Basic Math Questions and Answers

Directions For each of the questions in this section show all work to get full marks 1 2 points When Sepideh and her husband s son was born at the end of every month they invested 80 in a Registered Education Savings Plan RESP that paid 6 per year compounded monthly Determine the amoun the RESP on the child s 18th birthday

E 2 points Jayson can invest his money in an account that pays 3 9 per year compounded monthly Determine the amount he must deposit at the end of each month to have 12000 in two years

4 4 points Tracy has several debts She owes approximately 8500 on a car loan approximately 3000 on a credit card and 12500 to her parents Determine the total amount paid on a five year consolidation loan that will cover the cost of these debts at 8 9 per year compounded monthly

3 4 points Abdul needs to repay a 25000 debt His bank offers personal loans at 7 8 compounded bi weekly Calculate the total interest paid by Abdul if he repays the debt with bi weekly payments over three years

3 5 Question 4 of 5 Cost of Home 370 000 Deposit 20 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 Points 4 This quiz 30 point s possible This question 7 point s possible Other Closing Costs 2 100 a The deposit due at signing is Type an integer or a decimal b The amount to pay in points is Type an integer or a decimal c The total amount due at closing is Submit quiz Type an integer or a decimal 2

D Y B B X Et a use the oLs method to estimate B b Pls prove unbiase namely El B B c what is Var B Yi Bixi Ei a Pls prove Xi Ji X b What is Var B Set a regression mode fi pls prove n X Y B lxy X Ji x x Cov X y Var X Note Exy To SWIE 13

Perpetual inventory using FIFO Beginning inventory purchases and sales for Item Zeta9 are as follows Oct 1 62 units 25 Oct 7 48 units Oct 15 73 units 26 Oct 24 Sale 22 units Assuming a perpetual inventory system and using the first in first out FIFO method determine a the cost of goods sold on October 24 and b the inventory on October Inventory Sale Purchase a Cost of goods sold on October 24 b Inventory on October 31 X X

A flush in the card game of poker occurs if a player gets five cards that are all the same suit clubs diamonds hearts or spades Complete parts a through c to obtain the probability of being dealt a flush in five cards a Initially concentrate on one suit say diamonds There are 13 diamonds in a deck Compute P five diamonds P first card is diamonds and second card is diamonds and third card is diamonds and fourth card is diamonds and fifth card is diamonds In a standard 52 card deck P five diamonds Round to six decimal places as needed b A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades Compute P five clubs or five diamonds or five hearts or five spades Note that the events are mutually exclusive In a standard 52 card deck P five clubs or five diamonds or five hearts or five spades Round to three decimal places as needed c A royal flush in the game of poker occurs if the player gets the cards Ten Jack Queen King and Ace all in the same suit Use the rocedure given in parts a and b to compute the probability of being dealt a royal flush na standard 52 card deck P royal flush

16 2 points Required information Net sales Expenses Cost of goods sold Depreciation expense Total operating expenses For Year Ended December 31 Other unusual and or infrequent gains losses Income tax expense Income from continuing operations Income from continuing operations Discontinued segment Gain on sale of wholesale business segment net of tax Loss from operating wholesale business segment net of tax Net income 1 582 000 X x 248 000 828 000 475 000 3 100 000 1 830 000 1 270 000 232 000 X 1 038 000 x 2 076 000 2 076 000 353 000 3 100 000 Retu

After the amount due on a sale of 46 600 terms n eom is received from a customer the seller consents to the return of the entire shipment for a cash refund The cost of the merchandise returned is 27 968 a What is the amount of the refund owed to the customer Feedback Check My Work b Journalize the entries made by the seller to record the return and the refund If an amount box does not require an entry leave it blank 88 Customer Refunds Payable Cash

tonio has read 147 pages of a book He has completed 70 of the book How re pages does he need to read to finish the book

Cross profit During the current year merchandise is sold for 217 900 cash and 399 800 on account The cost of the goods sold is 401 500 What is the amount of the gross profit

Macmillan Learning Find solutions of the equation sin t cos t Suggestion Think about the special angles that you know Select the correct solutions 3 0 1 2 T 0 SA 4 0 0 0 5T 4 3 4 9n 4

Macmillan Learning Find the values of the six trigonometric functions of the angle One or more of the trigonometric functions may not be defined If so enter UNDEFINED for the function or functions Remember that radian measure is indicated when degrees are not explicitly stated Express numbers in exact form Use symbolic notation and fractions where needed Simplify your answers completely sin T tan T sec T OS cot n csc T

Macmillan Learning Find the values of the six trigonometric functions of the angle 90 One or more of the trigonometric functions may not be defined Express numbers in exact form Use symbolic notation and fractions where needed Simplify your answers completely Enter UNDEFINED if any of the trigonometric functions is not defined sin 90 tan 90 sec 90 cos 90 cot 90 csc 90

tem A cosine function has a maximum point at 4 28 The next minimum point occurs at the point 12 Determine the coordinates of the next maximum point A 12 28 D 28 8 B 20 8 E 28 28 C 20 28

passage Out of Place yapmayaca m I will not do that He e my shoes he stole my guitar Erkan s ed impudent beneath his dark brow as s reddened in fury His gray whiskered pled as his hand gripped tightly around s wrist The nurse carefully but firmly self from Erkan s grasp He then turned Togiver who was assisting him smiled How is Michelle different at the end of the story than she is at the beginning beceranstal She disciplines herself to work hard at unpleasant tasks She strives to attain high goals for her life She realizes what career path she should pursue connect with

Divide by using an area model Then check your work 1 168 12 2 Divide Then check your work 414 18 1 8 4 1 4 Check 168 X 12 Check 414 x 18

A piston cylinder device initially contains 0 6 m of saturated water vapor at 250 kPa At this state the piston is resting or a set of stops and the mass of the piston is such that a pressure of 300 kPa is required to move it Heat is now slowly transferred to the steam until the volume becomes 1 400 m Use the data from the steam tables Determine the final temperature Round the final answer to three decimal places The final temperature is C

3 10 Given that the particular solution to the nonhomogeneous differential equation y 3y 2y 10e x is Yp e x and that the particular solution to the nonhomogeneous differential equation y 3y 2y sin x is yp differential equation 1 10 sin x 3 cos x give a particular solution to the nonhomogeneous 10 y 3y 2y 10e3x sin x

2 ats Skipped eBook Hint Print ferences Complete this question by entering your answers in the tabs below Express the following comparative income statements in common size percents Using the common size percents which item is most responsible for the decline in net income Income Statement Reason for Decline in Net Income Using the common size percents which item is most responsible for the decline in net income Using the common size percents which item is most responsible for t decline in net income Income Statement Reason for Decline in Net Help Cost of goods sold Operating expenses Sales Save Exit Submit Check my work

point s possible COLLE List all the ways to select two different members from S without repetition The order in which members are selected is important For example AB is not the same selection as BA S Q R S T U Submit quiz Identify the list of all the ways to select two members from S Choose the correct answer below O A QQ QR QS QT QU RR RS RT RU SS ST SU TT TU UU OB QR QS QT QU RQ RS RT RU SQ SR ST SU TQ TR TS TU UQ UR US UT OC QR QS QT QU RS RT RU ST SU TU O D QS QT QU RS RT RU ST SU 2

1 10 Use Euler s method with a step size of h 0 1 to obtain a three decimal approximation of y 2 2 for the initial value problem y y xy y 2 3

Due Date 10 26 2023 1 Draw a flow net and calculate the seepage loss per meter length of the sheet pile at the right angle to the cross section shown H 6 m H 1 5 m D 3 m D m D Sheet pile EK D k 4 x 10 4 cm s Impermeable layer NOTE Show all the calculation steps

7 10 Use the method of Variation of Parameters to find the general solution to the differential equation y y csc x 1

5 10 Use the method of Undetermined Coefficients to find the general solution to the differential equation y 6y 5x x 2e x

Match the following terms with their definitions 1 Cash price minus down payment 2 A revolving charge account 3 Used to calculate rebate of finance charge 4 Total of all monthly payments plus down payment 5 Sum of daily balance divided by number of days in billing cycle 6 Total of all payments minus amount financed 7 A payment process 8 Doesn t dictate interest rates 9 Initial cash payment 10 Effective interest rate 11 Used in calculation of average daily balance 12 Purchase till maximum credit reached Amortization Amount financed APR Average daily balance

8 10 Give the general solutions to the Cauchy Euler differential equation x y 5xy 4y 0

10 Here are some Canadian hockey players and the year they were born Jennifer Botterill 1979 Jonathan Cheechoo 1980 Roberto Luongo 1979 Jordin Tootoo 1983 Hayley Wickenheiser 1978 For each association below use these data to represent a relation in different ways a was born in b is the birth year of

4 10 Give the general solution to the differential equation y 2y 5y 0

What is an insurgent 1 point a person of mixed Indigenous and European heritage a person who acts against their government a person from northern Mexico O a person who owns land and has power

YOU TRY 1 A computer software company models the profit on its latest game using the relation P x 2x 28x 90 where x is the number of games it produces in hundreds of thousands and P is the profit in millions of dollars a How many games must it produce to earn a maximum profit b What is the maximum profit the company can earn

