Answer:
Lets say that P(n) is true if n is a prime or a product of prime numbers. We want to show that P(n) is true for all n > 1.
The base case is n=2. P(2) is true because 2 is prime.
Now lets use the inductive hypothesis. Lets take a number n > 2, and we will assume that P(k) is true for any integer k such that 1 < k < n. We want to show that P(n) is true. We may assume that n is not prime, otherwise, P(n) would be trivially true. Since n is not prime, there exist positive integers a,b greater than 1 such that a*b = n. Note that 1 < a < n and 1 < b < n, thus P(a) and P(b) are true. Therefore there exists primes p1, ...., pj and pj+1, ..., pl such that
p1*p2*...*pj = a
pj+1*pj+2*...*pl = b
As a result
n = a*b = (p1*......*pj)*(pj+1*....*pl) = p1*....*pj*....pl
Since we could write n as a product of primes, then P(n) is also true. For strong induction, we conclude than P(n) is true for all integers greater than 1.
Answer:
6
Step-by-step explanation:
You have to put the number and count how many there are. Something like this.
You need to find "two-fifths of 30." Of here means multiplication:
![\begin{aligned}\dfrac{2}{5}\cdot 30 &= \dfrac{2}{5}\cdot\dfrac{30}{1}\\[0.5em] &= \dfrac{60}{5}\\[0.5em] &= 12\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cdfrac%7B2%7D%7B5%7D%5Ccdot%2030%20%26%3D%20%5Cdfrac%7B2%7D%7B5%7D%5Ccdot%5Cdfrac%7B30%7D%7B1%7D%5C%5C%5B0.5em%5D%20%26%3D%20%5Cdfrac%7B60%7D%7B5%7D%5C%5C%5B0.5em%5D%20%26%3D%2012%5Cend%7Baligned%7D)
There are 12 athletes in the club.
