The coordinates of the vertices of triangle ABC are A(1, -1), B(1, 4), and C(8, 4). What is the length, in units, of the line segment that connects vertex A and vertex B?

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?

Find the product. type your answer in the space provided. use / for a fraction bar (example: 1/2) and ^ for an exponent (example: x^5). do not put spaces in your answer. (x -1 y 5)^2 · (2xy -2)^5

You work for a landscape company that just got a contract to re-mulch a park. the area that needs mulching is 30 feet by 60 feet. they want a 3 inch layer of much on the area. the company has bags of mulch that cover 2 cubic yards that cost $4.00 per bag. how much will it cost the consumer just in materials to re-mulch the area (round to the nearest dollar)?