Answer:
-8x3 - 4x2 + 8x - 4
Step-by-step explanation:
 
        
                    
             
        
        
        
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
 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
 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:6
Step-by-step explanation:
 
        
             
        
        
        
<span>Given: Right △ABC as shown where CD is an altitude of the triangle. We  prove that 

Because △ABC and △CBD both have a right angle, and the same angle B is
in both triangles, the triangles must be similar by AA. 
Likewise, △ABC
and △ACD both have a right angle, and the same angle A is in both
triangles, so they also must be similar by AA. 
The proportions 

 and 

 are
true because they are ratios of corresponding parts of similar
triangles. 
The two proportions can be rewritten as 

 and 

.
Adding 

 to both sides of first equation, 

, results in the
equation 

. 
Because 

 and ce are equal, ce can be
substituted into the right side of the equation for 

, resulting in the
equation 

. 
Applying the converse of the distributive
property results in the equation 

.
The last sentence of the proof is 
Because f + e = c, 

.</span>
 
        
        
        
Answer:
A) 5/2
Step-by-step explanation:
It's right. You can trust me.
<3