One hundred tickets, numbered 1, 2, 3, . . , 100, are sold to 100 different people for a drawing. four different prizes are awarded, including a grand prize (a trip to tahiti). how many ways are there to award the prizes if a) there are no restrictions? b) the person holding ticket 47 wins the grand prize? c) the person holding ticket 47 wins one of the prizes? d) the person holding ticket 47 does not win a prize? e) the people holding tickets 19 and 47 both win prizes? f) the people holding tickets 19, 47, and 73 all win prizes? g) the people holding tickets 19, 47, 73, and 97 all win prizes? h) none of the people holding tickets 19, 47, 73, and 97 wins a prize? i) the grand prize winner is a person holding ticket 19, 47, 73, or 97? j) the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes?

The equation shown below represents function f. f(x)= -2x+5 the graph shown below represents function g. which of the following statements is true? a. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is less than the y-intercept of function g. b. over the interval [2, 4], the average rate of change of f is greater than the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. c. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. d. over the interval [2, 4], the average rate of change of f is less than the average rate of change of g. the y-intercept of function f is the same as the y-intercept of function g.