EXAM 3, PART 2 MATH 2009 CTFA 6. Find a matrix X such that the equation AX = B holds, where A = (2 o) and Friday, December 10, 2021 B = (1 3) . There are 10 problems. . Problems 1-6 should be done without a calculator. . Problems 7-10 can be done with a calculator. CALCULATOR EXERCISES . Submit your solutions onto Blackboard by 11:59pm Friday, December 10. 7. The following table lists the amount of ice cream consumed in the United States (in millions of gallons) for the years 2018 through 2021: 1. What is the reduced row echelon form (RREF) of the matrix 01 1 Year 2018 2019 2020 2021 Amount 213 251 281 324 2. A company manufactures computers. The company has an overhead cost of $3000 (a) Find the linear regression line. and a manufacturing cost of $100 per computer. If the company sells computers (b) Use the regression line to estimate the amount of ice cream that will be at a price of $200 per computer. Determine the number of units the company consumed in the United States in the year 2025, in millions of gallons. must sell to break even. 8. A particle's position at time t is given by s(t) = -6t* + 19t + t + 4, where s is 3. Which of the following statements can be true when solving a system of linear in units of feet, and t is in units of seconds (for t > 0). Determine the value(s) equations containing 4 variables and 3 equations? of t for which the velocity is 0 ft/sec (and t > 0). Report your answer(s) to the nearest tenth. (a) There are no solutions. (b) There is a unique solution. (c) There are an infinite number of solutions. 9. Find all solutions (x, y, z) for the following linear system: -2.x - y z -4 + y 32= 4. In a study of the relationship between the year and the number of lottery winners, r + 4y 52 scientists applied a regression analysis but could not find any significant linear relation between the two factors. Which of the following is the most likely value of the correlation coefficient? 10. The table below gives values for a differentiable function f(x). What is an ap- (a) 0.05 proximate value of f'(4)? (b) 0.93 (c) -0.91 X 3.998 3.999 4.000 4.001 4.002 f(x) 1.31625 1.31616 1.31598 1.31598 1.31589 (d) -1 (e) 1.25 Hint: Approximate the instantaneous rate of change by the average rate of change over a small interval. 5. The demand function for a product is given by p + 2x = 100 and the supply function is given by p - 3x = 60. Find the market equilibrium price