Math - Others Questions

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

3x b Is y e x y e 2x y e x e 2x a fundamental solution set for this differential equation Answer yes or no and justify your answer

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

B Key Bartolomeu Dias Vasco Da Gama Christopher Columbus Ferdinand Magellan 84 54

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

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

2 10 a Show that y c e x c e 2x is a solution to the differential equation y y 6y 0 b Is y e x y e 2x y3 e x e x a fundamental solution set for this differential equation Answer yes or no and justify your answer

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

2 For each function i a Find the axis of symmetry Find the optimal value ii y 3x 12x 11 b y 4x 10x 3

c y 5 x 3 x 7 d y x 2 x 10

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

3 The height h in meters of a springboard diver above the surface of the water t seconds after the leave the board is given by h t 4 9t 8 8t 3 Determine the diver s maximum height above the springboard

Write the following functions in vertex form State if the vertex is a minimum or maximum 1 y x 10x 6 2 y 2x 12x 16

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

md Starting with the 3 scores 10 20 and 30 what 2 additional scores must be included to create a set of 5 scores that has a median of 28 and one mode Write your answers joined by the word and such as 100 and 150 A

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

The following statistical study gives a sample statistic and a margin of error Find the confidence interval and answer any additional questions A national survey of 1513 respondents reached on land lines and cell phones found that the percentage of adults who favor legalized abortion is 43 The study claimed that the error attributable to sampling is 6 percentage points Would you claim that a majority of people are not in favor of legalized abortion The confidence interval for the study is to docimale Hea necending order

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

K the mean and standard deviation of the frequency distribution The mean is Type an integer or a decimal Do not round X f 3 4466 W 5 7 13402 D

As the manager of the human resources department at your firm you are investigating the number of sick days employees took during the last calendar year For employees in the marketing area the average number of sick days is 4 6 with standard deviation 2 3 for those in the research and design R D the mean is 5 3 with standard deviation 3 2 Compute and compare the coefficients of variation for each set of data What is the coefficient of variation for the marketing area CV V Round to one decimal place as needed

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 G Points 0 of 1 Score Frequency 73 5 74 1 77 5 81 6 83 2 84 1

Prorate the given expenses to find the monthly cost Keiko pays 340 per month for food a semi annual health insurance premium of 1600 and an annual car insurance premium of 650 Round your answer to the nearest dollar

a Give the five number summary for the distribution and b draw a box and whisker plot 9 23 23 18 28 30 47 19 45 29 35 35 47 46 53 a The five number summary for this data set is 9 23 30 46 53 Use ascending order Simplify your answers b Choose the correct box and whisker plot OA 5 10 15 20 25 30 35 40 45 50 55 O C F 5 10 15 20 25 30 35 40 45 50 55 oo OB 5 10 15 20 25 30 35 40 45 50 55 O D 5 10 15 20 25 30 35 40 45 50 O Oo

K Use the given graph to find the mean median and mode of the distribution Find the mean Select the correct choice below and fill in any answer boxes in your choice A The mean is 8 3 Type an integer or a decimal B There is no mean for this distribution Find the median Select the correct choice below and fill in any answer boxes in your choice OA The median is Type an integer or a decimal B There is no median for this distribution C

K A The mean is 400 43 Round to two decimal places as needed Part 4 of 4 The accompanying table gives the gross domestic receipts for the top 10 movies Find the mean median and mode for each data set Explain which measure best describes a typical value in this distribution Click the icon to view the data table A The median is 345 Round to two decimal places as needed OB There is no mean for these data Find the median Select the correct choice below and if necessary fill in the answer box to complete your choice OB There is no median for these data Find the mode s Select the correct choice below and if necessary fill in the answer box to complete your choice Points 0 75 of 1 A The mode s is are Round to two decimal places as needed Use a comma to separate answers as needed B There is no mode for these data Domestic Receipts of Top 10 Movies Movie Title Movie A Movie B Movie C Movie D Movie E Movie F Movie G Movie H Movie I Movie J Print Which measure best describes a typical value in this distribution A For this distribution the mean median and mode are equal so any value can be used to describe this distribution B The mean best describes a typical value in this distribution since the distribution is roughly symmetrical and does not contain any extreme values C The median best describes a typical value in this distribution since the distribution appears to be slightly asymmetrical and contains some extreme values distribution since each value occurs roughly the same number of times Save Total Gross millions 457 0 201 8 352 0 356 7 652 2 338 0 200 0 936 2 281 8 228 6 Done

Stephen sets up an IRA with an APR of 4 at age 26 At the end of each month he deposits 57 in the account How much will the IRA contain when he reaches 65 Round your answer to the nearest dollar

Calculate the monthly payment for a student loan of 20 934 at a fixed APR of 8 for 12 years Round to the nearest hundredth

Use the TVM solver for compounding more than once a year to determine the accumulated balance after the stated period 6000 deposit at an APR of 3 with daily compounding for 7 years Round your answer to the nearest dollar

Use the IVM solver for compounding more than once a year to determine the accumulated balance after the stated period 16 000 deposit at an APR of 4 with semiannual compounding for 12 years Round your answer to the nearest dollar

Use the TVM solver for compound interest to determine the accumulated balance after the stated period Assume that interest is compounded annually 3000 is invested at an APR of 7 for 12 years Round your answer to the nearest dollar