Answer:
![\dfrac{14}{29}](https://tex.z-dn.net/?f=%5Cdfrac%7B14%7D%7B29%7D)
Step-by-step explanation:
Let <em>P(A) </em>be the probability that goggle of type A is manufactured
<em>P(B) </em>be the probability that goggle of type B is manufactured
<em>P(E)</em> be the probability that a goggle is returned within 10 days of its purchase.
According to the question,
<em>P(A)</em> = 30%
<em>P(B)</em> = 70%
<em>P(E/A)</em> is the probability that a goggle is returned within 10 days of its purchase given that it was of type A.
P(E/B) is the probability that a goggle is returned within 10 days of its purchase given that it was of type B.
will be the probability that a goggle is of type A and is returned within 10 days of its purchase.
will be the probability that a goggle is of type B and is returned within 10 days of its purchase.
![P(E \cap A) = P(A) \times P(E/A)](https://tex.z-dn.net/?f=P%28E%20%5Ccap%20A%29%20%3D%20P%28A%29%20%5Ctimes%20P%28E%2FA%29)
![P(E \cap A) = \dfrac{30}{100} \times \dfrac{5}{100}\\\Rightarrow P(E \cap A) = 1.5 \%](https://tex.z-dn.net/?f=P%28E%20%5Ccap%20A%29%20%3D%20%5Cdfrac%7B30%7D%7B100%7D%20%5Ctimes%20%5Cdfrac%7B5%7D%7B100%7D%5C%5C%5CRightarrow%20P%28E%20%5Ccap%20A%29%20%3D%201.5%20%5C%25)
![P(E \cap B) = P(B) \times P(E/B)](https://tex.z-dn.net/?f=P%28E%20%5Ccap%20B%29%20%3D%20P%28B%29%20%5Ctimes%20P%28E%2FB%29)
![P(E \cap B) = \dfrac{70}{100} \times \dfrac{2}{100}\\\Rightarrow P(E \cap B) = 1.4 \%](https://tex.z-dn.net/?f=P%28E%20%5Ccap%20B%29%20%3D%20%5Cdfrac%7B70%7D%7B100%7D%20%5Ctimes%20%5Cdfrac%7B2%7D%7B100%7D%5C%5C%5CRightarrow%20P%28E%20%5Ccap%20B%29%20%3D%201.4%20%5C%25)
![P(E) = 1.5 \% + 1.4 \% \\P(E) = 2.9\%](https://tex.z-dn.net/?f=P%28E%29%20%3D%201.5%20%5C%25%20%2B%201.4%20%5C%25%20%5C%5CP%28E%29%20%3D%202.9%5C%25)
If a goggle is returned within 10 days of its purchase, probability that it was of type B:
![P(B/E) = \dfrac{P(E \cap B)}{P(E)}](https://tex.z-dn.net/?f=P%28B%2FE%29%20%3D%20%5Cdfrac%7BP%28E%20%5Ccap%20B%29%7D%7BP%28E%29%7D)
![\Rightarrow \dfrac{1.4 \%}{2.9\%}\\\Rightarrow \dfrac{14}{29}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B1.4%20%5C%25%7D%7B2.9%5C%25%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B14%7D%7B29%7D)
So, the required probability is ![\dfrac{14}{29}.](https://tex.z-dn.net/?f=%5Cdfrac%7B14%7D%7B29%7D.)
(1/40) - (1/x) = (1/60)
x = 1/(1/40) - (1/60)) =
<span>A.) 120</span> minutes
Its similar to the other question.
Answer:
22.5 lbs
Step-by-step explanation:
First you find the cubic feet. That is the volume of the object which is length*width*height.
In your example, they are using inches. So you have to convert all units to feet. That would be 0.5 inches, 0.5 inches, and 5/3 inches. The volume would be 0.5*0.5*5/3 which is about 5/12 cubic feet
You then take that 5/12 cubic feet and multiply it by the 54 lbs/cubic foot. The answer would be 22.5 lbs
Answer:
212 and I= 2000+212
=2212
Step-by-step explanation: