The roller coaster below is the shape of a parabola. The quadratic equation that represents the roller coaster is h(x) = - x² + 6x – 4, where h(x) is the height of the roller coaster in meters when x, in meters, is the distance from one of the bases under the roller coaster. What is the height of the roller coaster 3 meters from one of the bases under the roller coaster? Show your work.

Which of the following correctly justifies statement four of the two column proof? a. corresponding angles theorem b. transitive property of equality c. vertical angle theorem d. substitution property of equality

What is the effect on the graph of the function f(x)=x when f(x) is replaced with -f(x)+4

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?