Question 2. A game requires a person to roll one die and then another.
2
3
4
5
6
7
3
4
5
6
7
8
4
5
7
8
9
5
6
7
8
9
10
6
7
8
9
10 11
8
9
10
11 12
Assume that the first die rolled lands on 6. Which of the following events is independent of the fact that
the first die rolled was a 6?
A. The number on the second roll is more than the number from the first roll.
B. After the second roll, the total combined number is 8.
C.
The second die rolled is a
D. The number on the second roll is less than the number from the first roll.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

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?

4. bob solved the inequality problem below incorrectly. explain his error and redo the problem showing the correct answer. −2x + 5 < 17 −2x + 5-5 < 17-5 -2x/-2 < 12/-2 x < -6