Answer:
51/4
Step-by-step explanation:
To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.
X~ Uniform(0,100)
Then the probability mass function is given as follows.
Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows
Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable 
, 
is a random variable as well, remember that there is a theorem that says that
![E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20E%5BD%28X%29%5D%20%3D%20%5Cint%5Climits_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20D%28x%29%20f%28x%29%20%5C%2C%5C%2C%20dx)
Where 
is the probability mass function of X. Using the information of our problem
![E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20%5Cint%5Climits_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20%20D%28x%29f%28x%29%20dx%20%5C%5C%3D%20%5Cfrac%7B1%7D%7B100%7D%20%5Cbigg%5B%20%5Cint%5Climits_%7B0%7D%5E%7B20%7D%20x%20dx%20%2B%5Cint%5Climits_%7B20%7D%5E%7B45%7D%20%28x-20%29%20dx%20%2B%5Cint%5Climits_%7B45%7D%5E%7B70%7D%20%2870-x%29%20dx%20%2B%5Cint%5Climits_%7B70%7D%5E%7B100%7D%20%28x-70%29%20dx%20%20%5Cbigg%5D%5C%5C%3D%20%5Cfrac%7B51%7D%7B4%7D%20%3D%2012.75)
Answer:
A
C
D
Step-by-step explanation:
Answer:
y=-3x+5
Step-by-step explanation: y=mx+b
to find slope (m) use the equation 
so
= -3
to find b
use y=mx+b
-1=-3(2)+b
-1=-6+b
5=b
Hope this helps :)
Answer:
An equation for this would be : 36=3+x+3+X+5+5
the simplified version would be: 20=2x
The value of x = 10 feet
Step-by-step explanation:
Since perimeter is all the sides added together, and 36 ft is the perimeter,
think of a rectangle, 2 sides would be 3+x and the other 2 would be 5.
thus,
36=3+x+3+x+5+5
now add all like terms and you get 36=16+2x
subtracting 16 on both sides,
20=2x
dividing by 2 both sides,
x=10 feet.
Answer:
2071
Step-by-step explanation:
Since, the decline model follows exponential- decay model
thus,
Here,
P₀ is the initial consumption
t is the time in years
P is the consumption after t years
k is the decay constant
now,
1985 is the base year, thus for year 1985; t = 0
at t = 0, P = 80
Therefore,
or
P₀ = 80 pounds
also,
in the year 1996 i,e t = 1996 - 1985 = 11 years
P = 67 pounds
thus,
or
0.8375 = 
taking the log both sides, we get
-0.177 = 11k
or
k = - 0.01612
Therefore,
For P = 20 pounds per person
we have
or
0.25 = 
taking natural log both the sides, we get
-1.3863 = (- 0.01612 )(t)
or
t = 85.99 ≈ 86 years
Hence,
the year will be 1985 + 86 = 2071
