<span>1m +
35cm = .35m +
3m +
90cm =.90 m +
25mm = .025m +
</span>
<span><span>+ 1.0 m
+ 0.35m
+ 3.0 m
+ 0.90 m
+ 0.025m</span>
= 5.275 meters
</span>
Answer:
0.4968 = 49.68% probability that the repair time takes between 2 to 4 hours
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)
Average repair time of 2 hours
This means that ![m = 2, \mu = \frac{1}{2} = 0.5](https://tex.z-dn.net/?f=m%20%3D%202%2C%20%5Cmu%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%3D%200.5)
What is the probability that the repair time takes between 2 to 4 hours
More than 2:
![P(X > 2) = e^{-0.5*2} = 0.3679](https://tex.z-dn.net/?f=P%28X%20%3E%202%29%20%3D%20e%5E%7B-0.5%2A2%7D%20%3D%200.3679)
Less than 4:
![P(X \leq 4) = 1 - e^{0.05*4} = 0.8647](https://tex.z-dn.net/?f=P%28X%20%5Cleq%204%29%20%3D%201%20-%20e%5E%7B0.05%2A4%7D%20%3D%200.8647)
Between two and four:
![P(2 \leq x \leq 4) = 0.8647 - 0.3679 = 0.4968](https://tex.z-dn.net/?f=P%282%20%5Cleq%20x%20%5Cleq%204%29%20%3D%200.8647%20-%200.3679%20%3D%200.4968)
0.4968 = 49.68% probability that the repair time takes between 2 to 4 hours
Answer:
27.8°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relationship between the angle and the relevant sides of the triangle is ...
Cos = Adjacent/Hypotenuse
In this case, the hypotenuse of the triangle is the length along the road; the distance parallel to the ground is the side adjacent to the angle of depression. So, you have ...
cos(angle) = (23 mi)/(26 mi)
angle = arccos(23/26) ≈ 27.8°
The angle of depression is about 27.8°.
_____
<em>Comment on the road</em>
The grade on such a road is about 53%. A road with an 8% grade for any distance is considered marginally safe for trucks. A 53% grade for 26 miles would wear out the brakes in no time.
The elevation drop on this road is about 12 miles, or more than 64,000 feet. The highest mountain on Earth is less than half that height, so this must be on a different planet.
14/2, 7 games per month.
Take the total amount of games and divide it by the time.
Answer:
23.7 - 10 = 13.7
Step-by-step explanation: