For the expression StartFraction 9 x squared minus 8 Over (3 x squared minus 4) squared EndFraction, which sum represents the correct form of the partial fraction decomposition? StartFraction A x + B Over 3 x squared minus 4 EndFraction + StartFraction C x + D Over (3 x squared minus 4) squared EndFraction StartFraction A Over 3 x squared minus 4 EndFraction + StartFraction B Over (3 x squared minus 4) squared EndFraction StartFraction A x + B Over (3 x squared minus 4) squared EndFraction + StartFraction C x + D Over (3 x squared minus 4) squared EndFraction StartFraction A Over (3 x squared minus 4) squared EndFraction + StartFraction B Over (3 x squared minus 4) squared EndFraction

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.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.