Functions Questions and Answers

weekend Frank shoots an air ball from center court The height h im Homework While feet of the ball is given by h t 8t 32t 6 a What is the height of the ball after 0 5 seconds b At what time s is the ball at a height of 30 feet

H Domain Range Function 5 5 5

Bayside Apartments is a 900 unit apartment complex When the apartments are 90 occupied monthly operating costs total 229 840 When occupancy dips to 80 monthly operating costs fall to 224 080 The owner of the apartment complex is worried because many of the apartment residents work at a nearby manufacturing plant that has just announced it will close in three months The apartment owner fears that occupancy of her apartments will drop to 60 if residents lose their jobs and move away Assuming the same relevant range what can the owner expect her operating costs to be if occupancy falls to 60 Let s begin by determining the formula that is used to calculate the variable cost slope Change in cost Change in volume Variable cost slope Now determine the formula that is used to calculate the fixed cost component Total operating cost Total variable cost Use the high low method to determine Bayside s operating cost equation y 64 x 178 000 Assuming the same relevant range what should the owner expect her operating costs to be if occupancy falls to 60 Round your answer to the nearest whole dollar The owner should expect her operating costs to be if occupancy falls to 60 Fixed cost Save

Match the function with its graph v 4 x 2 3 77 Question Help Video Submit Question Ray W

Question 7 Let f z 4 2 If g z is the graph of f z shifted up 6 units and right 2 units write a formula for g z g x Enter z as sqrt x

f a in the box

2 2 points What is y r for a function defined by the equation x cos xy y 3e as it passes through x 0

Move the slider kt so that the graph of g gets shifted up 2 units Then type the new function f z in the answer bax 7 T B 9 HO 3 2 T 2 2 f x 1 3 Ok 0 00 Don t forget to shift the graph up Using function notation i e f x enter the function that results from the transformation

Question 11 Given the following functions find each of the values f z z z 30 g z 5 f g 2 f g 3 f g 5 Question Help Video Submit Question

Question 9 The function h z defined as 1 8 Question Help Video can be expressed in the form f g z where g z z 8 and f z is U

Identify the type of angle

Banks often estimate inflation You can see what they think inflation will be if you know how much they charge for loans and how much they expect to earn Suppose the nominal interest rate is 7 and the real interest rate is 5 Given these interest rates the bank thinks inflation will be

Use the Fisher equation to fill in the blanks in the following table Inflation rate 3 Real interest rate 3 Nominal interest rate 7 6

Use the savings plan formula to answer the following question You put 300 per month in an investment plan that pays an APR of 4 5 How much money will you have after 28 years Compare this amount to the total deposits made over the time After 28 years the investment plan will contain Do not round until the final answer Then round to the nearest cent as needed GILB

Question 7 The number of bacteria in a refrigerated food product is given by N T 2572 1487 99 6 T 36 where Tis the temperature of the food When the food is removed from the refrigerator the temperature is given by T t 3t 1 2 where t is the time in hours Find the composite function N T t N T t Submit Question Find the time when the bacteria count reaches 8239 Time Needed hours

Question 13 432 N Find the absolute maximum and minimum for the given graph Give your answer as an ordered pair 433 Absolute maximum Absolute minimum Y 20 Question Help Video

us No 5 4 3 2 1 3 2 las 12 3 4 bat The function graphed above is Increasing on the interval s A Decreasing on the interval s

L Based on the graph above estimate to one decimal place the average rate of change from z 1 to z 3

Question 15 Determine the domain and range of the function using the graph below 45 44 18 12 10 9 8 y Domain Range sas SUS T 4

Complete the following truth table pVq r pqr 0000 0 0 1 0 1 0 0 11 100 101 1 2 3 4 5 1 10 6

Let p q be the following propositions p 7 17 q 1 8 Match each proposition with its symbolic representation 1 If 717 then 1 8 2 1 8 if and only if 7 17 3 7 17 or 1 8 4 7 17 and 18 5 If 18 then 1 8 A qp B p q C p Aq D q q E p F p q G p V q q

