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In Exercises 5–6, use matrix inversion to find the production
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- The Internal Revenue Service Restructuring and Reform Act (RRA) was signed into law by President Bill Clinton in 1998. A major objective of the RRA was to promote electronic filing of tax returns. The data in the table that follows show the percentage of individual income tax returns filed electronically for filing years 2000–2008. Since the percentage P of returns filed electronically depends on the filing year y and each input corresponds to exactly one output, the percentage of returns filed electronically is a function of the filing year;so P(y) represents the percentage of returns filed electronically for filing year y. (a) Find the average rate of change of the percentage of e-filed returns from 2000 to 2002. (b) Find the average rate of change of the percentage of e-filed returns from 2004 to 2006. (c) Find the average rate of change of the percentage of e-filed returns from 2006 to 2008. (d) What is happening to the average rate of change as time passes?arrow_forwardFind the demand matrix for the following input-output and production matrices using the open model. 13 14 A = 0.4 0.4 0.3 0.5 X= The demand matrix is (Type an integer or decimal for each matrix element.)arrow_forwardexercise 6 part 1arrow_forward
- Let y represent the annual income of an individual in 2018. Let z represent the number of days the individual worked in 2018. Let x represent the number of days the individual spent snow skiing in 2018. Let w represent the number of days the individual did not work in 2018. Which of the following models violate A3 (MLR.3)? O y = Bo+B1 + 2 + O y = Bo + B₁x + B₂z+u O y = Bo + Bi +B2 z tu All of the above.arrow_forward0.1 0.4 (units in millions of dollars) is a demand vector. 10 Matrix A =| is an input-output matrix associated with an economy, and matrix D = 0.3 0.2 Find the final outputs of each industry such that the demands of the industry and consumer sector are met.arrow_forwardNational Debt The size of the total debt owed by the UnitedStates federal government continues to grow. In fact,according to the Department of the Treasury, the debt perperson living in the United States is approximately $53,000(or over $140,000 per U.S. household). The following datarepresent the U.S. debt for the years 2001–2014. Since thedebt D depends on the year y, and each input correspondsto exactly one output, the debt is a function of the year. SoD1y2 represents the debt for each year y. Source: www.treasurydirect.govDebt (billions Debt (billionsYear of dollars) Year of dollars)2001 5807 2008 10,0252002 6228 2009 11,9102003 6783 2010 13,5622004 7379 2011 14,7902005 7933 2012 16,0662006 8507 2013 16,7382007 9008 2014 17,824 (a) Plot the points 12001, 58072, 12002, 62282, and so on ina Cartesian plane.(b) Draw a line segment from the point 12001, 58072 to12006, 85072. What does the slope of this line segmentrepresent?(c) Find the average rate of change of the debt from 2002…arrow_forward
- Use a matrix method to find the equilibrium prices and quantities where the supply and demand functions for Good 1, Good 2 and Good 3 are asarrow_forwardHermann Ebbinghaus (1850–1909) pioneered the study of memory. A 2011 article in the Journal of Mathematical Psychology presents the mathematical model R(t) = a + b(1 + ct)−? for the Ebbinghaus forgetting curve, where R(t) is the fraction of memory retained t days after learning a task; a, b, and c are experimentally determined constants between 0 and 1; ? is a positive constant; and R(0) = 1. The constants depend on the type of task being learned. (a) What is the rate of change of retention t days after a task is learned?arrow_forward. Let the national income model be; Y = C + I0 + G , C = a + b ( Y – T) , G = g Y Identify endogenous variables Find the equilibrium national income Find equilibrium consumption(using static equilibrium & matrix algebra both)arrow_forward
- 5. Determine the matrix of the transformation that first reflects points through the horizontal x-axis and then reflects points through the line y = x.arrow_forwardIn Exercises 19–22, evaluate the (4X4) determinants. Theorems 6–8 can be used to simplify the calculations.arrow_forwardCS21.pdf 1 - 3 2.arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage