Math - Others Questions

rove that the relation R defined on the set X Z by mRn 3m 2 n is divisible by 5 is an equivalence relation Determine its equivalence classes 0 R 7 R 1 many different equivalence classes does this relation h

Starting at the same point on a straight road Anna and Benny begin biking with velocities in mi hr given by VA t 2t 2 and VB t 5 t respectively Complete parts a through c below 10 0 01 2 3 4 0 1 2 3 4 L hour s 4 hour s while Anna rides 8 miles in hour s while Benny rides 8 miles in V 0 0 1 2 3 4 5 What does this mean geometrically A The area under the line representing Benny s velocity from 0 to 1 is more than the area under the line representing Anna s velocity from 0 to 1 OB The line representing Benny s velocity is decreasing while the line representing Anna s velocity is increasing OC The lines intersect at a t value before the given time indicating that Benny has passed Anna OD The area under each line from 0 to 1 is the same for both riders 4 b If the bikers ride for 1 hour who rides farther Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals A Since Benny rides 4 5 mile s and Anna rides 3 mile s Benny rides farther OB Anna and Benny both ride mile s OC Since Benny rides mile s and Anna rides mile s Anna rides farther hour s hour s 07 13 012 34 c If the bikers ride for 8 miles who wins the race Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals OA They tie in the race because they both ride 8 miles in O B Benny wins the race because she rides 8 miles in OC Anna wins the race because she rides 8 miles in Save

A large tank of fish from a hatchery is being delivered to a lake The hatchery claims that the mean length of fish in the tank is 16 inches and the standard deviation is 4 inches A random sample of 36 fish is taken from the tank Let X be the mean sample lengt of these fish What is the probability that x is within 0 5 inch of the claimed population mean Round your answer to four decimal places USE SALT

Required information Let P x be the statement the word x contains the letter a What is the truth value of P true The truth value is Click to select Click to select false true

Suppose the following plate is placed on a vertical wall so that the top of the plate is 1 m below the surface of a pool that is filled with water Compute the force on the plate 3 A plate shaped like an isosceles triangle with a height of 3 m and a base of length 2 If a y axis in the vertical direction is drawn on the face of the triangle where the origin is the vertex of the triangle find the width function w y for each value of y on the face of the triangle w y m The force on the plate is N Tupe an integer or decimal rounded to one decimal place as needed eufee

Required information Let Q x y denote the statement x is the capital of y Determine the truth value of Q Detroit Michigan The truth value of Q Detroit Michigan is Click to select Click to select true false

Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to th Show that each of these conditional statements is a tautology by using truth tables Complete the truth table given below for the conditional statement p A p q q p p q og p p q T q Click to select T P q T Click to select FT Click to select K The given conditional Click to select Click to select True False F Click to select Click to select Click to select Click to select statement is not a tautology 4

Required information Let P x be the statement the word x contains the letter a What is the truth value of P orange The truth value of Plorange is Click to select Click to select false true

The Customer Service Center in a large New York department store has determined that the amount of time spent with a custome about a complaint is normally distributed with a mean of 8 3 minutes and a standard deviation of 2 3 minutes What is the probability that for a randomly chosen customer with a complaint the amount of time spent resolving the complaint will be as follows Round your answers to four decimal places USE SALT a less than 10 minutes 0 7700 b longer than 5 minutes c between 8 and 15 minutes 0 5501

Complete the truth table given below for the conditional statement p a A q p pa q P Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Show that each of these conditional statements is a tautology by using truth tables pq r TIT T TIT F TFT FIF T T F T Click to select F T T F p q T T F F T T T T F T F T The given conditional statement is a tautology Click to select Click to select Tru FIT FF 9 r T Click to select v pg 91 T Click to select F F T F Click to select p r T F T Click to select T T T T T Click to select

Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Show that each of these conditional statements is a tautology by using truth tables Complete the truth table given below for the conditional statement p V q A pr q n r r p V q p1 9 1 T T F T F F T F T F T F P T T T T F F F F q T T F F T T F F p V q T T T T T T Click to select Click to select The given conditional statement is a tautology Click to select Click to select True False p 1 T Click to select Click to select F T T T T Click to select F Click to select T F F Click to select T T F T T p V q p 9 T F Click to select F Click to select F F F pVg p 1 q r T Click to select T Click to select T Click to select T

pA pv q q A p q v q pv T by negation law p pv q q pv qv q by associative law FV p q q by negation law pvF by negation law pv q vq by De Morgan s law

Required information NOTE This is a multi part question Once an answer is submitted you will be una Fill the given truth table Fill the truth table for Click to select p You must provide an Click to select noving to the next part PAP Click to select P p

Complete the truth table given below to verify the first De Morgan law p Aq p V q p q 7P79 TT Click to select F p q Click to select T PV q FF Click to select T TA FIT FT Click to select F Click to select TF Click to select TIT T T V

