A teacher has written types of math problems on slips of paper for her students to present to the class. She puts the slips of paper into a jar and randomly selects 1 for each student. Once the student has read the slip of paper, it is placed back into the jar: The jar has 18 geometry slips, 16 algebra slips, and 14 word problems slips. Which of the following statements is true?

A. The events are independent because replacing the first slip does not affect the probability of selecting the second slip.

B. The events are dependent because replacing the first slip does not affect the probability of selecting the second slip.

C. The events are conditional and the probability is equal to 1.

D. The events are dependent because replacing the first slip affects the probability of selecting the second slip.

E. The events are independent because replacing the first slip affects the probability of selecting the second slip.

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.

3/20

step-by-step explanation:

well, there are 20 outcomes, and 3 of them you want. so, 3/20

the answer to your question is b.