The function f(x) = 50 ⋅ 0.8^x models the number of ants in Jonathan's ant farm after it is stricken by a deadly ant disease, where x represents the number of weeks since the first ant became sick. Which of the following are true statements? Select all that apply.

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?