The sum of two consecutive numbers is 77. The difference of half of the smaller number and one-third of the larger number is 6. If x is the smaller number and y is the larger number, which two equations
represent the sum and difference of the numbers?
O x - y = 77 and 1/2 x + 1/3 y = 6
O x + y = 77 and 1/2 x - 1/3 y = 6
Ox-y=6 and 1/2 x + 1/3 y = 77

Tom and maria typed in words in the ratio of 1 : 5 in 20 minutes. they typed 864 words altogether. find the number of words that each of them typed

Scrub a dub toothbrushes are $4.00 each. there is a 10% discount, but there is also a 6% sales tax after the discount is applied. what is the new price after tax? round to the nearest penny

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?