Find the limit. lim  θ→0  cos(4θ) − 1 / sin(7θ) can't figure this out. any is appreciated!

The appalachian trail is a hiking trail that passes through the appalachian mountains. three members of a teen hiking group hiked a section of the trail. the hikers stopped at a rest area and equally shared 3 4 gallon of water. how much water did each person get?

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?

Alex took his brother to a birthday party. the party was scheduled to last for 1 and 3/4 hours but they stayed for 4/5 of an hour more. how long did she stay at the party?