 12 16 OD 4 8 4 12 4 16 8 12 8 16 12 16 4 8 12 16

Find an element of set A that is not an element of set B A y y is a month of the year B y y is during the spring Choose the correct answer below O September O May O March O April

K Replace the with either E or to express a true statement 4 x x is a rational number Choose the correct answer below O 4 x x is a rational number O 4 E x x is a rational number

Use an alternative method to express the following set 2 4 6 Choose the correct set below OA x x is a natural number less than or equal to 6 O B O C x x is an even natural number x x is an even natural number less than or equal to 6

e ne 6 he 15 87 Two smooth disks A and Beach have a mass of 0 5 kg If both disks are moving with the velocities shown when they collide determine their final velocities just after collision The coefficient of restitution is e 0 75 of 15 88 Two smooth disks A and Beach have a mass of 0 5 kg If both disks are moving with the velocities shown when they collide determine the coefficient of restitution between the disks if after collision B travels along a line 30 counterclockwise from the y axis CA 6 m s

F 3 ft r 3 ft B d Prob 15 66 15 67 The three balls each weigh 0 5 lb and have a coefficient of restitution of e 0 85 If ball A is released from rest and strikes ball B and then ball B strikes ball C determine the velocity of each ball after the second collision has occurred The balls slide without friction B C

2x 3y 11 x 3y 1 What is the solution x y to the given system of equations O 1 4 O 4 1 4 11 O 11 4

For the same probability density function in problem 13 f x 600x 2 for 100 m x 120 m and zero for x elsewhere find the variance and the standard deviation of the probability density function Be sure to round your answer to three decimal places O Variance 123 186 St Dev 11 099 O Variance 13 681 St Dev 3 699 O Variance 23 245 St Dev 4 821 O Variance 33 186 St Dev 5 761

In manufacturing process involving several machines the average down time t in hours is giv by the probability density function f t 0 5e 0 5t for t 0 and f t 0 fort 0 find the probability that the average down time is 2 hours or more 0 368 1 06 O 0 06

If I perceive what appears to be a red door then there really is a red door there There really is a red door there Therefore perceive what appears to be a red door What is this argument Valid Invalid strong Weak

ange the following number to polar form and then perform the operation Express the result in polar form and rectangular form Check your result by taking the power of the original number in rectang 3 2j Write the complex number to the power in polar form 3 21 3 cos j sin Simplify your answers Round to two decimal places as needed Type any angle measures in degrees Use angle measures greater than or equal to 0 and less than 360 Convert the expression in polar form to rectangular form Use the answer from the previous part to find this answer Simplify your answer Type your answer in the form a bj Round to the nearest integer as needed Check your answer by taking the power of the rectangular form 3 2j Simplify your answer Type your answer in the form a bj

orm the indicated operation Leave the result in polar form 50 214 4 12 175 37 SCELE 0 214 4 12 175 37 mplify your answers Type integers or decimals rounded to two decimal places as needed Type your answer in degrees Use angle measures greater than or equal to 0

5 The number is a solution of sin z 0 close to 3 see Figure 4 You will use Newton s method for sin z 0 to create numerical estimates for wh 10 Z2 Figure 4 Graph of y sin z a Write out the recursion for Newton s method used to solve sin z 0 b Using Newton s method for sin r 0 with z 3 find the first n for which z and Int1 agree to 5 digits after the decimal point Use radians not degrees

Thursday 1 Find the number that makes an equivalent fraction 7 10 40 3 Use or to compare the fractions 4 3 5 10 2 Find the number that makes an equivalent fraction 1 10 4 4 Determine if the fraction shown is less more or equal to half 1

1 Recall the test IVP y Ay and y 0 a We consider the so called implicit Trapzoidal method h W 1 W 7 f t 1 W 1 f ti wi to solve the test IVP which is a stiff system a Write down the stability function Q hA for the implicit Trapzoidal method Hint Q hX is obtained by applying the implicit Trapzoidal method to the test IVP see Lec 11 Theorem 1 b For the stability function show that if hA is a real number and h 0 we have Q hA 1 c Optional For the stability function verify that for any h such that Re hA 0 we have Q hA 1 This shows the implicit trapezoidal method is A stable

A four sided closed field traverse has the fol lowing angles A 81 53 30 B 70 28 30 C 86 09 30 D 121 30 30 The lengths of the sides are as follows AB 636 45 ft BC 654 45 ft CD 382 65 ft DA 469 38 ft The bearing of AB is S 17 17 W BC is in the N E quadrant a Balance the field angles b Compute the bearings or the azimuths

Find n A for the following set A x x is a living German chancellor born before 1700 n A Type a whole number

Section 3 Thinking Inquiry Directions For each of the questions in this section show all work to get full marks 8 1 point A scatter plot is created for a set of data A linear model for the data has a coefficient of determination of R 0 7306 A quadratic model for the data has a coefficient of determination of R 0 9131 An exponential model for the data has a coefficient of determination of R2 0 9727 What is the model best fits the data

2 points The volume of a cylindrical container with a height equal to its radius is given by the equation If the volume of the container is 817 cm then the radius to the nearest tenth of a centimetre is

Instructions Use algebraic techniques to solve problems unless otherwise instructed Show the calculations leading to your answers except basic arithmetic Simplify and circle your final answers 1 6 pts Hyperbolic Sine Function Is this function even odd or neither Prove your answer using the symmetry tests What type of symmetry if any does its graph exhibit ex e X sinh x 2 73 2 6 1 5 9e 2 10 pts Consider the logistic model of world population given by P t 0 is the year 2000 and the population is measured in billions a Use the model to estimate the world population in the years 2080 and 2150 0 02t where time

