The following table shows the number, in millions, graduating from high school in the United States in the given year.t After 1992, the number of high school graduates has increased each year.Year Number graduating (in millions)19852.8319872.6519892.4719912.29(a) By calculating differences, show that these data can be modeled using a linear function. (Let d be years since 1985 and N the number of graduating high school students, in millions.)1985 to 19871987 to 19891989 to 1991✓✓x✓XXChange in dChange in N20.18(b) What is the slope for the linear function modeling high school graduations? (Round your answer to two decimal places.)-0.09✔million per year.Explain in practical terms the meaning of the slope.This means that each year fewer✔✔ high school students graduated.Calculate that value.2.2(c) Find a formula for a linear function that models these data. (Let d be years since 1985 and N the number of graduating high school students, in millions.)N = -0.09d + 181.48Need Help?20.18(d) Express, using functional notation, the number graduating from high school in 1992.N( 1992x )millionRead It20.18XMaster It

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Answered: The following table shows the number,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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The follow table shows total dollar sales (in thousands) for a local retailer for various years. Year 2019 2020 2021 2022 2023 Sales ($) 16 21 26 31 36 a) What was the dollar amount of sales for 2022? $ b) By how much did sales increase each year? $ c) Find a linear function S(x) that models the above data, where x is the number of years after 2018 (so that the year 2019 corresponds to x = 1, the year 2020 corresponds to x = 2, and so on) and S(x) is the dollar amount of sales in thousands. S(x) = X + d) Use S(x) to predict sales in 2025. $ If needed, round answer to 5 decimal plates. Enter DNE for Does Not Exist, oo for Infinity Question Help: Message instructor Submit Question thousand thousand thousand
The following table shows the average yearly tuition and required fees, in dollars, charged by four-year American private universities in the school year beginning in the given year. Date Average tuition 2012 $27,870 2013 $29,004 2014 $30,138 2015 $31,272 2016 $32,406 (a) Show that these data can be modeled by a linear function. For each change of 1 year in time there is an increase of $ in tuition. Find its formula. (Let d be the date in terms of number of years since 2012 and T tuition in dollars.) T(d) = 27,870+1134d (b) Plot the data points and add the graph of the linear formula you found in part (a). (c) What prediction does this formula give for average tuition and fees at four-year American private universities for the academic year ending in 2018?$
4. A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. а. What is the dependent variable in this relationship? b. What is the independent variable in this relationship? с. Can this relationship be modeled by a linear function? Provide evidence to support your claim. forch car Which of the mb of beaodelod bya linear tion deled y a line fcion wite a function that de o of tie t 5. A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? a. b. What is the independent variable in this relationship? с. Can this relationship be modeled by a linear function? Provide evidence to support…
5.7 x 10 D. 7.8 x 106 3. The number of tables a banquet hall sets up is a function of the number of guests in at an event. The ordered pairs below represent the number of guests and number of tables at the past four events. What is the domain for the given data? {(65, 9), (125, 15), (195, 25), (84, 11)} A. {65, 195} B. (65, 84, 125, 195) C. (9, 15, 11, 25} D. (9, 15, 11, 25, 65, 84, 125, 195} Name: PRE-ALGEBRA REVIEW 1. Which is most likely the equation of the line graphed? Date: 4. F C C S P n B. 2. Sol
The numbers of polio cases in the world are shown in the table for various years. Year Number of Polio Cases (thousands) 1988 1992 1996 2000 2005 2007 350 138 33 3 3.2 1.3 Let f(t) be the number of polio cases (in thousands) t years after 1980. Copy the data to Desmos to draw a scatterplot of the data. Make sure to adjust the years so they represent years after 1980. a) Is it better to model the data with a linear or with an exponential model? [Select an answer b) Use regression in Desmos to find an appropriate model for f. Make sure to check Log mode in the parameter window in Desmos if you are fitting an exponential model. f(t) Round the coefficients to 4 decimal places. Hint: Use the variablet from the drop down menu when entering the equation. Do not just type in t. c) Predict the number of polio cases in 2013. d) Find the approximate half-life of the number of polio cases. Round the answer to one decimal place. years
Data in the table comes from the NASA Global Climate Change website. It gives the average globaltemperature, in Celsius, for the given year. Use both rows for your calculations. For this problem, youwill see how well year correlates with the average temperature. Let ? be the number of years since1984 and ? be the average global temperature in degrees Celsius.Year 1984 1986 1988 1990 1992 1994 1996 1998 2000Temp 0.16 0.18 0.38 0.45 0.22 0.31 0.33 0.61 0.40Year 2002 2004 2006 2008 2010 2012 2014 2016 2018Temp 0.63 0.54 0.64 0.54 0.72 0.64 0.75 1.02 0.85a. Make a scatterplot of the data. Being sure to clearly label each axis. Keep in mind howeach variable is defined. Based on this scatterplot, is a linear model reasonable for this data set?Briefly explain.b. Determine the correlation coefficient for this data. Interpret this value in context.c. Determine the coefficient of determination for this data. Interpret this value incontext.d.State the regression line for the data.e. What does the…
The following table gives estimates of the percent of a certain country's population below the poverty level for 1998–2008. Year Percent 1998 12.8 2000 11.2 2002 12.1 2004 12.7 2006 12.9 2008 13.2 Find the least squares line that relates years to percent below the poverty level. (Let x = 0 represent the year 1998. Enter a mathematical expression.

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