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:
$1200
Step-by-step explanation:
3/4 of 1600 is 1200
Camel back Mountain = 15,168 inches (1,264 feet)
1 Penny = 0.061 (.0610) Inches
10 Penny = 0.61 (.610) Inches
100 Penny = 6.1 (6.10) Inches
1,000 Penny = 61 (61.0) Inches
10,000 Penny = 610 (610.0) Inches
-SOLVING-
10,000 Penny = 610 inches PLUS
1,000 Penny = 61 inches AND 61 inches x 5 = 305 (5,000 Penny)
100 Penny = 6.1 inches PLUS
10 Penny = 0.61 inches AND 0.61 inches x 6 = 3.66 (60 Penny)
1 Penny = 0.061 inches AND 0.061 inches x 8 = 0.488 (8 Penny)
-FINAL ANSWER-
610 + 305 + 6.1 + 3.66 + 0.488 = 925.248 Penny it would take.
Answer:
The solution is:

Step-by-step explanation:
The first step to solve this equation is placing everything with the logarithmicto one side of the equality, and everything without the exponential to the other side. So

It already is in the desired format.
Now, we have that, since e and ln are inverse operations

So, we apply the exponential to both sides of the equality


Answer:
$2.9
Step-by-step explanation:
<u>Given the following data;</u>
Total cost of package = $14.50
Number of package = 5
To find the cost of each package;
Substituting into the equation, we have;
Cost per package = $2.9
<em>Therefore, the cost per package of bottled water is $2.9.</em>