Basic Math Questions and Answers

1 1 point The Cauchy Schwarz Inequality tells us that if we have two vectors u and in R then Note that on the left stands for absolute value and on the right denotes the length of a vector Verify the Cauchy Schwarz Inequality for 1 1 0 and 0 1 1

15 A road construction company is considering the purchase of a new bulldozer They can purchase one for 380 000 if they pay in one installment Or they can pay 120 000 every quarter for one year Compute the effective annual rate of interest for the quarterly payment Use incremental IRR analysis to solve Fill in the incremental difference table below then calculate the incremental IRR Quarter Annual payment Qtrly payment Incremental diff annual qtriy 0 1 PV PMT

You have 5 000 in the bank comfortably earning 48 interest compounded monthly Your cousin needs 5 000 to buy a new car In order to get the same total return what interest rate r should you request from her if the money you lend her is to be compounded continuously Exact Interest rate without using a calculator r 48 Interest rate as a percent rounded to 2 decimal places 48

e top of a ladder slides down a vertical wall at a rate of 0 675 m s At the moment when the bottom of the ladder is 6 m from the wall it slides away from the wall at a rate of 0 9 m s How long is the lad

Two cars start moving from the same point One travels south at 48 mi h and the other travels west at 20 mi h At what rate is the distance between the cars increasing two hour

Process oriented layout Deals with low volume high variety production also called job shop or intermittent production True False Question 14 4 points The following statement describes Materials are moved directly from receiving to shipping and are not placed in storage in the warehouse A Cross Docking B Picking from a bin location C Bot A and B

2 A physician wants to develop criteria for determining whether a patient s pulse rate is atypical The physician collects a sample of n 40 men and determines that the sample has a mean pulse rate of M 69 4 and a standard deviation of SM 12 3 The researcher also collects al sample of nw 35 women and determines that the sample has a mean pulse rate of w76 3 and a standard deviation of sw 12 5 a Construct a 95 CI estimate for the mean pulse rates of males and a 95 CI estimate for the mean pulse rates of women b By comparing the preceding results do you think it s reasonable to conclude that the mean pulse rates for males and females are different Why or why not

1 point A street light is at the top of a 13 5 ft tall pole A man 5 3 ft tall walks away from the pole with a speed of 5 0 feet sec along a straight path How fast is the tip of his shadow moving when he is 40 feet from the pole Your answer 1 962962 ft sec Hint Draw a picture and use similar triangles

Nolan Walker decided to buy a used snowmobile since his credit union was offering such low interest rates He borrowed 3 100 at 3 75 on December 26 2021 and paid it off February 21 2023 How much did he pay in interest Assume ordinary interest and no leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Interest paid

5 A city is planning a new children s park Two contractors are bidding for the project Contractor A will construct the playground for 2 500 000 and estimates annual maintenance to cost 100 000 Contractor B will construct the playground for 3 500 000 and annual maintenance will be 75 500 In both cases the contractors will maintain the park for 20 years The relevant rate of interest is 8 On the basis of NPV analysis which contractor would you recommend

es On April 5 2022 Janeen Camoct took out an 10 25 loan for 31 000 The loan is due March 9 2023 Janeen s terms are ordinary interest Sabrina Bowers took out the same loan as Janeen Sabrina s terms however are exact interest Ignore leap year Use Days in a year table a What is Sabrina s difference in interest Note Do not round intermediate calculations Round your answer to the nearest cent Difference b What will Sabrina pay on March 9 2023 Note Do not round intermediate calculations Round your answer to the nearest cent Amount

Harold Hill borrowed 15 200 to pay for his child s education at Riverside Community College Harold must repay the loan at the end of 10 months in one payment with 4 interest a How much interest must Harold pay Note Do not round intermediate calculation Round your answer to the nearest cent Interest to pay b What is the maturity value Note Do not round intermediate calculation Round your answer to the nearest cent

Nolan Walker decided to buy a used snowmobile since his credit union was offering such low interest rates He borrowed 3 100 at 3 75 on December 26 2021 and paid it off February 21 2023 How much did he pay in interest Assume ordinary interest and no leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Interact poid

On May 3 2020 Leven Corporation negotiated a short term loan of 630 000 The loan is due October 1 2020 and carries a 5 20 interest rate Use ordinary interest to calculate the interest What is the total amount Leven would pay on the maturity date Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Maturity value

1 How much must be deposited into a savings account in year 0 that pays 7 interest in order to make the following withdrawals Year Cash flow 0 1 0 2 3000 3 4000 4 2500 5 4500

