Afountain on a lake sprays water in a parabolic arch modeled by the equation
y = −0.4x2 + 3x, where y is the height in feet and x is the horizontal distance. a beam of light is passed through the fountain to create a rainbow effect. if the beam is directed at an angle modeled by the equation -2.2x + 4.9y = 8.18, at what distance from the ground will the beam first touch the water spray?

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?