Index-Fund Fees When a mutual fund company charges a fee of
Let
In September
Find the fee that maximizes the revenue of the company and determine the maximum revenue.
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- An outpatient operating room charges each patient a fixed amount per surgery plus an amount per minute for use. One patient was charged 250 for a 30-minute surgery and another patient was charged 450 for a 90-minute surgery. Determine the linear function that would be used to compute the charges. Use the function to determine the charge when a patient has a 45-minute surgery.arrow_forwardHow do you find the value of a function?arrow_forwardA dairy spends $24,000 per year to maintain its barns and equipment. It costs $2000 per year to feed and care for each dairy cow. (a) Using C for the number of dairy cows and E for the total yearly expense, in dollars, find a formula that gives the total yearly expense as a linear function of the number of dairy cows. E = (b) Use functional notation to express the total expense if the dairy has 40 cows. E(40) E(40C) 40E E(2000) E(24,000) (c) Calculate the value from part (b). $arrow_forward
- U.S. Population Over Age 16 The table gives theprojections of the population, in millions, of U.S.residents over age 16 for selected years 2015 to 2060.a. Graph the data, with y equal to the population inmillions and x equal to the number of years after2010.b. Find a linear function that models the data, with yequal to the population in millions and x equal to thenumber of years after 2010.c. Graph the model and the data on the same axesand comment on the fit of the model to the data.d. What does the model predict that the populationwill be in 2042?e. In what year does the model predict that the population will be 336.827 million?arrow_forwardMembership at a private arcade club costs a one-time initiation fee of $50 plus $10 per month. Part A: Write a function expressing the total amount of money spent on membership as a function of the number of months. Part B: Identify the independent variable and the dependent variable in this situation. Part C: How much total money has been spent on membership after 12 months?arrow_forwardIn 2005 a house was appraised at $143,000 ; in 2011 the same house re-appraised, this time at $179,000. The value of the house H is a linear function of time t, where t represents the number of years since 2005. Write the linear function H(t). H(t)=arrow_forward
- Patty’s Parasols recorded the monthly rainfall and their umbrella sales for an entire year. The following table shows the inches of rainfall and the number of umbrellas the store sold each month. The relationship between the inches of rainfall and umbrella sales can be modeled using a linear function. Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec. Rainfall (in.) 2.5 3.1 4.0 4.3 3.6 2.4 1.2 0.6 1.5 1.4 1.1 2.6 Umbrella sales 132 140 162 170 156 103 98 87 84 78 110 125 Using technology, determine the correlation coefficient for the data to the nearest hundredth. Explain the steps you used. What does the correlation coefficient for the data indicate about the direction and strength of the linear association between the monthly rainfall and the number of umbrellas sold?arrow_forwardPatty’s Parasols recorded the monthly rainfall and their umbrella sales for an entire year. The following table shows the inches of rainfall and the number of umbrellas the store sold each month. The relationship between the inches of rainfall and umbrella sales can be modeled using a linear function. Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec. Rainfall (in.) 2.5 3.1 4.0 4.3 3.6 2.4 1.2 0.6 1.5 1.4 1.1 2.6 Umbrella sales 132 140 162 170 156 103 98 87 84 78 110 125 Using technology, determine the correlation coefficient for the data to the nearest hundredth. Explain the steps you used. What does the correlation coefficient for the data indicate about the direction and strength of the linear association between the monthly rainfall and the number of umbrellas sold Im stuck on this questionarrow_forwardSoutherly Showtime Movie Theaters, Inc. owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. (Let x1 represent Television Advertising ($100s), x2 represent Newspaper Advertising ($100s), and y represent Weekly Gross Revenue ($100s).) Market Weekly Gross Revenue ($100s) Television Advertising ($100s) Newspaper Advertising ($100s) Market 1 101.3 4.9 1.4 Market 2 51.9 2.9 3.1 Market 3 74.8 3.9 1.4 Market 4 126.2 4.4 4.2 Market 5 137.8 3.7 3.9 Market 6 101.4 3.4 2.4 Market 7 237.8 5.1 8.5 Market 8 219.6 7.0 5.7 (a) Develop an estimated linear regression equation with the amount of television advertising as the independent variable. (Round your numerical values to four decimal places.) ŷ = Test for a significant relationship between the amount spent on television…arrow_forward
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