Question In a carnival game, a person can win a prize by guessing which one of 5 identical boxes contains the prize. After each guess, if the prize has been won, a new prize is randomly placed in one of the 5 boxes. If the prize has not been won, then the prize is again randomly placed in one of the 5 boxes. If a person makes 4 guesses, what is the probability that the person wins a prize exactly 2 times? 2! (a) (0.2) (0.2) 5! (c) (0.8)2 (a) (0.2) (0.8) (e) None of these * 11

Computers in some modern motorcycles calculate variousquantities related to performance. One of these is fuel efficiency,or gas mileage, usually expressed as miles per gallon (mpg). Forone motorcycle equipped this way, the miles per gallon wererecorded each time the gas tank was filled and the computer wasthen reset. Here are the mpg values for a random sample of 20 ofthese records:57.5 62.3 67.2 58.1 59.6 71.9 55.2 57.6 71.9 68.869.1 65.3 62.3 64.7 59.9 62.1 63.5 62.9 66.7 61.3Part A Construct and interpret a 95% confidence interval for themean fuel efficiency for this vehicle. Part B A new motorcycle claims to have improved fuel efficiencyover the previous model, getting a greater number ofmiles per gallon. An independent consumer agency takes a randomsample of 30 records for fuel efficiency for this newmodel, and finds that the sample average is 65.9 mpg with a samplestandard deviation of 3.2 mpg. Does this provideconvincing evidence that the new model has greater fuel efficiencythan the previous model? Explain. Part C Instead of the 95% confidence interval, the consumer agencydecides to construct a 98% confidence interval forthe mean fuel efficiency of the older model of motorcycle. What isthis new confidence interval, and what does it meanin the context of this situation? Part D Does your response to Part C change your conclusion in PartB? Why or why not? Be sure to specifically addressthe confidence level in your explanation. Part E The consumer agency responsible for checking fuel efficiencyclaims wants to estimate the mean fuel efficiencyfor this new type of motorcycle within 0.5 mpg. How large a sampleshould be used?

The SP Corporation makes 41,000 motors to be used in the production of its sewing machines. The average cost per motor at this level of activity is: Direct materials Direct labor $ 10.00 $9.00 $ 3.70 $ 4.65 Variable manufacturing overhead Fixed manufacturing overhead An outside supplier recently began producing a comparable motor that could be used in the The SP Corporation makes 41,000 motors to be used in the production of its sewing machines. The average cost per motor at this level of activity is: Direct materials Direct labor $ 10.00 $9.00 $ 3.70 $ 4.65 Variable manufacturing overhead Fixed manufacturing overhead An outside supplier recently began producing a comparable motor that could be used in the sewing machine. The price offered to SP Corporation for this motor is $25.45. If SP Corporation decides not to make the motors, there would be no other use for the production facilities and none of the fixed manufacturing overhead cost could be avoided. Direct labor is a variable cost in this company. The annual financial advantage (disadvantage) for the company as a result of making the motors rather than buying them from the outside supplier would be: (2.5%) 1) $112,750 2) $264,450 3) $190,650 4) ($77,900)

Find the equation of the plane that passes through the point (2, 1,2) and is tangent to the surface x² + 4y + 3z? = 20 at (2, 1,2). Write it in the form indicated below. Equation: 4(x – 2)+ (y- (z- )= 0

Find the equation of the plane tangent to apy2 + 2-9= 0 at x = 1, y = 2. The equation of the plane is

(1 point) Show that S = {0,4, 8, 12, 16, 20} is a subring of Z24 by showing that it satisfies the requirements of the subring test: (i) nonempty (clearly satisfied), (ii) closed under subtraction (completely the first table below), (iii) closed under multiplication (complete the second table below). (ii) Show that S is closed under subtraction by completing the following table, where the body of the table contains "a - b", where a is the element in the left column, b is the element in the top row, and operations are carried out modulo 24. alb 0 4 8 12 16 20 0 4 8 12 16 20 (iii) Show that S is closed under multiplication by completing the following table, where the body of the table contains "ab", where a is the element in the left column, b is the element in the top row, and operations are carried out modulo 24. alb 0 4. 8 12 16 20 0 4

Find the differential of the function f(x, y) = 5 sin(xy). NOTE: Enclose arguments of functions in parentheses. For example, sin(2x). df dat Idy