The sales of Sherwin-Williams paint in different regional markets depends on several input variables. One variable that partially drives selling price, which in turn affects sales, is the costto get the product to market. When other input variables are held constant, sales can be modeled ass(x) 597.3(0.9214x +12) thousand gallonswhen it costs x dollars to get a gallon of paint to market, data from 0 s x s 2.T(a) How many gallons of paint are sold when it costs 45 cents for a gallon to reach the market? (Round your answer to three decimal places.)thousand gallons(b) How quickly are sales changing when x = 0.45? (Round your answer to three decimal places.)thousand gallons per dollar

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Answered: The sales of Sherwin-Williams paint in…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Employment. According to the U.S. Bureau of Labor Statistics, the number of professional services employees fluctuated during the period 2000-2009, as modeled by E(t) = -28.31t³ +381.86t² - 1162.07t + 16,905.87, where t is the number of years since 2000 (t = 0 corresponds to 2000) and E is thousands of employees. (Source: www.data.bls.gov.) Find the relative extrema of this function, and sketch the graph. Interpret the meaning of the relative extrema.
The idea of a large, stable middle class (defined as those with annual household incomes in 2010 between $42,000 and $126,000 for a family of three), is central to America's sense of itself. But the U.S. middle class shrank steadily from 61% of all adults in 1971 (t = 0) to 51% in 2011 (t = 4), where t is measured in decades. Research has shown that this decline was approximately linear.† (a) Find a linear function f(t) giving the percentage of middle-income adults in decade t, where t = 0 corresponds to 1971. (b) If this trend continues, what will the percentage of middle-income adults be in 2041?
Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. consumer price index (CPI) can be modeled by the function y = 0.0682x² + 1.76x + 96.0 where x is the number of years past 2010 and y is the CPI in dollars. With a reference of 100 in 2012, a CPI of 120 in another year means that goods and services costing $100 in 2012 are expected to cost $120 in that other year (a) Use a table to determine a viewing window that shows a complete graph of this function for the years from 2010 to 2050. 2050 corresponds to an x value of which corresponds to a y value of The y maximum should be -Select-than this function value (b) Graph the function. y 300 250 200 150 100 50 0 y 300 250 200 150 100 50 X = Need Help? 51 F Partly sunny 10 10 20 Read It 20 30 30 T X 40 40 y 300 250 200 150 100 50 0 0 10 (c) Use the graph to estimate when the CPI is predicted to reach 250. (Round your answer to the nearest whole year.) years 20 30 Q Search 40 y 300 250 200…
This value represents how much a change in one variable can be predicted from its relationship witha completely different variable .......
The mtcars data set contains data on 32 cars from the 1974 Motor Trend US magazine. The data set has 11 variables that measure different aspects of the cars, such as miles per gallon (mpg), horsepower (hp), weight (wt), and number of cylinders (cyl). The data set can be used to study the relationship between fuel consumption and car performance, as well as other factors that affect the efficiency and design of the cars. What is the maximum and minimum number of the range regarding the explanatory variable for which the regression model can make valid predictions?
Recently there has been a rise in fatal accidents caused by “distracted driving.” The United States National Highway Traffic Safety Administration (NHSTA) defines a distraction as anything that diverts attention from driving. The following model estimates the trend in distracted driving accidents over time based on data from the NHSTA:D = 0.015t - 29.97 In this model, D is the decimal to be turned into a percentage of all fatal accidents caused by distracted driving, and t is any calendar year between 2000 and 2020. Use the model to estimate the rate for 2005 and 2020. Note: this means to plug n 2005 for t and simplify and then turn your answer into a percent. Then plug in 2020 for t and simplify and then turn your answer into a percent.
The following data was collected to explore how the number of square feet in a house, the number of bedrooms, and the age of the house affect the selling price of the house. The dependent variable is the selling price of the house, the first independent variable (x1�1) is the square footage, the second independent variable (x2�2) is the number of bedrooms, and the third independent variable (x3�3) is the age of the house. Effects on Selling Price of Houses Square Feet Number of Bedrooms Age Selling Price 11191119 33 33 100900100900 13081308 33 44 119800119800 14521452 33 66 189800189800 16931693 33 66 190500190500 20052005 33 66 196900196900 22102210 33 99 216600216600 23012301 44 99 250900250900 23452345 44 1010 267800267800 28532853 55 1313 270000270000 Copy Data Step 1 of 2 : Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places
When coastal power stations take in large quantities of cooling water, it is inevitable that a number of fish are drawn in with the water. Various methods have been designed to screen out the fish. A particular article examined intake fish catch at an English power plant and several other variables thought to affect fish intake. y = fish intake (number of fish)x1 = water temperature (°C)x2 = number of pumps runningx3 = sea state (values 0, 1, 2, or 3)x4 = speed (knots) Part of the data given in the article were used to obtain the estimated regression equation(based on n = 26). SSRegr = 1486.6 and SSResid = 2230.1 were also calculated. (a) What proportion of observed variation in fish intake can be explained by the model relationship? (Round your answer to four decimal places, if needed.)R2 = (b) Estimate the value of σ. (Round your answer to three decimal places, if needed.)se = (c) Calculate adjusted R2. (Round your answer to four decimal places, if needed.)Adjusted R2 = Adjusted R2…
Suppose that the number of tee shirts sold (N) depends linearly on the price charged (x). Write an equation showing this dependence.
The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below. Price 0.00 0.45 0.60 0.75 1.00 1.25 1.40 1.50 Profit 0.00 $720 $900 $990 $845 $625 $560 $300 What factors might influence how much is to be made from the candy sale? Give at least two. What happens to the profit as the price of each candy bar increases? Explain possible reasons for your observations. How do you suppose the other bands determined the price at which to sell each candy bar? Do any data values seem unusual? Yes or…

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