Fast pls!

what is the measure of the indicated central angle?

a) 70 degrees

b) 80 degrees

c) 90 degrees

d) 110 degrees

e) none of the above

Step-by-step explanation:

Given,

r=3

arc=3/2*pi

we know that,arc=theta(angle)*2*Pi*r/360

theta*2*pi*3/360=3*pi/2

pi and 3 cancel on both sides

theta*2/360=1/2

theta/180=2

theta=180/2

Hence theta or the angle required=90 degrees(option C)

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.

54 it just is

step-by-step explanation: