Answer:
x=16
Step-by-step explanation:
First, minus 80 from 180 because the sum of all the angles in a triangle is 180. Then use linear equations. 100=(4x-4)+(0.5x+32)
After that, you will get 100=4.5x+28
x=16
The last one is the answer
Answer:
0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
![f(x) = \mu e^{-\mu x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cmu%20e%5E%7B-%5Cmu%20x%7D)
In which
is the decay parameter.
The probability that x is lower or equal to a is given by:
![P(X \leq x) = \int\limits^a_0 {f(x)} \, dx](https://tex.z-dn.net/?f=P%28X%20%5Cleq%20x%29%20%3D%20%5Cint%5Climits%5Ea_0%20%7Bf%28x%29%7D%20%5C%2C%20dx)
Which has the following solution:
![P(X \leq x) = 1 - e^{-\mu x}](https://tex.z-dn.net/?f=P%28X%20%5Cleq%20x%29%20%3D%201%20-%20e%5E%7B-%5Cmu%20x%7D)
The probability of finding a value higher than x is:
![P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%201%20-%20P%28X%20%5Cleq%20x%29%20%3D%201%20-%20%281%20-%20e%5E%7B-%5Cmu%20x%7D%29%20%3D%20e%5E%7B-%5Cmu%20x%7D)
The mean time for the component failure is 2500 hours.
This means that ![m = \frac{2500}, \mu = \frac{1}{2500} = 0.0004](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2500%7D%2C%20%5Cmu%20%3D%20%5Cfrac%7B1%7D%7B2500%7D%20%3D%200.0004)
What is the probability that the lifetime exceeds the mean time by more than 1 standard deviations?
The standard deviation of the exponential distribution is the same as the mean, so this is P(X > 5000).
![P(X > x) = e^{-0.0004*5000} = 0.1353](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%20e%5E%7B-0.0004%2A5000%7D%20%3D%200.1353)
0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations
Answer:
4
Step-by-step explanation:
Variable: X = Unknown Number
2x + 4 = x + 8
2x - x = 8 - 4
x = 4
Check:
2(4) + 4 = 4 + 8
8 + 4 = 12
12 = 12
3 + x/2 = 7
x = (7-3)*2 = 8 = the number