Assume that IQ scores are normally distributed with a standard deviation of 15 points and a mean of 100 points If 120 people are chosen at random what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points Round your answer to four decimal places LAUSE SALT

Required information NOTE This is a multi part question Once an answer is submitted you will be unabl Fill the provided truth tables and check whether the given conditional statements a contingency pv q Click to select Click to select T Click to select F Click to select The given conditional statement is Click to select Click to select tautology P T T F F 9 T F contingency contradiction p pv q Click to select Click to select Click to select Click to select V

P T T p p q Click to select Click to select Click to select Click to select Click to select Click to select Click to select The conditional statement is p p q is a Click to select Click to select F Required information NOTE This is a multi part question Once an answer is submitted you will be L Fill the provided truth tables and check whether the given conditional stateme contingency F q T F T p F F T T F p q Click to select contigency tautology contradiction

P T TFF Required information NOTE This is a multi part question Once an answer is submitted you will be Fill the provided truth tables and check whether the given conditional staten contingency q paq F T Click to select Click to select Click to select F Click to select T p q p Click to select Click to select Click to select Click to select The conditional statement p A q pis a Click to select Click to select contradiction contigency

Fill the following truth table P 9 T T T F T F Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this pa Show that each of these conditional statements is a tautology by using truth tables F F P F F T T pv q Click to select T T F p pv q F Click to select T Click to select PA pv q T T Click to select q

p T Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Complete the truth table given below to verify the associative laws T T T F F F F q T T F F T T F F r T F T F T F T F pv q T T T T T T F F p V q V r T T Click to select Click to select Click to select Click to select q Vr T T T F T T T F PV qVr T T T T Click to select Click to select Click to select Click to select

Determine whether p and p are logically equivalent or not by completing the given truth table 4 p p T Click to select F Click to select

p T T T T F F F F Required information NOTE This is a multi part question Once an answer is submitted you will be unable to rete Complete the truth table given below to verify the associative laws q r T T T F F T T F F F T F T F T F p q T T F F F F F F p q Ar T F F F Click to select Click to select Click to select Click to select qAr T F F F T F F F p q T F F F Click to select Click to select Click to select Click to select

The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews From the past records they have found that the length of a first interview is normally distributed with mean 36 minutes and standard deviation 9 minutes Round your answers to four decimal places LUSE SALT a What is the probability that a first interview will last 40 minutes or longer b Eleven first interviews are usually scheduled per day What is the probability that the average length of time for the eleven interviews will be 40 minutes or longer

Given that x is a normal variable with mean 49 and standard deviation 6 3 find the following probabilities Round your answers to four decimal places LUSE SALT a P x 60 b c P x 50 X X P 50 x 60

y 29 5 X

What is the real size in um of a cell that s 90mm wide on a photograph The scale bar on the photo is 2 7cm long and it represent 5 m Your Answer to

ROBLEM 1 2j 2 j17 Express solution in algebraic and trigonometric forms 9 7j 1 3j 3p Solve z j 3 Express solution in algebraic form 4p Compute 3p Mark on the complex plane solutions of 3 z z 4

In the following problem check that it is appropriate to use the normal approximation to the binomial Then use the normal distribution to estimate the requested probabilities Based on long experience an airline found that about 8 of the people making reservations on a flight from Miami to Denver do not show up for the flight Suppose the airline overbooks this flight by selling 263 ticket reservations for an airplane with only 255 seats USE SALT a What is the probability that a person holding a reservation will show up for the flight 0 92 b Let n 263 represent the number of ticket reservations Let r represent the number of people with reservations who show up for the flight What expression represents the probability that a seat will be available for everyone who shows up holding a reservation P rz 263 P r 255 P r 263 P r 255 c Use the normal approximation to the binomial distribution and part b to answer the following question What is the probability that a seat will be available for every person who shows up holding a reservation Round your answer to four decimal places

Calculate 0 03cm 3 73mm 0 027m 340 m Give the result in mm do not round up your answer Write exact answer Your Answer I

5 6 the A Show that the amount of salad is a rational number B Write the amount of salad as a decimal 7 375 C What will Rafael pay for the salad The temperature dropped steadily by 40 F over a 20 hour period Find the quotient 40 20 and explain what it means in this context Mr Nguyen s credit card Find the quotient 2103 and explain what it The balance on Mr Finch s credit card is 210 It is 3 times the balance on means in this context MP Use Repeated Reasoning Use the table shown A Convert each fraction in the table to a pattern in the results decimal Describe a B Does this pattern continue Why or why not Fraction 100 100 m 00 8 8 Michelle has to find the decimal equivalent of 15 yards How can she do this without first writing the mixed number as a fraction Decimal

