Answer:
The proposition is true.
Step-by-step explanation:
Now we proceed to demostrate that expression given is true by algebraic means:
1) 
Given
2) 
3) 
Distributive property/
4) 
Commutative, associative and modulative properties/Existence of additive inverse/
5) ![[(x\cdot y)^{-1}]^{-1}\cdot (x^{-2}+y^{-2})](https://tex.z-dn.net/?f=%5B%28x%5Ccdot%20y%29%5E%7B-1%7D%5D%5E%7B-1%7D%5Ccdot%20%28x%5E%7B-2%7D%2By%5E%7B-2%7D%29)
Commutative property/Definition of division
6) 
7) 
Distributive property/Associative property/
8) 
Modulative property/Existence of additive inverse/
9) 
Distributive property
10) 
11) 
Commutative property/Definition of division/Result
Answer:
B) 4
Step-by-step explanation:
We can solve this by observing some pattern.
The powers ending in 4 as unit digit are:
The exponents form the sequence:
2,6,10,14,20,...
We need to check if 62 belongs to this sequence.
This is an arithmetic sequence with a common difference of 4 and a first term of 2.
The explicit formula is
We equate this to 62 and solve for n.
Since n is a natural number, 62 belongs to the sequence.
Hence
will have a unit digit of 4.
If there are x boys, there are 2x girls. boys+girls=27 gives x+2x=27. Solving, 3x=27 or x=9. Since there are 2x girls, there are 2*9=19 girls.