The following graph gives the labor market for laboratory aides in the imaginary country of Sophos The equilibrium hourly wage is 10 and the equilibrium number of laboratory aides is 150 Suppose the federal government of Sophos has decided to institute an hourly payroll tax of 4 on laboratory aides and wants to determine whether the tax should be levied on the workers the employers or both in such a way that half the tax is collected from each party Use the graph input tool to evaluate these three proposals Entering a number into the Tax Levied on Employers field initially set at zero dollars per hour shifts the demand curve down by the amount you enter and entering a number into the Tax Levied on Workers field initially set at zero dollars per hour shifts the supply curve up by the amount you enter To determine the before tax wage for each tax proposal adjust the amount in the Wage field until the quantity of labor supplied equals the quantity of labor demanded You will not be graded on any changes you make to this graph Note Once you enter a value in a white field the graph and any corresponding amounts in each grey field will change accordingly WAGE Dollars per hour 2222 NO 20 18 16 14 12 10 6 4 2 0 I 1 Levied on Employers Dollars per hour 4 I 0 2 1 1 0 30 60 90 120 160 180 210 240 270 300 LABOR Number of workers Tax Proposal Levied on Workers Supply Dollars per hour 0 Demand 4 2 Graph Input Tool Market for Laboratory Aides Wage Dollars per hour Labor Demanded Number of workers Quantity Hired Number of workers Demand Shifter Tax Levied on Employers Dollars per hour For each of the proposals use the previous graph to determine the new number of laboratory aides hired Then compute the after tax amount paid by employers that is the wage paid to workers plus any taxes collected from the employers and the after tax amount earned by laboratory aides that is the wage received by workers minus any taxes collected from the workers 375 0 Labor Supplied Number of workers After Tax Wage Paid by Employers Dollars per hour Supply Shifter Tax Levied on Workers Dollars per hour 0 0 After Tax Wage Received by Workers Dollars per hour

Complete the following table assume the overtime for each employee is a time and a half rate after 40 hours Note Do not round intermediate calculations Round your overtime rate and gross earnings to the nearest cent Employee Monday Tuesday Wednesday Thursday Friday Saturday Tagney 14 5 8 9 9 Total regular Total overtime hours hours Regular rate 7 60 Overtime rate Gross earnings

Complete the following table Note Round your gross pay to the nearest cent Employee Bernie Roy Monday Tuesday Wednesday Thursday Friday 6 9 6 9 7 Hours Rate per hour S 8 95 Gross pay

15 35 The bus B has a weight of 15 000 lb and is traveling to the right at 5 ft s Meanwhile a 3000 lb car A is traveling at 4 ft s to the left If the vehicles crash head on and become entangled determine their common velocity just after the collision Assume that the vehicles are free to roll during collision VB 5 ft s B Prob 15 35 UA 4 ft s J

1 State the optimal value and if it is a maximum or minimum value for each function c y 0 5 x 3 a y 2 x 5 8 b y x 2 9

1 7m 9 45 SCHO 105 2 3 4d 23 1 29 0 4 3m 36 108 56ct8 40 6 4m 22 88

This chart shows how real GDP per capita in 2010 U S dollars has changed for some important countries and regions over the last two centuries Real per 145 000 capita GOP 40 000 35 000 30 000 25 000 20 000 15 000 10 000 5 000 0 43 629 1st attempt United States 30 642 Western Europe 9 026 Latin America 1800 1900 2000 5 243 China 2 900 India 2 254 Africa Source Angus Maddison Statistics on World Population GDP and Per Capita GDP 1 2008 AD Based on the chart above check the boxes next to all of the statements that are true Choose one or more A China grew faster than India in the twentieth century B There were no differences among any of these regions in 1800 OC Western Europe has grown more slowly than the United States in the last 100 years D The United States and Western Europe had similar real GDP per capita in 1800 DE Neither China nor India grew much between 1800 and 1900 F Latin America had the highest sustained growth rates over the past 200 years See Hint

Comparing the 40 poorest nations with the high income OECD nations are the following living conditions higher or lower in poorer nations Items 8 items Drag and drop into the appropriate area below female literacy rates access to clean water GDP per capita Higher male literacy rates infant mortality Lower access to improved sanitation life expectancy

