1) the mean is 12.5
2) X is 36
3) the median mass is 40.5 KG
4) the mode is 8, 13
5) the range is 9
Answer:

Step-by-step explanation:
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). It is a particular case of the gamma distribution". The probability density function is given by:

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

We can assume that the random variable t represent the number of years that the radio is already here. So the interest is find this probability:

We have an important property on the exponential distribution called "Memoryless" property and says this:

Where a represent a shift and t the time of interest.
On this case then 
We can use the definition of the density function and find this probability:


![=[lim_{x\to\infty} (-e^{-\frac{1}{8}x})+e^{-1}]=0+e^{-1}=e^{-1}](https://tex.z-dn.net/?f=%3D%5Blim_%7Bx%5Cto%5Cinfty%7D%20%28-e%5E%7B-%5Cfrac%7B1%7D%7B8%7Dx%7D%29%2Be%5E%7B-1%7D%5D%3D0%2Be%5E%7B-1%7D%3De%5E%7B-1%7D)
Answer:
x = 7
Step-by-step explanation:
Given
y = 5x - 3 ← equate 5x - 3 to 32
5x - 3 = 32 ( add 3 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7 ← input
Y = -7x - 2
Use the two points given to find the slope (m)
m = (y2 - y1) / (x2 - x1)
m = ( 12-5 ) / (-2 - (-1))
m = -7
Now we have y = -7x + b where 'b' is our y-intercept. We can solve for 'b' by choosing one of the (x,y) coordinate points and plugging them in.
Let's choose the point (-1,5). Plug -1 in for 'x' and 5 in for 'y' and solve for 'b'.
y = -7x + b
5 = -7(-1) + b
b = -2
Final eqn: y = -7x - 2
As it's already graphed their inetresection point is solution for both functions
- Red one is g(x) as it's linear
- Other one is f(x) as it's modulus
The solution is (1,5)