Answer:
![0.66](https://tex.z-dn.net/?f=0.66)
Step-by-step explanation:
GIVEN: Suppose that in a certain county
of voters are registered as Democrats,
as Republicans,
as Green party, and the rest are considered Independents. You conduct a poll by calling registered voters in the county at random.
TO FIND: Probability that the first call will be to either a Democrat or a Republican.
SOLUTION:
Lets total population of county be
.
voters registered as Democrats ![=37\%=\frac{37}{100}\times100x](https://tex.z-dn.net/?f=%3D37%5C%25%3D%5Cfrac%7B37%7D%7B100%7D%5Ctimes100x)
voters registered as Republicans ![=29\%=\frac{29}{100}\times100x](https://tex.z-dn.net/?f=%3D29%5C%25%3D%5Cfrac%7B29%7D%7B100%7D%5Ctimes100x)
voters registered as Green party ![=7\%=\frac{7}{100}\times100x](https://tex.z-dn.net/?f=%3D7%5C%25%3D%5Cfrac%7B7%7D%7B100%7D%5Ctimes100x)
![=7x](https://tex.z-dn.net/?f=%3D7x)
Probability that first call will be to Democrats
![=\frac{37x}{100x}=0.37](https://tex.z-dn.net/?f=%3D%5Cfrac%7B37x%7D%7B100x%7D%3D0.37)
Probability that first call will be to Republican
![=\frac{29x}{100x}=0.29](https://tex.z-dn.net/?f=%3D%5Cfrac%7B29x%7D%7B100x%7D%3D0.29)
probability that the first call will be to either a Democrat or a Republican
![=P(A)+P(B)](https://tex.z-dn.net/?f=%3DP%28A%29%2BP%28B%29)
![=0.37+0.29](https://tex.z-dn.net/?f=%3D0.37%2B0.29)
![=0.66](https://tex.z-dn.net/?f=%3D0.66)
Hence the probability that the first call will be to either a Democrat or a Republican is ![0.66](https://tex.z-dn.net/?f=0.66)
![\bf \begin{array}{llllll} \textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\ \textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\ y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x} \\ &&y=\cfrac{{{ k}}}{x} \end{array}\\\\ -----------------------------\\\\ \textit{p is inversely proportional to the cube of (q-2)}\implies p=\cfrac{k}{(q-2)^3} \\\\\\ now \quad \begin{cases} p=6\\ q=3 \end{cases}\implies 6=\cfrac{k}{(3-2)^3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bllllll%7D%0A%5Ctextit%7Bsomething%7D%26%26%5Ctextit%7Bvaries%20inversely%20to%7D%26%5Ctextit%7Bsomething%20else%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Ctextit%7Bsomething%7D%26%3D%26%5Ccfrac%7B%7B%7B%5Ctextit%7Bsome%20value%7D%7D%7D%7D%7B%7D%26%5Ccfrac%7B%7D%7B%5Ctextit%7Bsomething%20else%7D%7D%5C%5C%20%5Cquad%20%5C%5C%0Ay%26%3D%26%5Ccfrac%7B%7B%7B%5Ctextit%7Bk%7D%7D%7D%7D%7B%7D%26%5Ccfrac%7B%7D%7Bx%7D%0A%5C%5C%0A%26%26y%3D%5Ccfrac%7B%7B%7B%20%20k%7D%7D%7D%7Bx%7D%0A%5Cend%7Barray%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bp%20is%20inversely%20proportional%20to%20the%20cube%20of%20%28q-2%29%7D%5Cimplies%20p%3D%5Ccfrac%7Bk%7D%7B%28q-2%29%5E3%7D%0A%5C%5C%5C%5C%5C%5C%0Anow%20%5Cquad%20%0A%5Cbegin%7Bcases%7D%0Ap%3D6%5C%5C%0Aq%3D3%0A%5Cend%7Bcases%7D%5Cimplies%206%3D%5Ccfrac%7Bk%7D%7B%283-2%29%5E3%7D)
solve for "k", to find k or the "constant of variation"
then plug k's value back to
![\bf p=\cfrac{k}{(q-2)^3}](https://tex.z-dn.net/?f=%5Cbf%20p%3D%5Ccfrac%7Bk%7D%7B%28q-2%29%5E3%7D)
now.... what is "p" when q = 5? well, just set "q" to 5 on the right-hand-side, and simplify, to see what "p" is
Step-by-step explanation:
option 1
option 3
.15% translates to
.0015, and "of" means to multiply. so .0015 multiplied with 43 is
.0645