Margie is practicing for an upcoming tennis tournament. her first serve is good 20 out of 30 times on average. margie wants to know the
estimated probability that her first serve will be good at least four of the next six times she serves. how could she design a simulation for this
scenario?
the scenario can be simulated by rolling a six-sided die times. the
i would represent the number of margie's
good first serves. if the
y appear in a set of outcomes one time each, it would mean that at least four of the next six
first serves that margie makes will be good.

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.

step-by-step explanation: