Christian is setting up his campsite. For his shelter, he is tying a rope between two trees, completely taught, and then setting a tarp over the rope. The distance between the two trees is 12.5 ft. The tarp is stretched over the rope, with no wrinkles, and there is 3 ft of rope left uncovered at each end. When the corners of the tarp are staked directly into the ground, both openings of the tarp shelter form an equilateral triangle. If the rope is 5 ft off the ground, what is the surface area of the tarp

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?