Functions Questions and Answers

In Problems 1 8 evaluate the given iterated integral 3 x xy 2 24xy dz dy dx

Question Given AC bisects LBCD prove AABC AADC by filling out the flowchart below For each bax choose a statement format from the dropdown menu You will then be able to change the letters to match the diagram for this problem Typ at Statement Type of Statement Reason Reason Typod Strtem n Reason Type of Stotrigo Reason

Lily has 650 000 saved for retirement in an account earning 2 05 interest compounded quarterly How much will she be able to withdraw each quarter if she wants to take withdrawals for 17 years Round your answer to the nearest dollar

Hypothesis testing of proportions using 3 methods 9 3 a Benford s Law states that in a random sample of numbers used in measurement with multiple digit integer values will be approximately 30 1 will have the leading digit of 1 Such a data set is being investigated for possible fraud The data set had 33 of its 20 000 pieces of data having a leading digit of 1 Is this data set odd Test this hypothesis using a confidence level of 99 Use z and p values tests b Benford s Law states that in a random sample of numbers used in measurement with multiple digit integer values will be approximately 30 1 will have the leading digit of 1 Such a data set is being investigated for possible fraud The data set had 29 5 of its 12 000 pieces of data having a leading digit of 1 Is this data set odd Test this hypothesis using a confidence level of 99 Use interval and p value tests c The historic rate of property crime in Metropolis City has been 12 for every 1 000 residents each year Last year an election year in the city a candidate for mayor claimed that crime had increased She cited a report of 190 property crimes for the 15 000 residents of Metropolis in the last year Test her hypothesis with a 90 confidence level Use both z value and interval tests

Maximize f 2x 9y subject to the following constraints x y 7 2x 2y 12 x 3y 15 x and y are non negative a Identify the constraints that are binding and the ones that are not binding b Identify if any constraint is redundant i e is not needed to delineate the feasibility region c Find the range of optimality of both of the objective function coefficients d Find the shadow prices of each of the constraints e Compute the amount by which the objective function changes if the right hand side of one of the constraints increases by 8

1 point Given the matrix a find its determinant 0 b does the matrix have an inverse Your answer is input Yes or No Your answer is 0 2 0 1 0 3 2 co do c

Use the following to answer question 40 Figure Market for Loanable Funds III Interest rate 30 27 24 21 18 10 5 15 12 9 6 3 0 200 400 E S D 600 800 1 000 1 200 Quantity of loanable funds billions of dollars A fall to 12 B rise to 16 5 C rise to 18 40 Figure Market for Loanable Funds III If the government in a closed economy is running a budget balance of zero when it decides to increase defense spending by billion and then finances the spending by selling bonds the equilibrium interest rat will

Tomika s credit rating was lowered and the credit card company raised her APR from 18 to 25 2 a If her average daily balance this month is 8 237 what is the increase in this month s finance charge due to the higher APR b If this amount is typical of Tomika s average daily balance all year how much would the rise year in interest rate cost her in a typical Round to the nearest ten dollars

4 What is the difference between the definitions of a motor vehicle in the Highway Traffic Act and vehicle in the Highway Traffic Act 1 marks Ref 5 Why is the difference question 4 important 1 marks Ref 6 Site the General stopping authority under the H T A 1 marks Ref 7 Site the Spot Check authority for R I D E under the H T A 1 marks Ref 8 Site the authority under the H T A to have a vehicle examined 1 marks Ref

Pierce Manufacturing determines that the daily revenue in dollars from the sale of x lawn chairs is R x 0 003x 0 03x 0 6x Currently Pierce sells 70 lawn chairs daily a What is the current daily revenue b How much would revenue increase if 73 lawn chairs were sold each day c What is the marginal revenue when 70 lawn chairs are sold daily d Use the answer from part c to estimate R 71 R 72 and R 73

Find the P value for the indicated hypothesis test A nationwide study of American homeowners revealed that 65 have one or more lawn mowers A lawn equipment manufacturer located in Omaha feels the estimate is too low households in Omaha Find the P value for a test of the claim that the proportion with law mowers in Omaha is higher than 65 Among 497 randomly selected homes in Omaha 3 had one or more lawn mowers O 0 0252 O 0 1505 O 0 1118

