15. Solve for x.
71°
(10x + 6)
(13x - 2)
(8x - 1)

x = 8

Step-by-step explanation:

Measure of unknown angle 'y' = 180° - 71° (linear pair of angles)

                                                   = 109°

Formula for the interior angle of a polygon = (n - 2) × 180°

Here n = number of sides of the polygon

Therefore, sum of the interior angles of the given polygon = (4 - 2) × 180°

                                                                                                  = 360°

(10x + 6) + (13x - 2) + (8x - 1) + y = 360°

(10x + 13x + 8x) + (6 - 2 - 1) + 109 = 360

31x + 3 + 109 = 360

31x + 112 = 360

31x = 360 - 112

31x = 248

x = 8

answer: rolling a number cube and flipping a coin.

step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.