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MAT 2377 Final: MATH 2377 ExamenFinalHiver2011Sol

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turquoisegnu128
31 Jan 2019
School
University of Ottawa
Department
Mathematics
Course
MAT 2377
Professor
All

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Xx=3 f (x) = 2 c + c + 2 c = 5 c c = P ({x = 4} {x 4}) P (x 4) f (4) f (4) + f (5) P (x ) = p (x 4) = f (4) + f (5) = 2. (a) the histogram is approximately symmetric and there is a linear ten- dency in the normal probability plot. It is reasonable to assume that the tar content is normally distributed. (b) we want to test h0 : = 14 against h1 : > 14. The observed value of the test statistic is t0 = x 14 s/ n. The p-value : p = p (t > 2. 894), where t has a t(24) distribution. From the table for the t distribution, we obtain 0. 0025 < p-value < We have su cient evidence to conclude that > 14 at = 5%. (c) a 95% con dence interval for the is x t0. 025,24 s.

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Related Questions

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f -1(x) = (x - 20)/2
b. f -1(x) = x - 20
c. f -1(x) = (x/2) - 20
d. f -1(x) = (x/2) + 20

Q19. If f(x) = 4x 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)

Q20. Find functions f and g so that f ∘ g = H(x) = (5 - 2x3)2.
a. f(x) = 5 - 2x3 ; g(x) = x2
b. f(x) = (5 - 2x)3 ; g(x) = x2
c. f(x) = x2 ; g(x) = 5 - 2x3
d. f(x) = x3 ; g(x) = (5 - 2x)2

Q29. 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)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.


a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. 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

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.


a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.


a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.


a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.


a. 224
b. 24
c. -72
d. 72

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3. (18 pts) MULTIPLE CHOICE ! ! ! A table of values for f(x) and f'(x) is shown below. Suppose that f is a one-to-one function and f (x) is its inverse. f' x 1 3 4 f (x) 3 4 6 (x) 4 5 3 CIRCLE THE CORRECT ANSWER IN EACH PART. (I) Evaluate f-1 (f (x)) at x = 3. (a) 1 ; (b) 3; (c) 6; (a) 4; (e) DOES NOT EXIST; (£) NONE OF THE PREVIOUS ANSWERS. (11) Evaluate e f (f (x)) at x = 3. (a) 6 ; (b) 25; (c) 5; (d) 15; (e) DOES NOT EXIST ; () NONE OF THE PREVIOUS ANSWERS. (111) Evaluate e In (f (x)) at x = 3. (e) DOES NOT EXIST; (f) NONE OF THE PREVIOUS ANSWERS. (IV) Evaluate f-1 (x) at x = 3. (a) 4; (a) 4 ; (b) 1; (b) 1 ; (com () 5; (d) 5; (e) DOES NOT EXIST; () NONE OF THE PREVIOUS ANSWERS. (v) Evaluate -? (x) at x = 3. (a) 1 ; (b) 4; (e) 5; () NONE OF THE PREVIOUS ANSWERS. (VI) Find the average rate of chnage of f over the interval (1, 3). (a) 2 ; (b)1; (c) ; (a) 5; (e) DOES NOT EXIST; () NONE OF THE PREVIOUS ANSWERS.

Secant Lines Consider the function and the point P (4, 2) on the graph of f.

(a) Graph f and the secant lines passing through P (4, 2) and Q(x, f(x)) for x-values of 1, 3, and 5.

(b) Find the slope of each secant line.

(c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P (4, 2). Describe how to improve your approximation of the slope.