Which THREE pairs of measurements are possible side lengths for a 30-60-90 triangle? C= 30, B = 90, A = 60

1. AB+4, BC = 4√3
2. 2√3, AC = 2
3. AB = 3, AC = 3√3
4. BC = 10, AC = 4√3
5. AB = 7, AC = 14
6. AB = 11, BC = 11√3

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?

Given sin28.4=.4756, cos28.4=.8796, and tan28.4=.5407 find the cot of 61.6

32a³b² 8ab² simplify the following expression.