2. The table shows the probabilities of winning or losing when the team is playing away or is playing at home. Home Away Total
Win 0.51 0.34 0.85
Loss 0.09 0.06 0.15
Total 0.6 0.4 1.00

(a) Are the events “winning” and “playing at home” independent? Show your calculations to justify why or why not.
(b) Are the events “losing” and “playing away” independent? Show your calculations to justify why or why not.

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step-by-step explanation:

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.

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest