5. Lily has 144 ceramic beads and 108 wooden beads. She plans to store the beads equally in 6 boxes. How many beads will be in each box? A: 6 beads
B: 36 beads
C:30 beads
D: 42 beads

D: 42 beads

Step-by-step explanation:

First, you would add 144 and 108 together, to get 252 beads.

Then, you would do 252 divided by 6, to get 42.

So 42 (D) beads would be in each box.

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.