Answer:
x=27
Step-by-step explanation
"5 more than x is equal to 32" basically means that you need to subtract 5 from 32, which gives you 27.
H(t) = f(t) - g(t)
= 500(1.2)^t - 380(1.15)^t
Taking out the greatest common factor, which is 20:
= 20[(25)(1.2)^t - (19)(1.15)^t]
This is the third choice.
Note that you cannot subtract the bases of the exponents, for example (1.2^t - 1.15^t) cannot be simplified into something like 0.05^t.
Let x = 63.63...(by repeating i assume you mean the 63 is repeated as 63.636363...)
therefore 100x = 6363.63..
100x-x =6300 (the recurring bit has been cancelled out which is what you should always aim to do)
99x=6300
x = 6300/99
cancel down
x = 700/11
The proportion of production that is defective and from plant A is
... 0.35·0.25 = 0.0875
The proportion of production that is defective and from plant B is
... 0.15·0.05 = 0.0075
The proportion of production that is defective and from plant C is
... 0.50·0.15 = 0.075
Thus, the proportion of defective product that is from plant C is
... 0.075/(0.0875 +0.0075 +0.075) = 75/170 = 15/34 ≈ 44.12%
_____
P(C | defective) = P(C&defective)/P(defective)
