Answer:
 
And if we solve for a we got
 
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  
Step-by-step explanation:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
 
  
Where  and
 and  
For this part we want to find a value a, such that we satisfy this condition:
 (a)
   (a)
 (b)
   (b)
As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842
If we use condition (b) from previous we have this:
 
  
 
But we know which value of z satisfy the previous equation so then we can do this:
 
And if we solve for a we got
 
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  
 
        
             
        
        
        
The difference is 45.
The modal number of the electoral votes is 5 because it appears the most.
The range of the electoral votes is 55 - 5 = 50 (Highest minus the lowest).
The difference between the two is found by subtracting them.
50 - 5 = 45
        
                    
             
        
        
        
solve for y by subtracting 3x from each side
-4y = -3x+8 
 divide by -4
y = 3/4 x -2
 
        
             
        
        
        
75.3982237 inches squared is the answer, round it to whatever decimal place your asked to.
        
             
        
        
        
Answer:
k=7
Step-by-step explanation:
first, plug in the given values
2x+3y=k --> 2(2)+3(1)=k
-->4+3=k
-->7=k
k=7