Define the process of mathematical modelling?

First-class Mail In 2015 the U.S. Postal Service charged$0.98 postage for first-class mail retail flats (such as an8.5" by 11" envelope) weighing up to 1 ounce, plus $0.22 foreach additional ounce up to 13 ounces. First-class rates donot apply to flats weighing more than 13 ounces. Developa model that relates C, the first-class postage charged, for aflat weighing x ounces. Graph the function.

a regression analysis on a set of data (with two variables, X and Y) outcomes a value of r-square = 78.5What would be the interpretation of this value?

18. Median Income The data in the table show the median incomes y (in thousands of dollars) for samples of householders of various ages a in the United States in 2017. (Adapted from U.S. Census Bureau) 20 30 40 50 60 70 40.1 62.3 78.4 80.7 68.6 41.1 a. Use the regression capabilities of a graphing utility to find a quadratic model for the data. b. Use a graphing utility to plot the data and graph the model. c. Use the model to approximate the median incomes for a sample of 27-year-old householders and a sample of 56-year-old householders.

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study investigated how the content of vitamin A in carrots is affected by the time being cooked. In this example: X represents the amount of time, in minutes, that the carrot slices were cooked Y represents the content of vitamin A (in milligrams) in the carrot slices   The least-squares regression equation for this relationship is:  Y = 22.4 – 0.65X Using the regression equation, predict the vitamin A content (in milligrams) for a carrot slice that was cooked for 15 minutes. Provide your answer as a numeric value rounded to two decimal places.

Part A) A bicycle rental company charges $15 for the first hour and $7.25 for each additional hour. Determine the maximum number of hours you can rent a bike if you only have $102. ________hours   Part B)The population of a town in 1920 was 3400 people. The town's population decreased linearly, and in 1928 the population was 3040. Find a formula for P, the town's population, in terms of t, the number of years since 1920. p(t)=_____   Part C) The sales tax on an item is 6%. Express the total cost, C, in terms of the price of the item, P.  C=____

House prices How does the price of a house depend on its size? Data from Saratoga, New York, on 1064 ran-domly selected houses that had been sold include data on price ($1000’s) and size (1000’s ft2 ), producing the following graphs and computer output:a) Explain in context what the regression says.b) The intercept is negative. Discuss its value, taking noteof its P-value.c) The output reports s = 53.79. Explain what thatmeans in this context.d) What’s the value of the standard error of the slope ofthe regression line?e) Explain what that means in this context.

Fill in the blanks.a. In multiple linear regression, a(n) _______ is a data point that lies far from the multiple linear regression plane, relative to the other data points.b. In multiple linear regression, a(n) _______ is a data point whose removal causes the multiple linear regression equation to change considerably.

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