Describe the term mutually exclusive. Provide some examples. Must the values of x in a discrete probability distribution always be mutually exclusive? Why or why not?

Acircular garden with radius of 8 feet is surrounded by a circular path with a width of 3 feet. what is the approximate area of the path alone? use 3.14 for π

Select the number of ways in which a line and a circle can intersect

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.