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%
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P(C | defective) = P(C&defective)/P(defective)
Every triangle equals 180 degrees, and we're trying to find the angle of DBA. So, we can identify DAB as a 90 degree angle to start. Then we can identify that ACB = ADB, meaning ADB is 30 degrees. With that information, we have this equation:
DBA = 180 - 90 - 30
DBA = 60
Her school is 2/3 miles away
2/3=4/6miles
So we need to find out how long it will take for her to run home from school...
School=4/6 miles
In 1 minutes she can run 1/6 miles
1min=1/6miles
In 2 minutes she can run 1/6+1/6 miles (1/6+1/6=2/6)
2min=2/6miles
3min=3/6miles
4min=4/6miles
It will take Erica 4 minutes to run 4/6 miles, so it'll take her 4 minutes to get home.