Assume that you have 12 000 to invest in bonds Use the table to the right which shows the probabilities for gain or loss for these investments over the next year What would be the expected gain or loss in dollars if you invested in bonds There would be an expected Type an integer or a decimal of dollars gain B Bonds Probability Change 0 6 Gain 7 0 2 0 2 No Change Lose 1

A certain game consists of rolling a single fair die If a four or five comes up you win 10 dollars otherwise you lose 5 dollars Find the expected winnings for this game Is this a fair game The expected value for this game is dollars

To the right are the probabilities and values associated with five outcomes of an experiment Calculate the expected value for the experiment The expected value for this experiment is Round to the nearest tenth as needed C Outcome A B C D E Probability 0 1 0 2 0 1 0 2 0 4 Value 3 8 1 3 9

K A game has two four sided dice having the numbers 3 6 9 and 2 on their faces Outcomes in the sample space are pairs such as 3 6 and 2 2 a How many elements are in the sample space b Express the event the total showing is even as a set c What is the probability that the total showing is even d What is the probability that the total showing is greater than 6 A The Analogies Principle OB The Draw Pictures Principle C The Be Systematic Principle OD The Choose Good Names for Unknown Strategies Principle a How many elements are in the sample space 16 b Express the event the total showing is even as a set 3 3 3 9 6 6 6 2 9 3 9 9 2 6 2 2 Type an ordered pair Use a comma to separate answers as needed c What is the probability that the total showing is even 1 2 Type an integer or a simplified fraction d What is the probability that the total showing is greater than 6

The graph given below summarizes statistics regarding distracted drivers below the age of 40 who were involved in fatal crashes Assume that we are selecting a driver at random from the 3 145 tallied If a driver in this group is under 20 what is the probability that the accident was related to cell phone use The probability is Round to three decimal places as needed Fatal Traffic Accidents Involving Distracted Driving Number 1500 1200 900 600 300 0 Age under 20 538 188 Fatal Traffic Accidents Involving Distracted Driving Age between 20 29 1191 Non Cell Phone Distraction GELER 387 Cell Phone Distraction Age between 30 39 650 191 X

Find the probability P SIN associated with the tree diagram What problem solving method should be used A Draw pictures B Be systematic C Relate a New Problem to an Older One OD The Three Way Principle What is P SIN P SIN Type an integer or decimal rounded to one decimal place as needed 0 3 M 0 4 N 0 3 Q 0 5 0 5 0 4 0 6 R S 0 3 R 0 7 R S S

Let g x 2 x 4 a Find the domain of Let f x b c 1 g x 8 x g x The function f x can be written as f x a x b a b e Z Find a and b e Hence or otherwise sketch f x d Find f x stating any domain restrictions Find the domain of g x

Let g x 2 x 4 a Find the domain of Let f x b 1 g x 8 x g x The function f x can be written as f x a x b a bez Find a and b

Is this problem one where we should take the percent of the other number shown in the problem Joy bought a 90 skirt on sale for 15 off What was the discount yes no

5 Kara enlisted her friend Frannie to help shovel all the driveways in her grandma s condominium community It takes Kara 40 minutes to shovel a driveway and it takes Frannie 45 minutes to shovel the driveway Write an equation for a function d that gives the number of driveways Kara and Frannie can shovel by working together for hours

Like James she was so light skinned that her friends sometimes called her names When they would get angry they would call me half white she said It would really really hurt my feelings Although she had friends who passed I was black and it was no doubt about it in my mind she said I never had any desires to pass We ve Got a Job What is the point of view in the first sentence of the paragraph O What is the point of view in the last sentence of the paragraph

Asample of Nickel oxide contains 64 5 nickel Calculate the mass of nickel present in 146g of nickel oxide convert a temperature 4o oF to c 3 A solid substance density of 2 18g m2 what volume 15 0g of this substance

