The manager of a local craft shop wants to conduct a survey to see what color will be popular among his customers during the upcoming season. He decides to poll every fifth customer that enters the shop for two weeks.
Are the results of the survey valid?

A.
No. The manager used a sample that represents the entire population of customers but is not randomly chosen.
B.
No. The manager used a sample that was randomly chosen but does not represent the entire population of customers.
C.
Yes. The manager used a sample that was randomly chosen and represents the entire population of his customers.
D.
No. The manager used a sample that neither represents the entire population of customers nor is randomly chosen.

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step-by-step explanation:

step-by-step explanation:

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

e) none of the above because the measure of angle cba is 101°