A total of 400 students were surveyed at a college to see if they live in on-campus dorms or if they live off-campus. The table shows the results of the survey
Dorms Off-Campus Total
Freshman
88
12
100
100
Sophomore
Junior
43
38
57
75
100
Senior
25
100
Total
218
182
400
What percentage of the students surveyed live off-campus?
OA 18.25
OB 41.28
OC 45.5%
OD 83.55

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.

the weight of the object inside the box!

$452.90 because you needed to round to the nearest cent