10 Dorothy invested 250 000 in a rental property She earns net revenue of 50 000 per year from the property If she keeps the property for 10 years what is her rate of return Here assume the salvage value is 0

13 The owner of a corner lot is trying to decide between two alternate uses for the land His options are Fast food rest Gas station Initial cost 800 000 1 100 000 Y1 net benefit 150 000 190 000 Y2 net benefit 150 000 225 000 Y3 to Y10 150 000 275 000 The salvage value for both options is 0 at the end of 10 years The owner has an MARR of 15 for all projects Using IRR analysis which project would you recommend

7 A company is planning to purchase a new machine to meet increased demand Both options under consideration have useful lives of 10 years and no salvage value at the end Cash flows for both are as follows Annual maintenance Annual Machine Initial Cost costs income A 400 000 20 000 80 000 B 650 000 30 000 160 000 Use NPV analysis to determine which machine would be a better option Interest rate is 8 Hint first compute the net annual benefit annual cost annual income

9 A company is planning to purchase a new generator Generator A has a useful life of 5 years while Generator B has a useful life of 10 years The salvage value of both is zero at the end of their useful lives Cash flows are as follows Generator Initial Cost Annual benefit Useful life A B 6 500 12 000 1 800 5 years 2000 10 years Use a 10 year analysis period and 8 interest rate to determine which generator the company should purchase

a 20 b C d

m n h P k

So T 26 a Classify the angle above and calculate the supplement and complement of the angle

146 125 130 X

c Identify the correct name for the diagram above O QR ORQ 111 O QR OR

Q O Rectangle O Rhombus O Trapezoid O Parallelogram

WAGE Assume that the accounting and actuarial industries employ people with similar skills Suppose a decrease in the their wages while the demand for accountants remains the same The following graph shows the labor market for accountants in the United States Show the effect of the fall in demand for actuaries on the U S labor market for accountants by shifting the labor demand curve the labor supply curve or both Supply Demand Demand Supply

38 42 Sylvester files as a single taxpayer during 2023 He itemizes deductions for regular tax purposes He paid charitable contributions of 7 700 real estate taxes of 1 100 state income taxes of 6 450 and mortgage interest of 2 900 on 30 450 of acquisition indebtedness on his home Sylvester s regular taxable income is 132 000 What is Sylvester s AMTI Answer is complete but not entirely correct

Suppose you owe 500 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account Assuming that the interest rate on your card is 2 per month on the unpaid balance and that the minimum payment is 3 of the total balance plus interest your balance after t months is given by 8 t 500 0 9894 Find your balance at each of the given times Complete parts a through e below

Use a calculator to evaluate the function at the indicated values Round your answers to three decimals 3x 9 x 3 M 9 3 xxxx Enter a number

The graph of a function f is given Sketch the graph of y f 2x 6 Note y f 2x 6 f 2 x 3

True of False The graph of a rational function can cross its horizontal asymptote True False

Sketch the graph of a rational function y f x that meets ALL of the following conditions x 3 is a zero of multiplicity 1 x 3 is a zero of multiplicity 1 yoo as x 1 yoo as x 1 yoo as x 4 yoo as x 4 y0 as x

A C 6 in 175 lb in 12 in 12 in B 100 lb in

bers use the assumed values and only 1 section Otherwise the math will not work 75 lb L K H A B C D E F 4 ft 4 ft 4 ft 4 ft 4 ft 4 ft 3 15 lb 55 lb 25 lb 35 lb 6 ft

125 lb H 75 lb G FL A B C ID 4 ft 4ft 4 ft 4 ft 4ft 90 lb 4 ft EI

Consider the following recursive function fun x y What is the value of fun 4 3 int fun int x int y if x O return y return fun x 1 x y O 10 O 11 O 12

Collins Company is preparing its master budget for April Use the given estimates to determine the amounts necessary for each of the following requirements Estimates may be related to more than one requirement a What should total sales revenue be if territories A and B estimate sales of 10 000 and 16 000 units respectively and the unit selling price is 48 b If the beginning finished goods inventory is an estimated 2 000 units and the desired ending inventory is 3 000 units how many units should be produced 27 000 c What dollar amount of material should be purchased at 4 per pound if each unit of product requires 3 pounds and beginning and ending materials inventories should be 5 000 and 4 000 pounds respectively x d How much direct labor cost should be incurred if each unit produced requires 1 5 hours at an hourly rate of 17 e How much manufacturing overhead should be incurred if fixed manufacturing overhead is 55 000 and variable manufacturing overhead is 2 50 per direct labor hour

