Apoint $(x, y)$ with integer coordinates is randomly selected such that $0 \le x \le 8$ and $0 \le y \le 4$. what is the probability that $x + y \le 4$? express your answer as a common fraction.

A20? -foot ladder is placed against a vertical wall of a? building, with the bottom of the ladder standing on level ground 19 feet from the base of the building. how high up the wall does the ladder? reach?

Which statement is true? n is a point of tangency on circle p. pt is a secant of circle p. is a secant of circle p. vu is a tangent of circle p.

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?