Answer:
(a) σ²  = 144
(b) s² = 12
Step-by-step explanation:
(a) Population variance σ² = ∑(X -  )² / N
)² / N
The arithmetic mean 
                                    
                                    
σ²  =  
      =  
      =  
      = 
σ²  = 144
(b) 
                                    
                                    = 12 
   
 
        
             
        
        
        
Answer:
44
Step-by-step explanation:
6x +22 + 7x + 16 = 90
13x +38 =90
13x = 52
x = 4
7 x 4 +16 = 44
 
        
             
        
        
        
Let x = the number of penguins we are finding
x ÷ 100 × 30 = 15
x = 15 ÷ 30 × 100
x = 50
hope this helps and have a great day :)
        
                    
             
        
        
        
For example:
x+2y=7
6x+7y=2
__________
x=7-2y *
6*(7-2y)+7y=2 **
__________
x=7-2y
42-12y+7y=2
__________
x=7-2y
-5y=-40
__________
x=7-2y
y=8
x=-9
        
             
        
        
        
Answer:
Step-by-step explanation:
Hello, please consider the following.

So this is divisible by 3.
Now, to prove that this is divisible by 9 = 3*3 we need to prove that
 is divisible by 3. We will prove it by induction.
 is divisible by 3. We will prove it by induction.
Step 1 - for n = 1
4+17=21= 3*7 this is true
Step 2 - we assume this is true for k so  is divisible by 3
 is divisible by 3
and we check what happens for k+1

 is divisible by 3 and
 is divisible by 3 and
 is divisible by 3, by induction hypothesis
 is divisible by 3, by induction hypothesis
So, the sum is divisible by 3.
Step 3 - Conclusion
We just prove that  is divisible by 3 for all positive integers n.
 is divisible by 3 for all positive integers n.
Thanks