Answer:
750 000
Step-by-step explanation:
45 000 000 ÷ 60 = 750 000 gallons of water per second
Answer:
![P(X = 2) = 0.2613](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%200.2613)
Step-by-step explanation:
Given
--- proportion
--- defective motors
--- sample size
Required
Determine the probability that exactly 2 is defective
This follows a Poisson distribution and will be solved using:
![P(X = x) = \frac{e^{-u} u^x}{x!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-u%7D%20u%5Ex%7D%7Bx%21%7D)
Where
u = Expected number of occurrence, and it is calculated as:
![u = np](https://tex.z-dn.net/?f=u%20%3D%20np)
![u = 60 * 4\%](https://tex.z-dn.net/?f=u%20%3D%2060%20%2A%204%5C%25)
![u = 60 * 0.04](https://tex.z-dn.net/?f=u%20%3D%2060%20%2A%200.04)
![u = 2.4](https://tex.z-dn.net/?f=u%20%3D%202.4)
So:
becomes
![P(X = 2) = \frac{e^{-2.4}2.4^{2}}{2!}](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20%5Cfrac%7Be%5E%7B-2.4%7D2.4%5E%7B2%7D%7D%7B2%21%7D)
![P(X = 2) = \frac{e^{-2.4}* 5.76}{2}](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20%5Cfrac%7Be%5E%7B-2.4%7D%2A%205.76%7D%7B2%7D)
![P(X = 2) = e^{-2.4}* 2.88](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20e%5E%7B-2.4%7D%2A%202.88)
![P(X = 2) = 0.09071795328* 2.88](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%200.09071795328%2A%202.88)
![P(X = 2) = 0.26126770544](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%200.26126770544)
![P(X = 2) = 0.2613](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%200.2613)
<em>Hence, the probability that exactly 2 out of 60 will be defective is 0.2613</em>
Answer:
![-6048](https://tex.z-dn.net/?f=-6048)
Step-by-step explanation:
![---------------------------------](https://tex.z-dn.net/?f=---------------------------------)
=
![because](https://tex.z-dn.net/?f=because)
![---------------------------------](https://tex.z-dn.net/?f=---------------------------------)
= ![?](https://tex.z-dn.net/?f=%3F)
= ![-108](https://tex.z-dn.net/?f=-108)
= ![?](https://tex.z-dn.net/?f=%3F)
= ![-6048](https://tex.z-dn.net/?f=-6048)
![---------------------------------](https://tex.z-dn.net/?f=---------------------------------)
<em>Hope this helps! <3</em>
![---------------------------------](https://tex.z-dn.net/?f=---------------------------------)
Answer:
20 cm
Step-by-step explanation:
A cube has 6 faces. Two of the faces are bases. The other four faces are lateral faces.
Let the area of 1 face = x
4x = 1600 cm^2
x = 400 cm^2
Since the area of 1 face is 400 cm^2, then the side length is sqrt(400 cm^2) = 20 cm
Answer: 20 cm
The value in this case would be going up. Since .75 being multiplied by an increasing number would only increase, the value must be doing the same.
However, if that t were an exponent, the value would be decreasing. The more a number between 0 and 1 is multiplied by itself, the smaller it gets.