A chemist has three different acid solutions. The first acid solution contains 25 % acid, the second contains 35 % and the third contains 80 % . He wants to use all three solutions to obtain a mixture of 40 liters containing 55 % acid, using 2 times as much of the 80 % solution as the 35 % solution. How many liters of each solution should be used?

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?