Answer: -7744.
Step-by-step explanation: ...
Chloe can buy 7 pencil boxes and have 1 dollar left
Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
Answer:
NOT PROPORTIONAL
Step-by-step explanation:
The given two fractions are: 
and 
.
Proportional fractions are those which have the same value when to reduced to the simplest form.
Consider two fractions 
and 
.
We say they are proportional if 
.
Or, if 
then we can say the fractions are proportional.
Here the fractions are: and .
LHS: 5 X 10 = 50.
RHS: 8 X 8 = 64.
Clearly they are not equal. So, we can say these two fractions are not proportional.
