Math - Others Questions

In 36 38 use the graph to solve 36 The fastest speed a table tennis ball has been hit is about 13 07 times as fast as the speed for the fastest swimming What is the speed for the table tennis ball 37 Look for Relationships How fast would 1 5 times the fastest rowing speed be Before you solve tell the number of decimal places in your answer 38 Which activity has a recorded speed about 7 times as fast as the fastest rowing speed Miles per Hour 110 100 90 80 70 60 50 40 30 20 10 0 5 35 Fastest Sporting Speeds 27 79 13 99 95 69 Fastest Fastest Swimming Running Rowing Luge 106 Fastest Fastest Fastest Thrown Baseball Human Activity

5 5 Vertical Intercept Horizontal Intercept 25 25 y Vertical Intercept x 5 X 25 5 5 Vertical Intercept Horizontal Intercept 100 100 y 100 Vertical Intercept Horizontal Intercent 5 x 100 X q

Listen The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars Use the information in the figure to answer the question Dollars 3 500 9000 2500 2000 1500 1000 500 No 400 Yes 600 R x 3x C x 1500 Break even Point 750 2250 X 200 800 Binoculars Produced and Sold Is there a profit when 752 binoculars are produced

Listen Given the cost function C x and the revenue function R x find the number of units x that must be sold to break even C x 5000x 18 000 R x 7000x 9 units 11 units 10 units 3 units

npie On June 24 1948 the former Soviet Union blocked all land and water routes through East Germany to Berlin A gigantic airlift was organized using American and British planes to bring food clothing and other supplies to the more than 2 million people in West Berlin The Americans had two types of planes available the C 47 Skytrain and the C 54 Skymaster The carrying capacity was 3 5 tons for a C 47 and 10 tons for a C 54 To break the Soviet blockade the Western Allies had to maximize carrying capacity but the Americans were limited by the following restrictions No more than 44 planes could be used per day Each C 47 required 4 crew members per flight and the crew requirement for the C 54 was 5 The total number of personnel available per day could not exceed 200 The Americans only had 32 C 54 s available Find the number of C 47 s and C 54 s the Americans used to maximize their carrying capacity a Convert each constraint from problem 2 into an equation by adding slack variables and set up the initial simplex matrix b Perform all pivots necessary using row operations to transform the matrix until the solution is feasible

5 Fill in the boxes below to complete your answer Use the Show Work feature to provide related calculations and additional reasoning to support your answer

2 0 t0s te R is a subspace of R by using only the definit 2 subspace Then explain why we know this is true by some theorem we discussed Exercise 6 6 3 Show that the plane P s

Let a a and b be integers Prove that if a b 1 and a b 1 then aa b 1

Ferris wheel on a coordinate plane The center of the Ferris wheel is at the origin and one car lies on the x axis at 125 0 5 Construct a graph that relates the amount of time the car is in motion from 0 to 40 seconds to the height of the car with respect to the center of the Ferris wheel Describe the steps you took to make your graph 6 From your graph what are the amplitude frequency and midline Write the equation describing the relationship you graphed Explain 7 From your graph and its equation what is the average rate of change of a car from 0 to 5 r What does the rato can in this coptout Ch

If any 3 in a vector space V is a linear combination of vectors a An prove that dim V n

2 2 In Applied Life Data Analysis Wiley 1982 Wayne Nelson presents the breakdown time of an insulating fluid between electrodes at 34 kV The times in minutes are as fol lows 0 19 0 78 0 96 1 31 2 78 3 16 4 15 4 67 4 85 6 50 7 35 8 01 8 27 12 06 31 75 32 52 33 91 36 71 and 72 89 Calculate the sample average and sample standard deviation Construct a dot diagram of the data recogniz The data 50 77 3 sample s 2 6 P tures is a study to

Use the value of the ratio to fill in the following two multiplicative comparison statement a The number of pancakes made is 1 5 b The amount of cups of flour needed is times the amount of cups of flour need of the number of pancakes made If Alyssa has to make 70 pancakes how many cups of flour will she have to use

4 An investor is considering three types of investments a high risk venture into oil leases with a potential return of 15 a medium risk investment in bonds with a 9 return and a relatively safe stock investment with a 5 return He has 50 000 to invest Because of the risk he will limit his investment in oil leases and bonds to 30 of the 50 000 and his investment in oil leases and stock to 50 How much should he invest in each to maximize his return assuming investment returns are as expected a Define the variables Be specific with descriptive words b Clearly state the constraints all inequalities related to the feasible region c State the objective function d Set up the initial simplex matrix needed to solve the linear programming problem using the Simplex Method Perform all niyots necessory using row onerations to transform the

2 14 The shear strengths of 100 spot welds in a titanium alloy follow Construct a stem and leaf diagram for the weld strength data and comment on any important features that you notice 5408 5431 5475 5442 5376 5388 5459 5422 5416 5435 5420 5429 5401 5446 5487 5416 5382 5357 5388 5457 5407 5469 5416 5377 5454 5375 5409 5459 5445 5429 5463 5408 5481 5453 5422 5354 5421 5406 5444 5466 5399 5391 5477 5447 5329 5473 5423 5441 5412 5384 5445 5436 5454 5453 5428 5418 5465 5427 5421 5396 5381 5425 5388 5388 5378 5481 5387 5440 5482 5406 5401 5411 5399 5431 5440 5413 5406 5342 5452 5420 5458 5485 5431 5416 5431 5390 5399 5435 5387 5462 5383 5401 5407 5385 5440 5422 5448 5366 5430 5418

Unit 5 QPA The first Ferris wheel was designed and built by an American engineer named George W G Ferris in 1893 The radius of the wheel was 125 feet A Ferris wheel modeled on the original design takes 20 seconds to complete one revolution counterclockwise 1 Suppose a Ferris wheel with the above characteristics is tested for functionality Two engineers are in non adjacent cars where the central angle between the cars TC is radians Find the arc length between 6 the cars of the engineers Show your work and round if needed An architect transposes a unit circle over a Ferris wheel drawing where the center of the cicle is the center of the Ferris wheel The start position for a car is when 0 0 2 The architect sketches the motion of the car to a position where cos 0 trigonometric identities to find the other trigonomatric ratios for 0 9 41 125 ft Use

29 A 90 m basement in a residence is found to be contaminated with radon coming from the ground through the floor drains The concentration of radon in the room is 1 5 Bq L under steady state conditions The room behaves as a CSTR and the decay of radon is a first order reaction with a decay rate con stant of 2 09 106 s If the source of radon is closed off and the room is vented with radon free air at a rate of 0 14 m s how long will it take to lower the radon concentration to an acceptable level of 0 15 Bq L

Increasing the down payment on a mortgage reduces both the size of the monthly payments and the total interest paid Calculate a the reduction in the monthly payment by increasing the down payment by the amount specified and b the amount saved on interest over the life of the loan Assume the mortgage is for 30 years and use the amortization table to find the monthly payments Increase in Down payment 15 000 Click the icon to view a table of monthly payments on a 1 000 loan Amount of Loan Interest Rate Down Payment 162 000 38 000 5 a The monthly payment will be reduced by 80 55 when the down payment is increased by 15 000 Round to the nearest cent as needed b Increasing the down payment by 15 000 saved Round to the nearest cent as needed CIL on interest over the life of the loan Monthly Payment on a 1 000 loan Annual Interest Rate 4 5 6 8 10 Number of Years for the Loan 4 20 10 22 58 10 12 23 03 10 61 6 06 6 60 11 10 7 16 12 13 8 36 13 22 9 65 3 29 53 29 97 30 42 23 49 31 34 24 41 32 27 25 36 30 4 77 5 37 6 00 7 34 8 78 X

All the accounts have normal balances The information below has been gathered at December 31 2019 1 Verne Cova Company borrowed 10 000 by signing a 12 one year note on September 1 2019 10 000 12 4 12 400 Dr Interest expense 400 Cr Interest payable 400

