Perform both sop and pos optimization for f(a, b,c, d) = ∑m(5,7,11,13,14), assuming that a and b can never both be 0 at the same time, and that c and d can never both be 0 at the same time (i. e., there are don’t cares). compare your results by estimating the number of transistors required for each solution.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

Charlie is at an amusement park that has 18 different rides. each ride costs $1.75. the function c(r) = 1.75r represents the total amount of money that charlie will spend if he goes on r rides, but he never goes on the same one more than once. what domain and range are reasonable for the function?

What is the geometric mean of 3 and 7? a) square root of 21 b) 2 square root of 6 c) 2 square root of 7 d) 21