Beverly needs to make a container in the shape of a rectangular prism that holds 1000 in3 of liquid. the height of the container must be 10 in. she wants to use the dimensions that will allow her to use the least amount of material possible. beverly’s mother says the difference in the amount of material will be too minor to worry about. beverly believes it is possible to save more than half the material needed if they pick the right dimensions. who is correct? support your answer with specific numbers, and explain your reasoning. the dimensions are measured in whole units.

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?