53. Use the given information to write the equation of each parabola.

a. vertex: (5, -3); directrix: x = 2

b. focus: (-2, 4); directrix: y = 2

c. axis of symmetry: x = 0;
vertex: (0, 0); directrix: y = 4

d. focus: (-3,5); vertex: (-1,5)

Find the area of the triangle shown 3 by 6

For what value of (y) is 3^3/3^y =1/9

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?