The length of a rectangle is 4 meters longer than the width. if the area is 21 square meters, find the rectangle's dimensions. round to the nearest tenth of a meter.
Answer:
look the photo
..............................
Answer:
0.2941 = 29.41% probability that it was manufactured during the first shift.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: Manufactured during the first shift.
Probability of a defective item:
1% of 50%(first shift)
2% of 30%(second shift)
3% of 20%(third shift).
So
![P(A) = 0.01*0.5 + 0.02*0.3 + 0.03*0.2 = 0.017](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.01%2A0.5%20%2B%200.02%2A0.3%20%2B%200.03%2A0.2%20%3D%200.017)
Probability of a defective item being produced on the first shift:
1% of 50%. So
![P(A \cap B) = 0.01*0.5 = 0.005](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.01%2A0.5%20%3D%200.005)
What is the probability that it was manufactured during the first shift?
![P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.005}{0.017} = 0.2941](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D%20%3D%20%5Cfrac%7B0.005%7D%7B0.017%7D%20%3D%200.2941)
0.2941 = 29.41% probability that it was manufactured during the first shift.
Answer:
i)16
ii)9
Step-by-step explanation:
![\sqrt{256} \\=\sqrt{16*16} \\=16\\\\ii)\ \sqrt[3]{729}\\ =\sqrt[3]{9*9*9} \\=9](https://tex.z-dn.net/?f=%5Csqrt%7B256%7D%20%5C%5C%3D%5Csqrt%7B16%2A16%7D%20%5C%5C%3D16%5C%5C%5C%5Cii%29%5C%20%5Csqrt%5B3%5D%7B729%7D%5C%5C%20%3D%5Csqrt%5B3%5D%7B9%2A9%2A9%7D%20%5C%5C%3D9)