Of all the students in a particular class, 50% have blue eyes. we want to run a simulation to predict how many blue eye students will be chosen if we randomly select 10 students. first, we need to assign digits to students that have blue eyes and students that do not have blue eyes. if we were to use single digits to represent both, which of the following would be a correct method of assigning these digits? a. blue eyes: 0, 1, 2, 3 other: 4, 5, 6, 7, 8, 9 b. blue eyes: 1, 2, 3, 4 other: 5, 6, 7, 8, 9, 10 c. blue eyes: 1, 2, 3, 4, 5 other: 6, 7, 8, 9, 10 d. blue eyes: 0, 1, 2, 3, 4 other: 5, 6, 7, 8, 9

Meghan has created a diagram of her city with her house, school, store, and gym identified. a. how far is it from the gym to the store? b. meghan also wants to walk to get some exercise, rather than going to the gym. she decides to walk along arc ab. how far will she walk? round to 3 decimal places.

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).