Answer:
0.1393 = 13.93% probability that an order of 50 units will have one or more faulty units.
Step-by-step explanation:
Mean for a number of units, which means that the Poisson distribution is used to solve this question.
Poisson Distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Mean:
3 defective for 1000, how many for 50?
3 - 1000
- 50
Applying cross multiplication:
![\mu = \frac{3*50}{1000} = 0.15](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%5Cfrac%7B3%2A50%7D%7B1000%7D%20%3D%200.15)
What is the probability that an order of 50 units will have one or more faulty units?
This is:
![P(X \geq 1) = 1 - P(X = 0)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29)
In which
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-0.15}*(0.15)^{0}}{(0)!} = 0.8607](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-0.15%7D%2A%280.15%29%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.8607)
![P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8607 = 0.1393](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29%20%3D%201%20-%200.8607%20%3D%200.1393)
0.1393 = 13.93% probability that an order of 50 units will have one or more faulty units.
Answer:
Width is 3 ft
length is 6 ft
Step-by-step explanation:
Let x = the width
Let 2x = the length
Let h = the height
We know that volume is given v = l×b×h
so we have v = volume ![= x*2x*h](https://tex.z-dn.net/?f=%3D%20x%2A2x%2Ah)
![2x^2*h = 36](https://tex.z-dn.net/?f=2x%5E2%2Ah%20%3D%2036)
![h = \frac{18}{x^2}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B18%7D%7Bx%5E2%7D)
surface area include 2 ends + 1 bottom and 2 sides excluding top
![S.A. = 2(x*h) + 1(2x*x) + 2(2x*h)](https://tex.z-dn.net/?f=S.A.%20%3D%202%28x%2Ah%29%20%2B%201%282x%2Ax%29%20%2B%202%282x%2Ah%29)
![S.A. = 2xh + 2x^2 + 4xh](https://tex.z-dn.net/?f=S.A.%20%3D%202xh%20%2B%202x%5E2%20%2B%204xh)
we have calculate![h = = \frac{18}{x^2}](https://tex.z-dn.net/?f=%20h%20%3D%20%3D%20%5Cfrac%7B18%7D%7Bx%5E2%7D)
![S.A = 2x^2 + 6x \frac{18}{x^2}](https://tex.z-dn.net/?f=S.A%20%3D%202x%5E2%20%2B%206x%20%5Cfrac%7B18%7D%7Bx%5E2%7D%3C%2Fp%3E%3Cp%3E)
![S.A = 2x^2 + \frac{108}{x}](https://tex.z-dn.net/?f=S.A%20%3D%202x%5E2%20%2B%20%5Cfrac%7B108%7D%7Bx%7D)
By graphing above equation we can calculate the value of x
Minimum S.A when x is 3 is the width so
2(3) = 6 is the length
![h = \frac{18}{3^2} = 2](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B18%7D%7B3%5E2%7D%20%3D%202)
1. 81 1/2 = 163/2
2. 32 1/5 - 64 1/3 =
483/15 - 965/15 =
-482/15 or -32 2/15
3. 16 1/4 = 65/4
4. 49 1/2 + 27 1/3 =
99/2 + 82/3 =
297/6 + 164/6 =
461/6 or 76 5/6
I think 55. It can’t be more than a 90 degree angle. And it doesn’t look like it would be 48 either.
Answer: Probably not
Step-by-step explanation:
It’s hard to tell without seeing the graph, but usually functions require that you can’t have one “x” (x=2) mapping to two “y”s (y=0,2).