A quality-assurance inspector periodically exam-ines the output of a machine to determine whether it is properly adjusted. When set properly, the machine pro-duces nails having a mean length of 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is 2.025 inches. Using the 0.01 level of significance, examine the null hypothesis that the machine is adjusted properly. Determine and interpret the p-value for the test.

Element x decays radioactively with a half life of 8 minutes. if there are 450 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 37 grams?

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.

John has 1/2 pound of oranges to share with julie. if they share the oranges equally, how much will each of them have?