It s true sand dunes in Colorado rival sand dunes of the Great Sahara Desert The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara extending over 700 feet in height However like all sand dunes they tend to move around in the wind This can cause a bit of trouble for temporary structures located near the escaping dunes Roads parking lots campgrounds small buildings trees and other vegetation are destroyed when a sand dune moves in and takes over Such dunes are called escape dunes in the sense that they move out of the main body of sand dunes and by the force of nature prevailing winds take over whatever space they choose to occupy In most cases dune movement does not occur quickly An escape dune can take years to relocate itself Just how fast does an escape dune move Let x be a random variable representing movement in feet per year of such sand dunes measured from the crest of the dune Let us assume that x has a normal distribution with 18 feet per year and a 3 2 feet per year USE SALT Under the influence of prevailing wind patterns what is the probability of each of the following Round your answers to four decimal places a an escape dune will move a total distance of more than 90 feet in 4 years X b an escape dune will move a total distance of less than 80 feet in 4 years c an escape dune will move a total distance of between 80 and 90 feet in 4 years

USE SALT a Use the binomial distribution to find the probability of exactly 10 successes Round your answer to three decimal places b Use the normal distribution to approximate the probability of exactly 10 successes Round your answer to four decimal places X c Compare the results of parts a and b These results are fairly different These results are almost exactly the same

Let x represent the dollar amount spent on supermarket impulse buying in a 10 minute unplanned shopping interval Based on a newspaper article the mean of the x distribution is about 26 and the estimated standard deviation is about 10 USE SALT a Consider a random sample of n 100 customers each of whom has 10 minutes of unplanned shopping time in a supermarket From the central limit theorem what can you say about the probability distribution of x the average amount spent by these customers due to impulse buying What are the mean and standard deviation of the x distribution The sampling distribution of x is not normal The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean 26 and standard error 0 1 26 and standard error 1 26 and standard error o x 10 Is it necessary to make any assumption about the x distribution Explain your answer It is not necessary to make any assumption about the x distribution because n is large It is necessary to assume that x has an approximately normal distribution It is necessary to assume that x has a large distribution It is not necessary to make any assumption about the x distribution because is large b What is the probability that x is between 24 and 28 Round your answer to four decimal places Probabilities should be between 0 and 1 c Let us assume that x has a distribution that is approximately normal What is the probability that x is between 24 and 28 Round your answer to four decimal places 0 1587 d In part b we used x the average amount spent computed for 100 customers In part c we used x the amount spent by only one customer The answers to parts b and c are very different Why would this happen The standard deviation is larger for the x distribution than it is for the x distribution The mean is larger for the x distribution than it is for the x distribution The sample size is smaller for the x distribution than it is for the x distribution The x distribution is approximately normal while the x distribution is not normal The standard deviation is smaller for the x distribution than it is for the x distribution In this example x is a much more predictable or reliable statistic than x Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer How does the central limit theorem tell us that the average customer is much more predictable than the individual customer The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation Thus the average customer is more predictable than the individual customer The central limit theorem tells us that small sample sizes have small standard deviations on average Thus the average customer is more predictable than the individual customer

A European growth mutual fund specializes in stocks from the British Isles continental Europe and Scandinavia The fund has over 121 stocks Let x be a random variable that represents the monthly percentage return for this fund Suppose x has mean 1 7 and standard deviation 0 6 LAUSE SALT a Let s consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks Is it reasonable to assume that x the average monthly return on the 121 stocks in the fund has a distribution that is approximately normal Explain Yes is x is a mean of a sample of n 121 stocks By the central limit theorem approximately normal b After 9 months what is the probability that the average monthly percentage return x will be between 1 and 2 Round your answer to four decimal places 0 9330 c After 18 months what is the probability that the average monthly percentage return x will be between 1 and 2 Round your answer to four decimal places X the x distribution d Compare your answers to parts b and c Did the probability increase as n number of months increased Why would this happen Yes probability increases as the standard deviation increases No the probability stayed the same Yes probability increases as the standard deviation decreases Yes probability increases as the mean increases e If after 18 months the average monthly percentage return x is more than 2 would that tend to shake your confidence in the statement that 1 7 If this happened do you think the European stock market might be heating up Round your answer to four decimal places x This would be very unlikely The probability that x was greater than 2 is than 5 of all such samples have means more than 2 One would suspect because less that the European stock market

In the following problem check that it is appropriate to use the normal approximation to the binomial Then use the normal distribution to estimate the requested probabilities Suppose it is estimated that 3 3 of the general population will live past their 90th birthday In a graduating class of 785 hig school seniors find the following probabilities Round your answers to four decimal places LUSE SALT a 15 or more will live beyond their 90th birthday 0 9887 b 30 or more will live beyond their 90th birthday X c between 25 and 35 will live beyond their 90th birthday d more than 40 will live beyond their 90th birthday 0 0018

