You should DM him...
Mrs. Read uses \(3^3 \pi {4 \over 3} = 36 \pi\) inches of yarn per mitten.
The bigger ball has a volume of \(9^3 \pi {4 \over 3} = 972 \pi\) inches of yarn per mitten.
Thus, she can make a total of \({972 \pi \over 36 \pi} = \color{brown}\boxed{27}\) mittens.
I personally disagree, but I fixed it.
Thanks, Guest!
The prime factorization of 300 is \(2 \times 2 \times 3 \times 5 \times 5\).
There are \({5! \over 2! 2!} = \color{brown}\boxed{30}\) ways to order these.
You need \({n \choose 3} \ge 365\)
The smallest number that satisfies this is \(\color{brown}\boxed{15}\)
Let's count them: 8-8-14, 9-9-12, 10-10-10 11-11-8, 12-12-6, 13-13-4, 14-14-2
In total there are \(\color{brown}\boxed{7}\)
Let point E be the midpoint of CD.
Now, \(DE = EC =10\).
We know that \(AB = OE = 12\)
Applying the Pythagorean Theorem to \(\triangle OEC\), we find the hypotenuse, or in this case, the radius to be \(\color{brown}\boxed{2 \sqrt{61}}\)
This question has already been answered on StackExchange. It's a pretty neat solution imo.
Link: https://math.stackexchange.com/questions/1463896/for-1-leq-n-leq-100-how-many-integers-are-there-such-that-fracnn1-is-a
Rational numbers can also be negative. For example, -2/5 is a rational number, because it is expressed as the ratio of -2 to 5.
It's up to interpretation. The problem isn't specific on what exactly it's asking for. You could interpret it as Chris did, with exactly one 1 and exactly one 2, or you could interpret it the way you did, where you need at least one 2.