For each independent situation below determine the missing amounts A B C D Beginnning inventory 6 000 x 2 000 X Produced 40 000 22 000 x 60 000 Available x x 26 000 69 000 Sold 45 000 33 000 X x Ending inventory x 10 000 11 000 3 000

The following is a report from a BLS survey taker There were 70 people in the houses I visited 12 of them were children under the age of 16 25 people had full time jobs and 6 had part time jobs There were 10 retirees 5 full time homemakers 5 full time students over age 16 and 2 people who were disabled and cannot work The remaining people did not have jobs but all said they would like one 1 of these people had not looked actively for work for three months however Find the labor force the unemployment rate and the participation rate implied by the survey taker s report Labor force people Instructions Enter your responses rounded to two decimal places Unemployment rate Participation rate

1 of 3 IS eBook Required information The following information applies to the questions displayed below In 2023 Juanita is married and files a joint tax return with her husband What is her tentative minimum tax in each of the following alternative circumstances Use Tax Rate Schedule Dividends and Capital Gains Tax Rates for reference Note Input all values as positive Leave no answer blank Enter zero if applicable a Her AMT base is 156 000 all ordinary income 1 AMT base Print Description ferences 2 Dividends taxed at preferential rate 3 Tax on dividends 4 AMT base taxed at regular AMT rates 5 Tax on AMT base taxed at 26 rate 6 Tax on AMT base taxed at 28 rate Tentative minimum tax Amount 156 000

Alice is single and self employed in 2023 Her net business profit on her Schedule C for the year is 191 200 What are her self employment tax liability and additional Medicare tax liability for 2023 Note Round your final answers to the nearest whole dollar amount Leave no answer blank Enter zero if applicable Answer is not complete Self employment tax liability Additional medicare tax liability 0

Ook This year Paula and Simon married filing jointly estimate that their tax liability will be 221 000 Last year their total tax liability was 184 000 They estimate that their tax withholding from their employers will be 191 100 Required a Are Paula and Simon required to increase their withholdings or make estimated tax payments this year to avoid the underpayment penalty b By how much if any must Paula and Simon increase their withholding and or estimated tax payments for the year to avoid underpayment penalties int Complete this question by entering your answers in the tabs below ences Required A Required B By how much if any must Paula and Simon increase their withholding and or estimated tax payments for the year to avoid underpayment penalties

Required information The following information applies to the questions displayed below Lacy is a single taxpayer In 2023 her taxable income is 51 600 What is her tax liability in each of the following alternative situations Use Tax Rate Schedule Dividends and Capital Gains Tax Rates for reference Note Do not round intermediate calculations Round your answer to 2 decimal places a All of her income is salary from her employer Tax liability

Required information The following information applies to the questions displayed below Julie paid a day care center to watch her two year old son while she worked as a computer programmer for a local start up company What amount of child and dependent care credit can Julie claim in 2023 in each of the following alternative scenarios Use Exhibit 8 9 c Julie paid 4 100 to the day care center and her AGI is 24 900 all salary Child and dependent care credit

Required information The following information applies to the questions displayed below Trey has two dependents his daughters ages 14 and 18 at year end Trey files a joint return with his spouse What amount of child tax credit either as a child or a qualifying dependent will Trey be able to claim in 2023 for his daughters under each of the following alternative situations Use Exhibit 8 8 c His AGI is 422 400 and his daughters are ages 10 and 12 Amount of child tax credit

Required information The following information applies to the questions displayed below Steve s tentative minimum tax TMT for 2023 is 249 200 Note Leave no answer blank Enter zero if applicable b What is his AMT if his regular tax is 258 500 Alternative minimum tax

When a certain drug is taken orally the concentration of the drug in the patient s bloodstream after t minutes is given by C t 0 06 0 0002t2 where 0 st s 240 and the concentration is measured in mg L When is the maximum serum concentration reached t min What is the maximum concentration mg L

f f x x x 1 and g x x 3 find the following a f g b f g c fog d gof e f g 2 f g f 2 g gogog

Find a fourth degree polynomial with integer coefficients that has zeros 41 and 1 with 1 a zero of multiplicity 2 P x

A person starts walking from home and walks 4 miles East 6 miles Southeast 6 miles South 5 miles Southwest 3 miles East This person has walked a total of miles Find the total displacement vector for this walk If this person walked straight home they d have to walk miles