The picture shows a triangular island: A right triangle is shown with an acute angle equal to 45 degrees. The length of the side of the triangle opposite to the acute angle is a. The length of the side of the triangle adjacent to the acute angle is b. The length of the hypotenuse is c. Which expression shows the value of c? b over tan 45 degrees b over cos 45 degrees a cos 45° a tan 45°

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?