Basic Math Questions and Answers

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

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

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

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

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

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

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

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

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

10 01 26 55 The assumption that in the absence of contrary information a business entity will continue indefinitely is the Multiple Choice Historical cost assumption Going concern assumption

1 6 List two examples of conceptual populations and two examples of physical populations For each population describe a question that could be answered by sampling from the population Describe how a random sample could be obtained Whe conti yield rand

1 2 A city has 20 neighborhoods How could the city tax appraiser select a random sample of single family homes that could be used in developing an empirical model to predict the appraised value of a house a What characteristics of the house would you recommend that the tax appraiser consider using in the model b Is this an enumerative study or an analytic study

Dean Male ct 7 two vi How many students in i Brown eyes 8 The Venn diagram shows information about a group of children The numbers shown in these sets represent the cardinal number of the set How many girls are in the group 12 10 asked Girl 18 ii How many brown eyed girls are in the group iii How many boys are in the group iv How many people are in the group 9 Given A factors of 48 and B factors of 2 i List the elements of set A and set B ii Draw a Venn diagram to represent A and iii Explain in words what the overlapping region means in this question iv Use your Venn diagram to find the HCF of 20 and 48

2 1 An important quality characteristic of water is the concentration of suspended solid material in mg l Twelve measurements on suspended solids from a certain lake are as follows 42 4 65 7 29 8 58 7 52 1 55 8 57 0 68 7 67 3 67 3 54 3 and 54 0 Calculate the sample average and sample standard deviation Construct a dot diagram of the data first y 126 Calcu Const 2 5 on vis

vehicle lontification Number is assig cars how many different VINS are Possible all

36 9 Fill in the integer values of each square root on the number line 25 49

The difference of a number and 7 is 20 What is the number

If Pablo drives 288 miles at a constant speed of 72 mph How long will it take Be sure to include the units Answer number then units

Use the perimeter formula P 21 2w to find the length 7 of a rectangular lot if the width w is 45 feet and the perimeter P is 220 feet

What equal payments in 3 years and 5 years would replace payments of 37 500 and 80 000 in 7 years and 8 years respectively Assume money can earn 3 30 compounded quarterly

The U Drive Rent A Truck company plans to spend 8 million on 280 new vehicles Each commercial van will cost 25 000 each small truck 30 000 and each large truck 40 000 Past experience shows that they need twice as many vans as small trucks How many of each type of vehicle can they buy They can buy vans small trucks and large trucks

Whole number division by hand stops when the number at the bottom of the stack is smaller than the divisor True False

0 06 At the end of t years the future value of an investment of 10 000 in an account that pays 6 APR compounded monthly is S 10 000 0 000 1 0 additional deposits how long will it take for the investment to amount to 50 000 The investment will grow to 50 000 in years Do not round until the final answer Then round to two decimal places as needed 121 dollars Assuming no withdrawals

a Find the value k of the exponential growth rate Assume V 271 k Round to the nearest thousandth Instructor tip Example Write an exponential function by first finding the rate of change k given the value is 239 in 1977 and 499 in 1985 Tip Use V t Voe kt V t and the Vo are both dollar amounts the tis the time it took for the original 1977 value Vo to grow to the second value in 1985 V t which means t 8 So you plug those 3 values into the equation and end up solving it for the k Setup 499 293e k 8 or 499 293e 8k Now to get k by itself 1st step

If 15 000 is invested at 6 interest compounded monthly find the interest eamed in 14 years The interest earned in 14 years is Do not round until the final answer Then round to two decimal places as needed

Beginning in Chicago a salesperson must visit San Francisco Los Angeles San Diego Austin Houston Jacksonville Washington DC New York City and Boston How many different itineraries are there Answer Chil How many different itineraries are there if San Francisco Los Angeles and San Diego must appear consecutively and in this order Answer

Suppose that 39 000 is deposited in an account and the balance increases to 49 578 72 after 4 years How long will it take for the account to grow to 93 649 74 Assume continuou compounding It will take about years for 39 000 to grow to 93 649 74 Round to the nearest tenth as needed

If 5000 is invested at 4 compounded continuously what is the amount after 6 years The amount after 6 years will be Round to the nearest cent

Based on data from 1920 and projected to 2050 the expected life span of people in Country A can be described by the function f x 10 963 14 319 Inx where x is the number of years from 1900 to the person s birth year a Estimate the birth year for which the expected life span is 75 years b Use graphical methods to determine the birth year for which the expected life span is 75 years Does this agree with the solution in part a a The birth year is approximately for which the expected life span is 75 years IP und to the nearest whole number as needed

An amount of 5000 is invested at 14 interest compounded daily a Find the future value in 5 years b Determine whether more or less money would have accrued if the money had been compounded quarterly a The total amount is Round to the nearest cent as needed

Suppose the weekly cost for the production of x units of a product is given by C x 3455 60 In x 1 dollars Use graphical methods to estimate the number of units produced if the total cost is 3554 Graph C x 3455 60 In x 1 when the total cost is 3554 Choose the correct graph below OA AC x 3704 34044 AC O 3704 34044 GITE Estimate the number of units produced if the total cost is 3554 Round down to the nearest unit OC ACO 3704 3404 OD 3704 Q

There are 10 job applicants at a company How many different positions Answer The number of ways is P n k where n The final numerical answer is Submit answer Ja different ways are there to select three of the applicants for three and k

How many different ways are there to arrange 6 people in a row for a picture Answer The number of ways is P n k where n The final numerical answer is C D and k

A total of 6 cats are to be lined up in a row for a picture In how many different ways can the cats be arranged C A

A PIN is a string of four digits For example 0119 and 4512 are PINs How many PINs consist of four different digits from the set 5 6 8 9 Answer

At a burger stand you can order toppings from a checklist similar to this one Toppings Lettuce Tomato Pickles Suppose that there are 9 toppings on the list In how many different ways can you order toppings for your burger Answer

A shop sells t shirts that can be printed with any one of 30 designs Each t shirt can also be any one of 5 colors and there are 5 choices for sizes How many different t shirts are possible

5 Compute 3k 2 k 2 Compute 2k 3 k 5

the 1142 2180 356 4 20 637 6 68 he prime 70 8 50

12 202 Determine the time needed for the load at B to attain a speed of 8 m s starting from rest if the cable is drawn into the motor with an acceleration of 0 2 m s B