Water leaks out from a tank at a rate proportional to the square root of the remaining volume of water.(a) Write down a differential equation that models this situation. Be sure to say exactly what eachvariable represents.(b) Solve your differential equation.(c) Suppose that the tank initially contains 200 L of water, and after one day 20 L has leaked out. When will the tank be half empty

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?