On July 1 of Year 1 West Company purchased for cash 20 10 000 bonds of North Corporation at a market rate of 6 The bonds pay 5 interest payable on a semiannual basis each July 1 and January 1 and mature in three years on July 1 The bonds are classified as trading securities West Company s annual reporting period ends December 31 Assume the effective interest method of amortization of any discounts or premiums Note When answering the following questions round answers to the nearest whole dollar Amortization Schedule Journal Entries in Year 1 Journal Entries in Year 2 a Prepare a bond amortization schedule for the life of the bonds using the effective interest method Date Stated Interest Jul 1 Year 11 Jan 1 Year 2 194 582 81 x S Jul 1 Year 2 Jan 1 Year 3 Jul 1 Year 3 0x 0x ox Market Discount Bond Interest Amortization Amortized Cost ox 0x1 0x 0x ox 000 0x Ooo 0x

Consider the price demand equation given by 8 1 p 5 2 500 Calculate E 0 25 where E is the elasticity of demand and select the correct interpretations of the result Select all that apply U 1 X When p 0 25 an increase in price will result in increased revenue When p 0 25 the elasticity of demand satisfies E 0 25 1 which is inelastic When p 0 25 the elasticity of demand satisfies E 0 25 1 which is elastic When p 0 25 an increase in price will result in decreased revenue

A college administration has conducted a study of 171 randomly selected students to determine the relationship between satisfaction with academic advisement and academic success They obtained the following information Of the 73 students on academic probation 40 are not satisfied with advisement however only 20 of the students not on academic probation are dissatisfied with advisement What is the probability that a student selected at random is not on academic probation and is satisfied with advisement The probability is Round to two decimal places as needed

Use the given spinner to answer the question Each green sector occupies 6 of the circle each blue sector occupies 9 each red sector occupies 19 and the yellow sector occupies 8 Assume that the spinner is spun once What is the probability that the spinner does not stop on yellow The probability is Type an integer or a decimal R Red G Green B Blue Y Yellow B G R B G R

Assume that P A 0 2 P ANB 0 15 and the probability that neither A nor B occurs is 0 4 What is the probability of E P B Simplify your answer Type an integer or a decimal

Assume a dart is thrown and hits somewhere in the diagram shown Find the probability that the dart hits the shaded region 5 in 3 in 10 in 7 in 1 in 3 in 4 in 5 in G

1 Briefly discuss the scope of Article 2 of the Uniform Commercial Code what sales are covered and what is not covered Briefly discuss the formation of sales contracts under the UCC terms and requirements of an Offer requirements on acceptance and the Statute of Frauds

Account Names 7 Cash 8 Accounts Receivable 9 Office Supplies 10 Prepaid Insurance 11 Equipment 12 Accumulated Depreciation Equipment 13 Accounts Payable 14 Salaries Payable 15 Greavy Capital 16 Greavy Withdrawals 17 Service Revenue 18 Depreciation Expense Equipment 19 Supplies Expense 20 Utilities Expense 21 Salaries Expense 22 Insurance Expense 23 Total GREAVY THEATER PRODUCTION COMPANY Worksheet December 31 2024 Unadjusted Trial Balance Debit Credit 4 300 5 900 1 900 4 550 30 000 30 500 C 5 500 27 500 110 150 7 600 3 600 21 950 77 000 110 150 Adjustments Debit Prepaid Insurance of 3 900 remained 1 Depreciation expense 4 000 Accrued salaries expense of 200 that hasn t been paid yet Credit Adjustment data at December 31 follow a As of December 31 Greavy had performed 500 of service revenue but has not yet billed customers b At the end of the month Greavy had 700 of office supplies remaining quirements Complete the worksheet Use letters a through e to label the five adjustments ournalize the adjusting entries G Adjusted Trial Balance Debit Credit

