The cross section of a metal ingot is a trapezoid. the cross section has an area of 39 square centimeters. the top base of the cross section is 12 centimeters. the length of the bottom base is 2 centimeters greater than the top base. how tall is the metal ingot?

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?