There was a sample of 750 milligrams of a radioactive substance to start a study Since then the sample has decayed by 7 3 each year Lett be the number of years since the start of the study Let y be the mass of the sample in milligrams Write an exponential function showing the relationship between y and t 0 M 8 08

A principal of 2600 was invested at 3 25 interest compounded annually Lett be the number of years since the start of the investment Let y be the value of the investment in dollars Write an exponential function showing the relationship between y and t 0 0 0 8 08 0 0

Graph the exponential function g x 3e 2 3 Plot two points on the graph of the function and also draw the asymptote Then click on the graph a function butto 10 8 6 8 10 5

If a buyer procures the same or similar goods as those involved in the sales contract breached by the seller the buyer lose all rights to prosecute for breach is said to have validated the seller s action is said to have covered is also a breach

Fraud in the inducement is a limited defense not available against a holder in due course universal defense available against all holders limited defense available against all holders universal defense not available against a holder in due course

A seller may cancel a sales contract if the buyer does any of the following except wrongfully rejects the goods repudiates the contract fails to make payment due on or before delivery rejects an improper tender

A check that is made out to Cash and signed by the writer is a void instrument an order instrument a revocable instrument a bearer instrument

The principal has a duty to perform all of the following except a duty to perform the contract according to its terms a duty to compensate the agent for services a duty to indemnify the agent for loss in some circumstances a duty of loyalty to the agent

Here are the masses in kilograms of 2 groups of dolphins Use the medians to decide which group is heavier on average 100 150 200 Group A Group B

An internet provider has analyzed the amount of time its customers are online per session It found that the distribution of connect times has a mean of 36 minutes and a standard deviation of 13 minutes For this distribution find the raw score that corresponds to a z score of 1 4 The raw score is Type an integer or a decimal

A competitive diver is competing for a medal His height in meters above the water can be modeled by the function f x 4 9x 14 7x 19 6 where x represents the time in seconds after he begins the dive Write an equation that can be used to find the time it takes for the diver to reach the water Solve that equation What domain makes sense for this scenario Write an equation that can be used to find the times the diver is 19 6 meters above the water Solve that equation Check your answer by graphing and finding f x 19 6

Score 33 75 55 39 55 answered Question 54 The cost C 2 where a is the number of miles driven of renting a car for a day is 49 plus 1 65 per mile What is the slope of the linear function and its units Select an answer B select the correct units What is the y intercept and its units Submit Question What is the linear function C x C a Select an answer select the correct units

Next question 5 Plot each point on the coordinate plane below 0 4 4 0 5 1 2 5 4 3 2 1 5 4 3 2 1 7 2 3 4 Get a similar question You can 5 1 2 3 4 5

Find the inverse Laplace transform f t F s of the function F s help formulool 6s 13 s 4s 13 s 2

On a multiple choice test over English vocabulary Alfredo got 15 out of 21 correct What percent of the problems did she miss Round your answer to the nearest tenth of a percent if necessary Vidon

13 1 point Which change would decrease the amount of interest paid over the life of a mortgage Choosing a longer amortization period Reducing the number of payments made per year Switching from weekly payments to monthly payments Making an Avra navment Ance ner vear b c

20 1 point Afewerk would like to borrow 3300 to purchase furniture His bank offered him a two year personal loan with monthly payments The interest rate on the loan is 7 5 per year compounded monthly Calculate the total amount Afewerk will have to pay to the bank 6871 20 b 3832 26 c 3564 00 d 5062 37

he next are regularly occurring expenses that are the same from one time period

The perimeter of a rectangle is 84 The length is 16 more than the width Find the width and length Width Length

A linear relation is modeled below Use this representation to create two other Table X 0 1 2 3 4 Graph 8 7 y y 1 2x

Identify the location of each of the following points Point 1 1 1 Select an answer Point 2 1 4 Select an answer Point 3 1 6 Select an answer Point 4 2 4 Select an answer Point 5 0 1 Select an answer Point 6 2 4 Select an answer