5 Let 0 and t 0 and let ao a1 02 n be sequence that satisfies and a 1S 1 8 a t for each i20 We will prove an inequality that is important for deriving the global error in Euler s method a Show that implies 1 1 8 a 1 t 1 1 8 b Show that and part a imply 0 1 1 s a 2 t 1 1 s 1 s c Use an inductive argument to show that a 1 1 s t 1 1 s 1 s 1 s d The term in brackets 1 1 s 1 s is a geometric series Use this fact to rewrite the inequality from c as t 9 1 1 8 0 e Finally use your answer from 04 to conclude

enex hik b Vertex 2 c Domain d Range 2 0 e axis of symmetry 2 y 2 x 4 1 3 4 1 25 5 4 1 25 a Minor Max b Vertex 4 1 C Domain d Range e axis of symmetry 3 y 2x44x 1 9 2 a Minor Max b Vertex 2 5 c Domain 00 d Range 4 e X intercepts 1 y y intercept 4 y 2x 4x 1 y 2x 4x 2 1 2 x 2 1 4 y x 2 5 V 2 5 x b 2 a 4 2 2 1

A mutual fund is currently valued at 90 per share and its value per share is increasing at a rate of 0 70 a day Let V f t be the value of the share days from now a Express the information given about the mutual fund in terms of f and f i 10 and b Assuming that the rate of growth stays constant estimate and interpret f 10

010 y 001 Z This gives x 20 y 35 and z 5 Thus the firm can produce 20 units of P 35 units of P and 5 units of P to make full use of its available raw material Remark One may observe that if the manufacturer decides to manufacture according to the available raw material and not according to the purchase orders of the two clients F and F as in Example 3 he she is unable to meet these purchase orders as F demanded 6 units of P where as the manufacturer can make only 5 units of P3 Example 5 A manufacturer of medicines is preparing a production plan of medicines M and M There are sufficient raw materials available to make 20000 bottles of M and 40000 bottles of M but there are only 45000 bottles into which either of the medicines can be put Further it takes 3 hours to prepare enough material to fill 1000 bottles of M it takes 1 hour to prepare enough material to fill 1000 bottles of M and there are 66 hours available for this operation The profit is Rs 8 per bottle for M and Rs 7 per bottle for M How should the manufacturer schedule his her production in order to maximise profit and M in order to maximise the Step 2 Let x be the number of bottles of type M medicine and y be the number of bottles of type M medicine Since profit is Rs 8 per bottle for M and Rs 7 per bottle for M therefore the objective function which is to be maximised is given by Solution Step 1 To find the number of bottles profit under the given hypotheses Z Z x y 8x 7y The objective function is to be maximised subject to the constraints Refer Chapter 12 on Linear Programming not 20 35 5 x 20000 y 40000 x y 45000 0 40 000 T 3x y 66000 x20 y20 Step 3 The shaded region OPQRST is the feasible region for the constraints 1 Fig A 2 3 The co ordinates of vertices O P Q R S and T are 0 0 20000 0 20000 6000 10500 34500 5000 40000 and 0 40000 respectively Rationalised 2023 24 x 20 000 MATHEMATICAL MODELLING S 5 000 40 000 y 40 000 1 R 10 500 34 500 203

2 Let D y t la t b c y d and let fe C D Suppose there exists L 0 such that y t L y t D Use the mean value theorem from calculus to show that f is Lipschitz on D with Lipschitz constant

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Closing Entries After the accounts have been adjusted at March 31 the end of the fiscal year the following balances were taken from the ledger of Cabriolet Services Co Retained Earnings 783 900 29 000 Dividends 612 350 402 000 96 500 36 180 12 060 Fees Earned Wages Expense Rent Expense Supplies Expense Miscellaneous Expense Journalize the two entries required to close the accounts If an amount box does not require an entry leave it blank Mar 31 Fees Earned Wages Expense Rent Expense Supplies Expense Miscellaneous Expense Retained Earnings Mar 31 Retained Earnings V

The balance in the prepaid insurance account before adjustment at the end of the year is 15 090 Journalize the adjusting entry required under each of the following alternatives for determining the amount of the adjustmer a The amount of insurance expired during the year is 11 470 If an amount box does not require an entry leave it blank Insurance Expense Prepaid Insurance Feedback Check My Work Insurance Expense Prepaid Insurance 38 b The amount of unexpired insurance applicable to future periods is 3 620 If an amount box does not require an entry leave it blank