Jake tossed a paper cup 50 times and recorded how it landed. The table shows the results: Position Open Side Up Closed Side Up Landing on Side Number of Times Landed in Position 3 7 40 Based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). Show your work.

Solve the system by the elimination method. x + y - 6 = 0 x - y - 8 = 0 when you eliminate y , what is the resulting equation? 2x = -14 2x = 14 -2x = 14

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 + 4x + 5 = 0

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?