The family budget is illustrated Distribution of Family Monthly Take-Home Pay in the figure to the right. What percent of the take-home pay is allocated for food? Food $375 Housing $400 Insurance $80 Education $70 Personal $80 Miscellaneous $70

Movieflix, an online movie streaming service that offers a wide variety of award-winning TV shows, movies, animes, and documentaries, would like to determine the mathematical trend ofmemberships in order to project future needs.   MovieFlix - Advertising and Subscriptions Year  Advertising Expenditure      $ 000   Membership Subscriptions 2013                    51 62 2014                    58 68 2015 62 66 2016 65 66 2017                    68 67 2018                    76 72 2019                    77 73 2020                    78 72 2021                    78 78 2022                    84 73 2023                    85 76                   (i) Plot the scattergraph for the data.

Federal Income tax owed by a married couple filing jointly can be found from the following table. Married Filing Jointly Taxable Income $0-$18,550 $18,551-$75,300 $75,301-$151,900 $151,901-$231,450 T(x) = $231,451-$413,350 $413,351-$466,950 $466,951 or more 10% if Tax Rate $1,855 plus 15% of the amount over $18,550 $10,367.50 plus 25% of the amount over $75,300 $29,517.50 plus 28% of the amount over $151,900 $51,791.50 plus 33% of the amount over $231,450 $111,818.50 plus 35% of the amount over $413,350 (a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned $130,578.50 plus 39.6% of the amount over $466,950 0 < x≤ 18,550 if 18,550 < x≤ 75,300 (b) Use the function to find T(40,000). $ if 75,300 < x≤ 151,900 (c) Find the tax due on a taxable income of $100,000. $ (d) A friend tells Jack Waddell not to earn any money over $75,300 because it will raise his tax rate to…

Many factors influence the retail price of gasoline. Suppose the following table shows the average retail price for a gallon of regular grade gasoline for each year from 2011 through 2014. (Round your answers to one decimal place.) Year Average Price ($) 2011 3.531 2012 3.618 2013 3.515 2014 3.348 (a) Use 2011 as the base year and develop a price index for the retail price of a gallon of regular grade gasoline over this four-year period. 2011 price index 100 100.0 2012 price index 2013 price index X X 100.1 2014 price index 100.1 X (b) Use 2012 as the base year and develop a price index for the retail price of a gallon of regular grade gasoline over this four-year period. 2011 price index X 100.0 2012 price index 100 2013 price index 100.0 X 2014 price index 100.1 X

Example 8. Represent the following data by a suitable diagram showing the difference between proceeds and costs: Proceeds and costs of a firm (in thousands of rupees). Year Total Proceeds Total costs 1999 22.0 19.5 2000 27.3 21.7 2001 28.2 30.0 2002 30.3 25.6 2003 32.7 26.1 2004 33.3 34.2

Year   Net Income Expenses 2013    $27,200       $19,800 2014.   $23,700       $18,500 2015    $31,500       $23,900 2016    $33,600       $25,800 2017.   $38,900       $29,200 2018    $41,400       $39,700 2019    $48,600       $37,300 a. What was Dana’s net income, in total for years 2013-19? b. In what year did Dana’s net income most exceed her expenses? c. Suggest a reasonable explanation for why Dana’s 2018 expenses were nearly as much as her income? (Use your business-minded logic, here. There are a number of possible explanations) d. What percent of Dana’s 2016 net income was needed for expenses? (to the nearest tenth of a %) e. What percent of her entire net income in these 7 years was Dana able to save? (nearest tenth of a %)

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Scatter Diagrams and High-Low Cost Estimation From April 1 through October 31, Will County Highway Department hires temporary employees to mow and clean the right-of-way along county roads. The County Road Commissioner has asked you to help her in determining the variable labor cost of mowing and cleaning a mile of road. The following information is available regarding current-year operations: Miles Mowed Labor Month and Cleaned Costs April 350 $8,000 May 300 7,500 June 400 9,000 July 250 5,500 August 375 8,500 September 200 5,000 October 100 4,800 Use the information from the high- and low-volume months to develop a cost-estimating equation for monthly labor costs. Monthly labor costs = $ 3,400 v + $ 14 v X Plot the data on a scatter diagram. Using the information from representative high- and low volume months, use the high-low method to develop a cost-estimating equation for monthly labor costs. Monthly labor costs 2$ 5,600 x + $ 3,400 x X Adjust the equation developed in…

(a) Use class intervals of $0 to <$3, $3 to <$6, $6 to <$9, etc., to create a relative frequency distribution for these data. (Round your answers for relative frequency to four decimal places.) Class Interval Frequency Relative Frequency $0 <$3 $3 <$6 $6 <$9 $9 <$12 $12- <$15 $15 <$18 $18 <$21 TOTAL (b) Construct a histogram. Frequency 14 12 10 8 6 4 Frequency 14 12 10 8 6 4 2 3 3 4 3 51 3 6 9 12 15 18 21 6 0.0588 9 0.0784 0.0588 12 15 18 21 Cost Cost Frequency 14 12 10 8 6 4 Frequency 15 10 5 3 6 9 3 6 9 12 15 18 21 12 15 18 Comment on its shape. O This is a unimodal distribution with a peak at the 0-3 class. The distribution is positively skewed. This is a bimodal distribution with peaks at the 12-15 and 18-21 classes. The distribution is negatively skewed. O This is a bimodal distribution with peaks at the 0-3 and 6-9 classes. The distribution is positively skewed. O This is a unimodal distribution with a peak at the 9-12 class. The distribution is reasonably symmetric. 21 Cost Cost…