Charles wants to find out if the students in foreign language classes spend more time in class speaking in english or in the foreign language they are studying. charles first gets class lists of all students taking foreign language classes. he then chooses 10 students from each different language class to survey. which best explains why the sample he chose may not be a representative sample?

a. the sample size is not large enough to represent the population.
b. the sample was not chosen at random.
c. the way the sample was chosen may overrepresent or underrepresent students taking certain language classes.
d. the way the sample was chosen does not sample students from each different language class.

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.