An article in Nature Genetics Vol 34 1 2003 pp 85 90 Treatment Specific Changes in Gene Expression Discriminate in Vivo Drug Response in Human Leukemia Cells reported the study of gene expression as a function of treatments for leukemia One group received a high dose of the drug while the control group received no treatment Expression data measures of gene activity from one gene are shown in the accompanying table for all of the treated subjects and some of the control subjects Compute the sample mean and standard deviation for each group separately Construct a dot diagram for each group separately Comment on any differences betweer the groups High Dose 16 1 134 9 52 7 14 4 124 3 99 0 24 3 16 3 15 2 47 7 12 9 Control 297 1 491 8 1332 9 1172 0 1482 7 335 4 528 9 24 1 545 2 92 9 337 1

6 Define the first law of thermodynamics and provide one example 7 Define the second law of thermodynamics and provide one example

The architect draws a 30 60 90 right triangle to show the location of a car on the Ferris wheel with respect to its center O 3 What are the sine and cosine ratios for ZO 0 center Unit 5 QPA location of car 30 4 What are the lengths of AB and AO Show your work and round if needed

2 3 Seven oxide thickness measurements of wafers are studied to assess quality in a semiconductor manufacturing process The data in angstroms are 1264 1280 1301 1300 1292 1307 and 1275 Calculate the sample average and sam ple standard deviation Construct a dot diagram of the data wins 2 13 Calc Con 2 7

2 10 Suppose that everyone in a company receives a pay raise of 200 per month How does that affect the mean monthly pay for that organization How does it affect the stan dard deviation of monthly pay

1 12 A quality control technician is instructed to sample a soft drink bottling process by going to the production line once each hour and selecting the three most recently produced bottles Is this a simple random sample of the bottles being produced

nodel Is y city tax mes that edict the 1 9 A population has four members a b c and d a How many different samples are there of size n 2 from this population Assume that the sample must consist of two different objects b How would you take a random sample of size n 2 from this population tall

cameras at random between 3 P M and 4 P M from the produc tion line output Is this a random sample 1 8 List three mechanistic models that you have used in your engineering studies

1 7 An engineer wants to obtain a random sample of the output of a process manufacturing digital cameras She sam ples on three different days and on each day she selects five cameras at random between 3 P M and 4 P M from the produc tion line output Is this a random sample

ook lint rint rences Paulson Company issues 9 four year bonds on January 1 of this year with a par value of 106 000 and semiannual interest payments Semiannual Period End 0 January 1 issuance 1 June 30 first payment Carrying Value 99 147 100 004 100 861 2 December 31 second payment Use the above straight line bond amortization table and prepare journal entries for the following a The issuance of bonds on January 1 b The first interest payment on June 30 c The second interest payment on December View transaction list Journal entry worksheet 1 2 3 Unamortized Discount 6 853 5 996 5 139

While collecting data the environmentalists found an injured male from the western area and two females from the eastern population These deer were transported back to the facility for treatment and rehabilitation The deer were kept in the same enclosure for over a year Despite observed attempts of the male to mate while the females were in heat no viable offspring were produced Genetic tests were run to determine if any problems were preventing fertilization and all came back with normal results More individuals were brought to the facility and again the deer from the different populations were unsuccessful in their attempts to breed Prompt Write a scientific claim that explains the impact the highway construction had on the whitetail deer populations Claim Evidence 8

2 Tano Company issues bonds with a par value of 81 000 on January 1 2021 The bonds annual contract rate is 6 and interest is paid semiannually on June 30 and December 31 The bonds mature in three years The annual market rate at the date of issuance is 8 and the bonds are sold for 76 753 S eBook Hint Print ferences 1 What is the amount of the discount on these bonds at issuance 2 How much total bond interest expense will be recognized over the life of these bonds 3 Prepare a straight line amortization table for these bonds Complete this question by entering your answers in the tabs below Required 1 Required 2 Required 3 Check my we

Shane has a retirement plan with an insurance company He can choose to be paid either 320 per month for 20 years or a lump sum of 35 000 Which is the better option Assume an annua interest rate of 12 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The present value of the retirement plan is Round to the nearest cent as needed this is worse than the lump sum of 35 000 OB The present value of the retirement plan is Round to the nearest cent as needed OC The present value of the retirement plan is the same as the lump sum of 35 000 this is better than the lump sum of 35 000

Marcus has won a 6 000 000 state lottery He can take his prize as either 15 yearly payments of 400 000 or a lump sum of 3 225 000 Which is the better option Assume an interest rate 9 Select the correct choice below and if necessary fill in the answer box to complete your choice Round to the nearest dollar as needed O A The present value of the lottery winnings is this is better than the lump sum of 3 225 000 OB The present value of the lottery winnings is OC The present value of the lottery winnings is the same as the lump sum of 3 225 000 this is worse than the lump sum of 3 225 000

the annual interest rate and a line of an amortization schedule for that loan complete the next line of the schedule Assume that payments are made monthly Annual Interest Rate Payment 7 9 413 66 Interest Paid 43 64 Fill out the amortization schedule below Annual Interest Rate 7 9 Interest Paid 43 64 Payment 413 66 Round to the nearest cent as needed Paid on Principal Balance 370 02 6 262 38 Paid on Principal 370 02 Balance 6 262 38

Assume that the mortgage is a 20 year adjustable rate mortgage a Use the table to find the monthly mortgage payments b Make a rough estimate of your monthly payments for year 3 by recalculating the monthly payments for a 20 year mortgage for the original amount at the new interest rate P 197 000 beginning interest rate 6 rate increases 2 each year Click the icon to view a table of monthly payments on a 1 000 loan Identify the problem solving method that should be used Choose the correct answer below OA The Always Principle B The Three Way Principle C Guessing is OK D Relate a New Problem to an Older One a The monthly payments for this loan are Type an integer or a decimal Monthly Payment on a 1 000 loan Annual Interest Rate 4 5 6 8 10 12 3 29 53 29 97 30 42 31 34 32 27 33 21 Number of Years for the Loan 20 4 22 58 10 10 12 6 06 6 60 10 61 23 03 23 49 11 10 7 16 24 41 12 13 8 36 13 22 9 65 14 35 11 01 25 36 26 33 30 4 77 5 37 6 00 7 34 8 78 10 29 X

21 Major Company reported 2024 income of 310 000 from continuing operations before income taxes and a before tax loss on discon operations of 78 000 All income is subject to a 25 tax rate In the income statement for the year ended December 31 2024 Maja Company would show the following line item amounts for income tax expense and net income Multiple Choice 58 000 and 388 000 respectively 77 500 and 174 000 respectively 58 000 and 232 500 respectively Sty G

Given the annual interest rate and a line of an amortization schedule for that loan complete the next line of the schedule Assume that payments are made monthly Annual Interest Rate Payment 13 245 79 Interest Paid 41 13 Identify the problem solving method that should be used Choose the correct answer below OA The Always Principle B Relate a New Problem to an Older One C The Three Way Principle OD Guessing is OK Fill out the amortization schedule below Annual Interest Rate 13 Paid on Principal 204 66 Interest Paid 41 13 Payment 245 79 Round to the nearest cent as needed Balance 3 592 87 Paid on Principal 204 66 Balance 3 592 87

1 Drag the numbers below to the correct area 0 2 0 05 1 5 0 02 0 20 1 50 1 20 2 100 5 100 I I I I I I Equals 20 Equals 2 MII Equals 5 I I

Use the information in the table to calculate a the deposit due at signing b the amount you pay in points and c the total amount that you must pay at closing for your house Other Closing Cost of Home 110 000 Costs 2 400 Deposit 25 Points 5 a The deposit due at signing is 27 500 Type an integer or a decimal b The amount to pay in points is Type an integer or a decimal

Linear Systems Month 122 1 Fitness R Us charges an initial fee of 100 and 30 month Fitness Club CanFit charges a 150 initial fee to join the club and a 20 monthly fee a Write an equation to represent the cost of membership at Fitness R Us 100 30 11 3 191 PR T b Write an equation to represent the cost of membership at CanFit 1 5 150 20X1 5 15 2 c Graph the two equations use the graph provided d Write the point of intersection e What does the point of intersection represent f If you are planning to join for 1 year which club should you join Explain your answer

Multiple Choice To plan your time for a research project it is best to 1 point O divide the time spent on each step evenly O keep your deadlines flexible O start at the beginning and plan from there work backward

