3/10/2017 MATH 105 Exam 3 MATH 105 Exam 3 40 Unanswered Please be sure to save at least once every 15 minutes. If you leave this page without saving, or if your session times out, any answers you have not saved will be lost. The Submit for Grading button will become available once you've answered all questions. Exams are not timed you do not have to finish an exam in one sitting as long as you have saved your answers. Q1. For the functions f(x) = x2 + 4 and g(x) = x2 + 1, find the composite function (f g)(x). a. x4 + 5 b. x4 + 17 c. x4 + 2x2 + 5 d. x4 + 8x2 + 17 Q2. Find the domain of the composite function f g if f(x) = 28/x and g(x) = 8/(x 7). a. {x | x 7} b. {x | x 0, x 7, x 4} c. {x | x 7, x 0} d. {x | x is any real number} Q3. The graph of a logarithmic function is shown. Select the function which matches the graph. https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 1/12 3/10/2017 MATH 105 Exam 3 a. y = log 2 (x + 1) b. y = log 2 (x 1) c. y = log 2 x d. y = log 2 x 1 Q4. If f(x) = 4 x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer. a. (log 4 12, 12) b. (log 4 12, 4) c. (log 4 12, 0) d. (12, 12) Q5. Find the amount that results from the investment of $480 invested at 6% compounded quarterly after a period of 3 years. a. $573.90 b. $93.9 c. $565.42 d. $571.69 Q6. The value of a particular investment follows a pattern of exponential growth. You invested money in a money market account. The value of your investment t years after your initial investment is given by the exponential growth model A = 5100e0.047t . How much did you initially invest in the account? a. $2550.00 b. $5345.42 c. $5100.00 d. $239.70 Q7. The graph of an exponential function is given. Match the graph to one of the following functions. a. f(x) = 3 x b. f(x) = 3 x c. f(x) = 3 x d. f(x) = 3 x Q8. Express 6log b m log b n as a single logarithm. a. log b m6 log b n https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 2/12 3/10/2017 MATH 105 Exam 3 b. log b (m6 n) c. log b (m6/n) d. log b (6m/n) Q9. Solve the equation log 72 (x2 x) = 1. a. {8, 9} b. {1, 72} c. {8, 9} d. {8, 9} Q10. Find the exact value of the logarithmic expression log 4 1/64. a. 1/3 b. 3 c. 1/3 d. 3 Q11. Write log 7 (xy)/15 as the sum and/or difference of logarithms. Express powers as factors. a. (1/2) log 7 xy (1/2) log 7 15 b. (1/2) log 7 x (1/2) log 7 y (1/2) log 7 15 c. (1/2) log 7 x + (1/2) log 7 y (1/2) log 7 15 d. (1/2) log 7 x + (1/2) log 7 y log 7 15 Q12. Find the exact value of the logarithmic expression ln e. a. 0 b. 1 c. 1 d. e Q13. Solve the equation 8 x 4 = 32 4x. a. {12/17} b. {4/3} c. {2} d. {4/17} Q14. Find the inverse of the function and state its domain and range. {(3, 4), (1, 5), (0, 2), (2, 6), (5, 7)} a. {(3, 4), (1, 5), (0, 2), (2, 6), (5, 7)} D = {3, 1, 0, 2, 5} R = {2, 4, 5, 6, 7} b. {(3, 4), (1, 5), (0, 2), (2, 6), (5, 7)} D = {3, 1, 0, 2, 5} R = {7, 6, 5, 4, 2} c. {(4, 3), (5, 1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7} R = {3, 1, 0, 2, 5} d. {(3, 4), (1, 5), (0, 2), (2, 6), (5, 7)} D = {3, 1, 0, 2, 5} R = {7, 6, 5, 4, 2} Q15. The halflife of silicon32 is 710 years. If 100 grams is present now, how much will be present in 200 years? (Round your answer to three decimal places.) a. 14.192 b. 82.263 c. 98.066 d. 0 Q16. If 5 x = 6,what does 5 2x equal? a. 1/36 b. 36 c. 1/12 d. 36 https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 3/12 3/10/2017 MATH 105 Exam 3 Q17. Find the present value to get $6500 after 2 years at 5% compounded quarterly. Round to the nearest cent. a. $5895.69 b. $614.91 c. $5885.09 d. $5958.65 Q18. Find the domain of the function f(x) = log 5 (100 x2). a. (10, 10) b. (, 10) (10, ) c. (100, 100) d. [10, 10] Q19. Solve the equation 3 x = 81. a. {27} b. {5} c. {4} d. {3} Q20. The graph of a onetoone function f(x) = x + 2 is given. Draw the graph of the inverse function f1 as a dashed line or curve. https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 4/12 3/10/2017 MATH 105 Exam 3 a. b. Q21. Solve the system of equations using substitution. a. x = 2, y = 4 x = 2, y = 4 x = 2, y = 0 or (2, 