Find the vertical, horizontal, and slant asymptotes, if any, for f(x)= 5x^3 -51x^2 +77x +100 / x^2 -11x +24:
a.
vertical: x=8, x=-3
horizontal: y = 0
b.
horizontal: y = 0
slant: 7=5x+4
c.
vertical: x=8, x=3
slant: y=5x+4
d.
vertical: x=-8, x=-3
slant: y=5x-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?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

Find the condition that the zeros of the polynomial f(x) = x^3+3px^2+3px+r may be in a.p.