Given triangle JKL which of the following is a proper representation of the sine law a sin K I k sin L b kx sin K I x sin L Oc sinsink J K K Od sink sin L Question 16 1 point Saved Corinne invested 3200 in a three year regular interest CSB that earns 7 annually How much will her investment be worth at the end of the term a 6720 b 6192 c 3872

Which of the following expressions is equivalen to x x A x10 B x 5 C X25 D X 30

Suppose an x distribution has mean 2 Consider two corresponding x distributions the first based on samples of size n 45 and the second based on samples of size n 81 LAUSE SALT a What is the value of the mean of each of the two x distributions for n 49 distribution for n 81 distribution b For which x distribution is P x 2 50 smaller Explain your answer The distribution with n 49 because the standard deviation will be larger The distribution with n 81 because the standard deviation will be smaller The distribution with n 49 because the standard deviation will be smaller The distribution with n 81 because the standard deviation will be larger c For which x distribution is P 1 50 x 2 50 greater Explain your answer The distribution with n 81 because the standard deviation will be larger The distribution with n 49 because the standard deviation will be smaller The distribution with n 81 because the standard deviation will be smaller The distribution with n 49 because the standard deviation will be larger

The mayor of a town believes that over 47 of the residents favor annexation of a new bridge Is there sufficient evidence at the 0 01 level to support the mayor s claim State the null and alternative hypotheses for the above scenario Answer Ho Keyp Keyboard Short Tables

Let f x x a Simplify f 13 h f 13 h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator Hint See Problem 9 on Assignment 2 2 for similar computations 1 13 h 13 b Evaluate lim f 13 h f 13 h 0 h If an answer does not exist enter DNE dne X c Determine the equation of the line tangent to y f x at x 13 y 1307

The graph of y f x is shown below b Is f x continuous at x 0 OYes No From left to right the graph starts below the x axis for negative values of x and decreases to negative infinity as x approaches zero from the left There is no point on the curve when x equals zero Then for positive values of x the graph decreases from positive infinity and approaches the x axis from above Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 0 OYes No c Is f x differentiable at x 0 Yes No 2

The graph of y f x is shown below 1 b Is f x continuous at x 1 OYes No Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 1 OYes No c Is f x differentiable at x 1 Yes No d Does lim f x exist X 2 OYes No The graph of a parabola that opens up with a hollow point on the graph when x 2 e Is f x continuous at x 2 OYes No f Is f x differentiable at x 2 2

The graph of y f x is shown below 3 X 2 Answer each of the following questions about f x You have one submission for each question a Does lim f x exist X 3 Yes ONO b Is f x continuous at x 3 Yes No c Is f x differentiable at x 3 Yes No d Does lim f x exist X 1 CYes No e Is f x continuous at x 1 Yes No 2 f Is f x differentiable at x 1

Determine whether each statement is true or false You have one submission for each statement a For every function f x if f x is continuous at x a then f x is also differentiable at x a True False b For every function f x if f x is differentiable at x a then f x is also continuous at x a True False

The graph of y f x is shown below b Does lim f x exist x 1 CYes No c Doesf Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 1 Yes No fix exist Yes No From left to right the graph is a horizontal line to a hollow point at 1 1 Then the graph jumps to a filled in point at 1 3 and continues to the right as a horizontal line c is fix continuous at x 1 CYes No 1 e Is x differentiable at x 1 CYND 2 3

The graph of y f x is shown below 3 2 b Is f x continuous at x 3 OYes No d Does lim f x exist X 1 OYes No The graph of the function decreases linearly with a slope of 1 to the point 1 1 and then increases linearly with a slope of 1 from the point 1 1 Answer each of the following questions about f x You have one submission for each question a Does lim f x exist X 3 Yes No c Is f x differentiable at x 3 Yes No e Is f x continuous at x 1 Yes No 1 f Is f x differentiable at x 1 Yes No 2 3

Let f x x a Simplify Computing derivatives using the limit definition f 13 h f 13 h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator Hint See Problem 9 on Assignment 2 2 for similar computations b Evaluate lim f 13 h f 13 h 0 h If an answer does not exist enter DNE y c Determine the equation of the line tangent to y f x at x 13

A website has 400 000 members The number y of members increases by 9 each year a Write an exponential function that represents the website membership after t years b How many members will there be after 3 years Round your answer to the nearest ten thousand a y b about memboro

Use the definition of an exponent to write the given product in exponential form Answer 3 5 5 5 5 5 7 7 Enter one base and one exponent in each box going from left to right All of the boxes may not be used 3 5 5 5 5 5 7 7

4 4 0 4 y 0x00 X