6 7
8
9
10
11
16 17 18
19
12 13 14 15
data
0
Based on the boxplot above, identify the 5 number summary

5 10 16 17 18

Step-by-step explanation:

Using the box plot above, the 5 number summary is this :

Minimum = value at the starting point of the left whisker = 5

Lower quartile = value at the start point of the box = 10

Median = value marked in between the box = 16

Upper quartile = value at the end point of the box = 17

Maximum = value at the endpoint of the whisker = 18

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.