FRED Millions of Chained 2012 0 60 000 54 000 2 000 40 000 44 000 40 000 34 000 22 000 210 000 24 000 20 000 Real Total Gross Domestic Product for Wyoming Real Total Gross Domestic Product for Alaska Real Total Gross Domestic Product for Vermont 1900 Shaded areas indicate US recessions State WY VT AK 2000 1st attempt sifanest 0 3 State WY VT AK 2002 The data from the last year of this graph are given below Wyoming by population are given on the following graph Real GDP in 2018 in millions 38 369 30 013 52 311 2006 Population 579 315 623 657 739 795 2000 Source US Bureau of Economic Analyses For the interactive version of this graph use the following link https fred stlouisfed org graph id WYRGSPAKRGSPVTRGSP 2910 2012 2014 2016 fred stoutsted org Part 1 3 points In 2018 the three smallest states had the following populations from https www worldatlas com articles us states by population html 2010 See Hint Using these populations and the data from FRED given in the table below the graph calculate the real GDP per capita for these three states

The following summary of a statistical study gives a sample statistic and a margin of error Find the confidence interval and answer any additional questions A poll is conducted the day before a state election for senator There are only two candidates running for this office The poll results show that 60 of the voters favor the Republican candidate with a margin of error of 4 percentage points Should the Republican expect to win Why or why not The confidence interval is from to Simplify your answers Use ascending order

Living Conditions in Poor Nations versus Rich Nations Life indicators GDP per capita PPP 2011 international Infant mortality rate per 1 000 live births Under 5 mortality rate per 1 000 Life expectancy at birth years Physicians per 10 000 people Access to improved water Access to improved sanitation Access to electricity Mobile cellular subscriptions per 100 people Secure Internet servers per million people Literacy rate adult male Literacy rate adult female Female male secondary enrollment ratio Female male postsecondary enrollment ratio Poor 1 872 53 76 62 2 1 68 7 37 1 31 2 55 1 43 68 53 0 89 0 65 Rich 40 651 1 50 4 5 81 29 3 99 6 99 9 99 7 1131 1 181 03 99 99 0 99 24 Source World Bank World Development Indicators Poor nations are 40 poorest rich nations are 31 high income OECD nations Data are generally from 2013 but some individual observations are from 2011 and 2012 Which of the following statements correctly describes a reason that economic growth matters as shown by the table Choose one A The infant mortality rate in rich nations is 53 per 1 000 births in rich nations and 4 per 1 000 births in poor nations B Almost 100 of the people in poor nations have access to improved water while only about 69 of those in rich nations have access to improved water C Ninety nine percent of adult females are literate in poor nations and 68 of adult females are literate in rich nations OD Rich nations have a higher per capita GDP than poor nations but by most other measures there is not a great difference in human welfare

The table on the right gives the annual income for eight families in thousands of dollars Find the number of standard deviations family G s income is Family A B C D E F G H from the mean Income 54 55 51 52 50 52 49 53 How many standard deviations is family G s income from the mean Round to three decimal places as needed D

K Part 2 of 2 Find the mean and standard deviation of the frequency distribution The mean is 4 9 Type an integer or a decimal Do not round The standard deviation is Type an integer or decimal rounded to two decimal places as needed CCEED X 3 4 5 6 7 f C 1 3 4 0 2 Points

Find the range mean and standard deviation of the data set 18 14 18 8 8 10 5 6 The range is 13 Type a whole number The mean is 10 875 Type an integer or a decimal The standard deviation is Type an integer or decimal rounded to two decimal places as needed

In the accompanying table there is a list of the monthly prices of a gallon of unleaded gasoline and diesel fuel in 2020 and summary statistics Use the coefficient of variation to determine wh gasoline prices or diesel prices were more stable in 2020 Click here to view the fuel price data The coefficient of variation of the gasoline prices in 2020 was Type an integer or decimal rounded to one decimal place as needed Fuel Price Data population mean population standard deviation o 2020 Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Gasoline Prices 2 55 2 58 2 77 3 07 3 31 3 16 3 17 3 05 2 87 3 02 2 88 3 07 gal gasoline diesel 2 958 0 235 3 092 0 109 Diesel Prices 3 15 3 09 2 98 3 07 3 34 3 06 3 03 2 95 2 98 3 21 3 11 3 13 C gal X

K Part 2 of 2 The table shows the scores of 20 people who took a paramedics licensing test Find the mean and standard deviation for these data The mean of the data is 78 The standard deviation is approximately Round to three decimal places as needed CICLE Points 0 of 1 Score Frequency 73 5 74 1 5 6 2 1 77 81 83 84

The following table lists the income tax rates for a single person earning 30 000 per year for several states Complete parts a and b A C D E F G H 5 17 7 85 4 17 3 66 5 91 2 27 3 51 5 27 State Income Tax Rate B a Find the mean and standard deviation for these data The mean is Type an integer or decimal rounded to three decimal places as needed

CV Round to two decimal places as needed Points 0 of 1 K A particular brand of laptop was sampled with regard to the time it can be used before it requires recharging The mean time was calculated to be 7 2 hours with a standard deviation of 2 13 hou Calculate the coefficient of variation for this example Save