Given a loan amount P an annual interest rate r and the length of the loan in years find the monthly payment R necessary to pay off the loan by completing parts a through c Represent t number of monthly payments by n Amount 120 000 n a Calculate P1 Rate 9 Time 15 years P 2 12 A Round to two decimal places as needed and call this number A

CLE Name Linear Systems Month 122 and 30 1 Fitness R Us charges an initial fee of 100 and 30 month Fitness Club CanFit charges 150 initial fee to join the club and a 20 monthly fee a Write an equation to represent the cost of membership at Fitness R Us P trR 100 30x 1201 3 19 2x 120 1 5 represent the cost of membership at CanFit

9 Tri Fecta a partnership had revenues of 369 000 in its first year of operations The partnership has not collected on 46 900 of its sales and still owes 39 900 on 175 000 of merchandise it purchased There was no inventory on hand at the end of the year The partnership paid 33 700 in salaries The partners invested 42 000 in the business and 21 000 was borrowed on a five year note The partnership paid 2 100 in interest that was the amount owed for the year and paid 9 700 for a two year insurance policy on the first day of business Compute net income for the first year for Tri Fecta 01 27 06 Multiple Choice 153 350

11 In the statement of shareholders equity Retained Earnings had a beginning balance of 26 800 During the period the company reports a net income of 11 800 and a dividend of 5 800 The ending balance in the Retained earnings account is 01 26 42 Multiple Choice O O 38 600 44 400 11 800

Show that quadrilateral FGHJ is a trapezold but is not a parallelogram Slope FG Slope GH 5 and slope HJ and slope JF The quadrilateral has select 2 1 0 G H 4 of parallel sides so it is a trapezoid but not a parallelogram

5 Indiana Company began a construction project in 2024 with a contract price of 163 million to be received when the project is completed in 2026 During 2024 Indiana incurred 38 million of costs and estimates an additional 85 million of costs to complete the project Indiana recognizes revenue over time and for this project recognizes revenue over time according to the percentage of the project that has been completed 1 28 22 In 2025 Indiana incurred additional costs of 56 million and estimated an additional 38 million in costs to complete the project Indiana Note Do not round intermediate calculations Multiple Choice recognized 9 72 million gross profit on the project in 2025 recognized 9 00 million gross profit on the project in 2025

2 01 29 00 Recent financial statement data for Harmony Health Foods HHF Incorporated is shown below Income before interest and taxes Interest expense Income before tax Income tax Net income Current liabilities 10 Bonds long term Total liabilities Shareholders equity Common stock Retained earnings Total shareholders equity Total liabilities and equity HHF s debt to equity ratio is Note Round your answer to 2 decimal places Multiple Choice 189 380 569 202 299 501 1 070 116 38 78 22 56

7 On October 28 2024 a company committed to a plan to sell a division that qualified as a component of the entity according to GAAP regarding discontinued operations and was properly classified as held for sale on December 31 2024 the end of the company s fiscal year The division s loss from operations for 2024 was 1 940 000 01 27 37 The division s book value and fair value less cost to sell on December 31 were 2 890 000 and 3 630 000 respectively What before tax amount s should the company report as loss on discontinued operations in its 2024 income statement Multiple Choice 1 940 000 loss 740 000 gain included in continuing operations and a 1 940 000 loss from discontinued operations h

1 28 36 Excerpts from Hulkster Company s December 31 2024 and 2023 financial statements are presented below Accounts receivable Merchandise inventory Net sales Cost of goods sold Total assets Total shareholders equity Net income Hulkster s 2024 profit margin is closest to Multiple Choice 2024 56 000 36 000 240 000 130 000 441 000 256 000 44 500 2023 44 000 51 000 230 000 116 000 413 000 233 000 36 000 D

3 01 28 48 The following information is provided for Sacks Company before closing entries Cash Supplies Prepaid rent Salaries expense Equipment Service revenue 12 400 4 900 2 400 4 900 65 400 31 600 20 400 3 400 5 400 Miscellaneous expenses Dividends Accounts payable Common stock Retained earnings What is the amount of total shareholders equity Multiple Choice 68 400 8 400