Solve each problem 1 Which expression s are equivalent to 2 6 A 2 6 B 2 6 C 2 6 D2 6 3 Which expression s are equivalent to 8 3 4 94 A 8 3 4 94 B 8 3 4 94 C 8 3 4 94 D 8 3 4 94 5 Which expression s are equivalent to 3 3 5 2 A 3 3 5 2 B 3 3 5 2 C 3 3 5 2 D 3 3 5 2 2 Which expression s are equivalent to 7 6 A 7 6 B 7 6 C 7 6 D 7 6 4 Which expression s are equivalent to 4 5 A 4 5 B 4 5 C 4 5 D 4 5 6 Which expression s are equivalent to 5 18 3 54 A 5 18 3 54 B 5 18 3 54 C 5 18 3 54 D 5 18 3 54 1 2 3

The diameter of a pipe is normally distributed with a mean of 0 7 inch and a variance of 0 0025 What is the probability that the diameter of a randomly selected pipe will exceed 0 8 inch You may need to use the standard normal distribution table Round your answer to three decimal places Hint take the square root of the variance to find the standard deviation 0 05 X

Given the information find the equation for the least squares line as well as the correlation coefficient n 8 x 40 y 48 Exy 240 Ex 210 y 288 E y r

The graph of a frequency distribution of a large number of measurements tends to look normal or X

Find the standard deviation rounded to the nearest unit for the data indicated clients Date Oct 23 Oct 24 Oct 25 Oct 26 Oct 27 Oct 28 No of Clients 11 8 11 15 11 10

Find the range and the standard deviation correct to two decimal places 775 776 777 778 779 range standard deviation

Let p and q represent the following simple statements p This is a kiwi q This is a fruit Write the following compound statement in symbolic form If this is not a kiwi then this is not a fruit The compound statement written in symbolic form is

7 This graph shows the volume of water in Liam s flask as he hikes the Trans Canada trail Water in Liam s Flask Volume L 2 0 215 1 0 0 5 0 00 8 Distance km 12 16 20 C a Describe what is happening for each line segment of the graph b How many times did Liam fill his flask c How much water was in Liam s flash start of his hike d Identify the denon nt and indener

9 Which of these graphs represents a function Justify your answer Write the domain and range for each graph a Heights and Ages of 8 Students Height cm 180 Number of bicycles 170 160 13 15 17 Age years b Number of Bicycles at School 30 20 8 10 05 0 08 00 16 00 Time

Consider a bundle of consumer goods that costs 100 in the United States The same bundle of goods costs 300 in Malaysia Holding constant the cost of the bundle in each country compute the real exchange rates that would result from the two nominal exchange rates in the following table Cost of Bundle in U S Dollars 100 100 Cost of Bundle in Malaysia Ringgit 300 300 Nominal Exchange Rate Ringgit per dollar 4 50 12 00 Real Exchange Rate Bundles of Malaysian goods per bundle of U S goods

Suppose the selling price of the three month forward British pound is 1 5134 per pound and the spot price is 1 5139 per pound Complete the ollowing formula for the per annum percentage premium or discount to calculate what the pound is worth in the three month forward market herefore the British pound is at a ne spot market against the U S dollar because it is worth in the three month forward market than in

Use the formula in this example to determine the sample size n The estimated prevalence is 25 and the desired confidence level is 95 with a margin of error of 5 This is the same as in the example except the margin of error has been changed Round your answer to the nearest integer n 288 72

T Use the graph to solve the equation tan 3x cos 2x if 0 x 44 Use decimal notation Give your answer to at least two decimal places

1 point Consider the relations R R R3 R R5 on A R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R3 1 1 1 2 2 1 2 2 3 3 4 4 R 1 2 2 3 3 4 R 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply DA R is not symmetric OB R is reflexive OC R is symmetric DD R is transitive DE R is reflexive OF R is transitive G R is not reflexive OH R is reflexive DI R is transitive 3 4 defined by J R3 is not transitive OK R is symmetric

Given the information find the equation for the least squares line as well as the correlation coefficient Round your values to two decimal places n 10 10 Ex 57 y 1 Exy 13 Ex 353 y 4 45 y

Suppose that a country has a GDP of 3 billion no autonomous consumption and total consumption of 2 90 billion The marginal propensity to consume in this economy is Give your answer to two decimals

First use the drag tool to shift the appropriate curve or curves demonstrating the change To refer to the graphing tutorial for this question type please click here Price level Change to Consumption The Classical View LRAS2 AD2

Which expression results in a rational number 1 2 18 2 5 5 3 2 2 4 3 2 2 3

1 point The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB as indicated in the diagram So the distance from P 0 4 3 to the line through the points A 4 2 4 and B 3 5 1 is 612 19 M

1 point Consider the relation R whose digraph is given below 4 2 5 8 3 6 7 List the equivalence classes of R Separate your answers using commas In sets containing more than one element write them from smallest to largest without spaces

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places Z 1 9 16 54 X

The answer above is NOT correct 1 point Consider the relations R R2 R3 R4 R5 on A 1 2 3 4 defined by R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R2 R3 1 1 1 2 2 1 2 2 3 3 4 4 R 1 2 2 3 3 4 R5 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply A R is not symmetric B R is reflexive C R is symmetric D R4 is transitive E R is reflexive F R5 is transitive G R5 is not reflexive H R3 is reflexive I R is transitive J R3 is not transitive K R4 is symmetric None of the above