MATH 204 Final, Summer 2005

Summer , 2005 SEC... 1. Doevecees 3... _____ orrectors only Grade of Written Part Grade of Multiple Choice Final Exam.. Grade | Number of Correct:....... X BFL Il ill Number of Wrong :......X(-1)=.......5. IV Vv Total M.C, Grad@=....... cece ccs ee sees Instructions: 1.Write your name and circle your section number. 2. The colored booklet is for scratch work and will not be corrected. PART ONE: MULTIPLE CHOICE : Circle your answer.The choice E is for non of the other options. You will receive five points for each correct and lose one point for each wrong answer. During a commercial break, a television station is to pass four ads , from a list of 10 distinct available ads. Answer questions :1-2-3 4. In how many ways can this be done if the order in which the ads are aired counts? A. 4050 B. 4800 Cc. 5040 D. 3040 E. 2. In how many ways can this be done if the order in which the ads are aired is not relevant? A, 210 B. 420 C. 640 D. 240 E. 3. In how many ways can this be done if the order in which the ads are aired is not relevant, but one ad is repeatec twice? A. 560 B. 660 C. 360 D. 460 E. Given that 30% of the people in an undeveloped country are illiterate. Eight persons are randomly selected from the population of the country. Answer questions 4- 5-6 . 4.. What is the probability that two persons are illiterate? A. 0.404 B. 0.296 C. 0.368 D. 0.741 5, What is the mean number of illiterate persons expected to be? orn A. 24 B. 1.4 C. 27 D. 2.4 5 6.What is the standard deviation of the number of illiterate persons? A. 1.474 B. 2.491 C. 1.296 D. 2.512 . 6 5 -3 Given the matrix 4=;-3 2 1 |. Answer questions7-8 - 9 hii ry, 0 3 4 . OF SEM j 7. The determinant of A is A. 117 B. 135 8. The cofactor of az3 is A. 24 B. Cc. 14 D. -14 9. The first row of the matrix product 4x 4. is A. (-6,-21,19) B.(6 21-19) C. (-5,13,-19) —-D. (21,31,-25) Given f(x, y)=x? ye***?” . Answer questions 10 - 11 10. Find £,(2,) A, 12e5 B. 14e5 C. 12e8 11. Find f,, (11) A. 15e5 . . 12e8 D. 14¢8 A normal variable X (giving the test scores), has a mean of 625 and a standard deviation of 20.Answer questions 12- 13 12. P(X<654) = A. 0.4265 B. 0.9265 C. 0.2324 D. 0.7234 13. Find k so that P(X<k) =0.33 A. 616.2 B. 900.7 C. 617.4 D. 622.0 Given the matrices 4 = (3, ;] and o-() 5} Answer questions 14 - 15 8 -5 A 4 B, -2 14, Find x if Ax B= [ 45. Find x if 4sap=() A. 10 B. -7 Cc. - D. 0 16. If y= f(u)=u’, and u=g(x)=7x~2,then™ atx=-3 will be: dx A. -322 B. 145 C. -201 D. 34 E. Of the 100 cars in a parking lot, 30 are black and 24 are of the AWD (all wheel drive) type, and 6 are black ant AWD. Answer questions 17 and 18: 17. Find the probability that a randomly selected car is black or AWD. A. 0,84 B. 0.28 C. 0.36 D. 0.48 18.What is the probability that an AWD car is black? A. 0.55 B. 0.25 C. 0.35 D. 0.15 + a i -PART TWO: (Written) x 8 oa 1, (20 Points) Consider the definite integral 7 = fx7e? dx Answer questions 4 - 2 Q 1. Approximate the integral using the trapezoidal rule with n=4. 2. Approximate the integral using Simpson's rule with n=4. “lk (32 Points)Evaluate every integral in the space provided for it ,and circle your final result. Write down all important steps. 1. = f(e+10)e ae 2. J= (4x + 60) Vx? + 30x + Ide 0 p= [ral (4x -16)dx (x — 4)(x +2) . “lL (24 Points) 1. . Find the area in the first quadrant , limited above by y=4 -3x and below by the curve y=x’ . ain - aN fo , 2. Find the volume of the solid of revolution generated when the region between the function f= (24+1nx) vx and the x-axis ( forl1<x<e) is rotated about the x-axis. » 2 V.(14 Points) Given that ° = f'(x)=12(x4+ (in x) x x ), with f(l)=12. Find f(e?). V.(20 Points). Determine the location and nature of all critical points of the function :. f(xy y= 74 4x? + y? ~48x-3y