1 T 3 5 4 3 2 1 A Domain Range 2 3 4 5 H x 5 4 2 X

0 product and is equal to the unit selling price p of the product times the number x of units actually in economics revenue R Is defined as the amount of money received from the sale of a sold That is R xp The Law of Demand states that p and x are related As one increases the other decreases Suppose that p and x are related by the following demand equation A Express the revenue R as a function of p x 4p 100 B What is the revenue if 18 units are sold c Sketch the graph of the revenue function D What quantity x maximizes revenue E What is the maximum revenue 0 p 25 700 600 500 400 300 Revenue dollars

8 3 Domain Range 543211 I H 4 5

3 TI 2 53211 12 f Domain Range y 7 WIT 234 5 X 4 XZ 2 1

21 The function g x x 1 has domain 1 3 2 1 0 1 2 3 a Show the function as an arrow diagram D C 3 2 1 0 1 2 3 96 35 C 3 1 3 b Find the range of g x

The volume of a sphere is given by the x where x is the radius of function f x the sphere Find a f 2 enees b f 10 3

If g x 2x 1 find 11 g 3 12 g 1 5

State whether each set of ordered pairs represents a function 1 2 5 1 10 0 15 1 20 2 0 1 1 1 1 2 2 1 2 2 3 3 9 4 6 5 25 6 30

1 If f x x 5 find 8 f 4 9 f 80 10 f 100

The following are the number of home runs hit by home run champions for the years 1975 to 1989 and for 2005 to 2019 Draw box and whisker plots for the distributions of the number of home runs hit for the two given time periods a 1975 1989 25 37 38 33 39 43 47 35 45 40 43 45 50 47 54 D b 2005 2019 49 58 49 48 47 43 38 40 31 32 43 40 59 37 53 a Choose the correct answer below A 20 25 30 35 40 45 50 O C H 20 25 30 35 40 45 b Choose the correct answer below OA 30 O C 35 40 35 40 45 45 50 50 50 55 55 55 55 60 60 E Q Q OB 20 25 30 35 40 O D 20 25 25 30 35 40 OB H 30 O D 35 40 45 t 30 35 40 45 50 45 50 55 55 45 50 55 55 60 Q Q Q Q G Q G

8 Which of these graphs represents a function Justify your answer Write the domain and range for each graph a b c e 4 2 0 2 y st 2 4 4 2 2 0 y y for 4 2 X 6 4 X X d 2 0 2 2 2 2 0 A y n 2 x 4

7 Match the graph of each function to its domain and range listed below a c y 24 0 4 2 0 y 2 4 2 4 X b d 4 2 0 4 ly 2 0 2 2 4 4 i domain 1 x 3 range 2 y 4 ii domain 1 x 3 range 1 y 4 iii domain x 0 range y 2 iv domain 1 x 4 range 1 y 2

4 List the domain and the range of the graph of each function a 4 c N 24 4 2 0 y 2 y 3 1 4 X b 4 2 4 2 O 2 4 y 2 X

OTES A graphing calculator is recommended hundred thousand dollars x years The value of a suburban plot of land being considered for rezoning is assessed at 4 2e0 014x from now Find the average value in dollars over the next 10 years year 0 to year 10 Round your answer to the nearest whole number 700 000 X

2 2 points Assume three real numbers between 0 and 1 are chosen randomly What is the probability their sum is greater than Answer the question by writing an iterated integral and evaluating it Hint think of the event set that the sum of three variables is less than 1

World consumption of antimony used in flame retardants and batteries is running at the rate of 137e0 013t thousand metric tons per year where t is the number of years since 2012 a Find a formula for the total amount of antimony consumed within t years of 2012 Round your coefficients to three decimal places C t b If consumption continues at this rate when in years since 2012 will the known resources of 2 100 thousand metric tons of antimony be exhausted Round your answer to one decimal place years t

Use Newton s method with the specified initial approximation x to find x3 the third approximation to the root of the given equation Round your answer to four decimal places x5 x 7 0 x 1 x3

4 3 5 6 Graph the solution to the system y 2 x 4 y x 7 Show Your Work