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:
The total number of figurines Janet has = 29
Step-by-step explanation:
Let the number of figurines Janet has = m
So, the Number of figurines marge has
= 3 x (Number of figurines Janet has)
or, Marge has 3 x m figurines.
Also, We are given that Marge has 87 figurines.
⇒ 3 x m = 87
or, 
or, m = 29
Hence, the total number of figurines Janet has = m = 29
Line 5 because line AB≈DF not DE
The range of years would be 493 to 745.
According to the empirical rule, 99.7% of data will fall within 3 standard deviations from the mean. Using this information, we have
619+3(42) and 619-3(42)
619+126 and 619-126
745 and 493
Answer:
-8
Step-by-step explanation:
(-32)^(3/5) is equivalent to (-2^5)^(3/5) and applying exponent rules then simplifying you can get your answer.
