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:
60 students
Step-by-step explanation:
The confidence interval of a proportion is given by:
Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.
If the confidence interval is from 0.584 to 0.816, then:
60 students were in the sample.
To get 1/10 -> 1000/10 =100
and 1% of 100 -> 100/100 = 1 or 1%
100 for question 1
1 for q2
The answer is
A. No, because 1 x-value corresponds to 2 different y-values
Answer:
The least number of hours that she would have to work is 11.
Step-by-step explanation:
First, make the equation be "12.75x +100=235". Then, subtract 10 from both sides of the equation. You would get
"12.75x= 135". Then, divide both sides of the equation by 12. 75x, and the equation turns out to say, "x=10.59".