4), (2, 4), (2, 0) b. x = 2, y = 4 x = 2, y = 0 or (2, 4), (2, 0) c. x = 2, y = 4 x = 2, y = 4 or (2, 4), (2, 4) d. x = 2, y = 4 or (2, 4) Q22. Solve using elimination. a. x = 5, y = 9 x = 5, y = 9 x = 5, y = 9 x = 5, y = 9 or (5, 9), (5, 9), (5, 9), (5, 9) b. x = 5, y = 9 x = 9, y = 5 x = 5, y = 9 x = 9, y = 5 or (5, 9), (9, 5), (5, 9), (9, 5) https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 5/12 3/10/2017 MATH 105 Exam 3 c. x = 5, y = 9 x = 9, y = 5 or (5, 9), (9, 5) d. x = 5, y = 9 x = 5, y = 9 or (5, 9), (5, 9) Q23. Use properties of determinants to find the value of the second determinant, if the value of the first is known. a. 9 b. 18 c. 18 d. 9 Q24. Write the partial fraction decomposition of the rational expression (14x + 1)/[(x 1)(x2 + x + 1)]. a. 5/(x 1) + (4x 5)/(x2 + x + 1) b. 5/(x 1) + (5x + 4)/(x2 + x + 1) c. 5/(x 1) + 5/(x + 1) + 4/(x 1) d. 5/(x 1) + (5x + 4)/(x2 + x + 1) Q25. Graph the inequality x + y < 5. a. https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 6/12 3/10/2017 MATH 105 Exam 3 b. c. d. Q26. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1. https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 7/12 3/10/2017 MATH 105 Exam 3 a. minimum: 7 b. minimum: 18 c. minimum: 24 d. minimum: 13 Q27. a. b. c. d. Q28. A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.03. Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost per patient per meal. a. z = 3y + 25y b. z = 0.25x + 0.03y c. z = 25x + 3y d. z = 0.03x + 0.25y Q29. Write a system of linear inequalities that has the given graph. https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 8/12 3/10/2017 MATH 105 Exam 3 a. b. c. d. Q30. Solve the system of equations using substitution. a. x = 6, y = 7 x = 7, y = 6 or (6, 7), (7, 6) b. x = 6, y = 7 x = 7, y = 6 or (6, 7), (7, 6) c. x = 6, y = 7 x = 7, y = 6 or (6, 7), (7, 6) d. x = 6, y = 7 x = 7, y = 6 or (6, 7), (7, 6) Q31. Find the inverse of the matrix. Be sure to check your answer. https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 9/12 3/10/2017 MATH 105 Exam 3 a. b. c. d. Q32. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. a. x = 2, y = 1, z = 0 (2, 1, 0) b. x = 2, y = 0, z = 1 (2, 0, 1) c. x = 0, y = 2, z = 1 (0, 2, 1) d. x = 0, y = 1, z = 2 (0, 1, 2) Q33. a. b. c. d. Q34. Solve the system of equations. a. x = 4, y = 4, z = 3 (4, 4, 3) https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 10/12 3/10/2017 MATH 105 Exam 3 b. x = 3, y = 4, z = 4 (3, 4, 4) c. x = 4, y = 3, z = 4 (4, 3, 4) d. inconsistent Q35. Write the partial fraction decomposition of the rational expression (125 19x)/(x3 10x2 + 25x). a. 5/x + 5/(x 5) + 12/(x 5)2 b. 5/x + 5/(x 5) + 6/(x 5)2 c. 5/x + 6/(x 5) + 5/(x 5)2 d. 5/x + 5/(x 5) + 6/(x 5)2 Q36. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5) 2. a. (4x 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2 b. (4x + 4)/(x2 + 5) + (20x 20)/(x2 + 5)2 c. (4x + 4)/(x2 + 5) + (20x 20)/(x2 + 5)2 d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2 Q37. A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 7 inches longer than the width. Find the width. a. 18 in. b. 29 in. c. 11 in. d. 25 in. Q38. Solve the system of equations using Cramer's Rule if it is applicable. a. x = 9, y = 2, z = 5 (9, 2, 5) b. x = 8, y = 4, z = 5 (8, 4, 5) c. x = 4, y = 5, z = 4 (4, 5, 4) d. x = 8, y = 4, z = 5 (8, 4, 5) Q39. The perimeter of a rectangle is 20 inches and its area is 21 square inches. What are its dimensions? a. 2 in. by 6 in. b. 3 in. by 7 in. c. 4 in. by 6 in. d. 2 in. by 8 in. Q40. Solve the system using the inverse matrix method. a. x = 33, y = 51, z = 26 (33, 51, 26) https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 11/12 3/10/2017 MATH 105 Exam 3 b. x = 31, y = 29, z = 6 (31, 29, 6) c. x = 36, y = 16, z = 10 (36, 16, 10) d. x = 1, y = 24, z = 35 (1, 24, 35) Privacy Policy | Contact Us | Copyright 19982017 University of Management and Technology (UMT) | Consumer Information Disclosure https://www.umtweb.edu/SRM/CE.aspx?d=0D708C31E10032D46999DC6DA278A951B015C230AE7E027C5642E735BCDDED0D887DF0E690217134 12/12