Answer: 1/3
Step-by-step explanation:
Here is the complete question:
machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 11.5 gallons per minute. Find the probability that between 9.0 gallons and 10.0 gallons are pumped during a randomly selected minute.
The Probability of the above question will be calculated as:
= (10-9) / (11.5 - 8.5)
= 1/3
The above is the easier way to solve this
F(g(2)) = 3(x^3 + 1)^2 - 7 = 3(x^6 + 2x^3 + 1) - 7 = 3x^6 + 6x^3 + 3 - 7 = 3x^6 + 6x^3 - 4
Answer:
tex]M=\beta ln(2)[/tex]
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate).
Solution to the problem
For this case we can use the following Theorem:
"If X is a continuos random variable of the exponential distribution with parameter
for some
"
Then the median of X is 
Proof
Let M the median for the random variable X.
From the definition for the exponential distribution we know the denisty function of X is given by:

Since we need the median we can put this equation:

If we evaluate the integral we got this:
![\frac{1}{\beta} \int_0^M e^{- \frac{x}{\beta}}dx =\frac{1}{\beta} [-\beta e^{-\frac{x}{\beta}}] \Big|_0^M](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cbeta%7D%20%5Cint_0%5EM%20e%5E%7B-%20%5Cfrac%7Bx%7D%7B%5Cbeta%7D%7Ddx%20%3D%5Cfrac%7B1%7D%7B%5Cbeta%7D%20%5B-%5Cbeta%20e%5E%7B-%5Cfrac%7Bx%7D%7B%5Cbeta%7D%7D%5D%20%5CBig%7C_0%5EM)
And that's equal to:

And if we solve for M we got:


If we apply natural log on both sides we got:

And then 
Finding the area between two points
Answer:
√26
Decimal Form:
5.09901951
Answer:
it does appear to be a right triangle