Define the process of mathematical modelling?

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.

plz solve question (c) with explanation within 30-40 mins and get upvotes

C) if a country increases its life expectancy, the happiness index will increase or decrease d) if the life expectancy is increased by 4.5 years in a certain country .how much will the happiness index change? Round two decimal places e) use the regression line to predict that happiness index of a country with a life expectancy of 89 years . Round to two decimal places  use the space below to type your answers

linear algebra  .  What is the definition of a characteristic equation?

Part 1) According to one mathematical model, the average life expenctancy for American men born in 1900 was 55 years. Life expectancy has increased by about 0.2 year for each birth year after 1900. If this trend continues, for which birth year will the average life expentancy be 75 years? a) Write an equation to model the problem. Let t represent the number of years after 1900. For example, t = 12 would represent the year 1912. Answer:   b) Solve the equation, then answer the question given above. (Note: You are asked for a year, not a value for t.)   Part 2) Wilma drove at an average speed of 50 mi/h from her home in City A to visit her sister in City B. She stayed in City B 25 hours, and on the trip back averaged 35 mi/h. She returned home 48 hours after leaving. How many miles is City A from City B