A drug test for athletes has a 5% false positive rate and a 10% false negative rate. Of the athletes tested, 4% have actually been using the prohibited drug. If a randomly chosen athlete tests positive, what is the probability that the prohibited drug has been used

0.4286 or 42.86%

Step-by-step explanation:

The probability that an athlete has used drugs and tests positive is given by the probability that he had been using drugs (4%) multiplied by the probability of a true positive (1 - false negative):

The probability that an athlete has NOT used drugs and tests positive is given by the probability that he had not been using drugs (100% - 4%) multiplied by the probability of a false positive (5%):

Finally,  the probability that the prohibited drug has been used given that an athlete tested positive is:

The probability is 0.4286 or 42.86%.

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.

add the table and i will answer correctly

step-by-step explanation: