Use the double-angle identities to find cos(2x) if tanx=12/5 and pi

What value of x is in the solution set of –5x – 15 > 10 + 20x?

Acertain volume of water contains 100000 hydrogen atoms and 50,000 oxygen atoms how many hydrogen atoms are in a volume of water containing 4 million oxygen atoms

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?