As an airplane comes in for a landing, it is descending at an angle of 10°with the horizontal. Its shadow, directly below it on the ground, travels 5000 meters until the plane touches the runway (ground). How far did the plane travel during that time (the actual "slanted" distance the plane moved)? please show proof.​

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?