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 standard issue license plates that can be produced if there are no restrictions on the letters and numbers = 175760000
Step-by-step explanation:
If there are no restrictions, all numbers and letters are available to be used then. And with no restrictions, every number or letter can appear more than once.
There are 7 spaces available; 3 spaces for letters, 4 spaces for numbers
The different combination of letters and numbers then becomes,
26 × 26 × 26 × 10 × 10 × 10 × 10
This is because, all 26 letters (A to Z) can occupy the first space, the second space and the third space. And all 10 digits (0 to 9) can occupy the fourth space, the fifth space, the sixth space and the seventh space.
So, the standard issue license plates that can be produced if there are no restrictions on the letters and numbers = 26 × 26 × 26 × 10 × 10 × 10 × 10 = 175760000 different standard issue license plates.
Answer:
Total surface area of the rectangular prism is 150.88 cm^2
Step-by-step explanation:
area of base = area of top
area of base = 5 x 3.1 = 15.5 cm^2
Area of small lateral surface having dimensions 3.1 cm x 7.4 cm is
=3.1 x 7.4 = 22.94 cm^2
Area of big lateral surface having dimensions 5 cm x 7.4 cm is
=5 x 7.4 = 37 cm^2
Total area of prism = 2 x 15.5 + 2 x 22.94 + 2 x 37 = 150.88 cm^2
total surface area of the rectangular prism is 150.88 cm^2
Answer:
the location of Y is 9.5
Step-by-step explanation:
-7+26 = 19
19/2 = 9.5
Step-by-step explanation:
I think it 1,180 yeah I think it is
