Answer:
8.72×10²
Step-by-step explanation:
- 8.72×10²=872
 
        
             
        
        
        
Given parameters: 
    Coordinates of the points =  (3,4) and (19, 16)
Unknown: 
The distance between the points = ? 
The midpoint  = ? 
Solution: 
   The distance between two points can be mathematically solved using; 
     D  = 
  where  x₁  = 3, x₂  = 19  and y₁  = 4, y₂  = 16
 Input the parameters and solve; 
    D  =  = 20
   = 20
Midpoint;
     The expression is given as; 
      x , y
 , y =
  =  ,
  , 
          input the parameters and solve; 
                    =  ,
  ,  
 
                    = 11 , 10
The midpoint is (11, 10)
   
 
        
             
        
        
        
H=3 because 27 divided by 9 is 3 
        
                    
             
        
        
        
The expected value is
![E[X]=\displaystyle\sum_xx\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x=\dfrac{0+1+\cdots+9+10}{11}=\dfrac{55}{11}=\boxed{5}](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Csum_xx%5C%2CP%28X%3Dx%29%3D%5Cfrac1%7B11%7D%5Csum_%7Bx%3D0%7D%5E%7B10%7Dx%3D%5Cdfrac%7B0%2B1%2B%5Ccdots%2B9%2B10%7D%7B11%7D%3D%5Cdfrac%7B55%7D%7B11%7D%3D%5Cboxed%7B5%7D)
The standard deviation is the square root of the variance, which is
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](https://tex.z-dn.net/?f=V%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2)
where
![E[X^2]=\displaystyle\sum_xx^2\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x^2=\dfrac{0^2+1^2+\cdots+9^2+10^2}{11}=\dfrac{385}{11}=35](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Csum_xx%5E2%5C%2CP%28X%3Dx%29%3D%5Cfrac1%7B11%7D%5Csum_%7Bx%3D0%7D%5E%7B10%7Dx%5E2%3D%5Cdfrac%7B0%5E2%2B1%5E2%2B%5Ccdots%2B9%5E2%2B10%5E2%7D%7B11%7D%3D%5Cdfrac%7B385%7D%7B11%7D%3D35)
so that
![V[X]=35-5^2=10](https://tex.z-dn.net/?f=V%5BX%5D%3D35-5%5E2%3D10)
making the standard deviation
![\sqrt{V[X]}=\sqrt{10}\approx\boxed{3.16}](https://tex.z-dn.net/?f=%5Csqrt%7BV%5BX%5D%7D%3D%5Csqrt%7B10%7D%5Capprox%5Cboxed%7B3.16%7D)