On a chessboard compute the expected number of plays it takes a knight, starting in one of the four corners of the chessboard, to return to its initial position if we assume that at each play it is equally likely to choose any of its legal moves. (no other pieces are on the board.)

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.

Which choice names the hypotenuse of triangle xyz? a. segment yx b. segment yz c. segment ab d. segment zx

Select the correct answer from each drop-down menu. let c(g) be the total cost, including shoe rental, for bowling g games at pin town lanes. c(g) = 5g+3 so, c(6) = 8? 33? 30? or 14? this means that for a $6 shoe rental? for $6 per game? for 6 games? for a total cost of $6? , the games are $8 each? total cost is $33? number of games is 14? or total cost is $30? reset next