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:
Based on what I can see, the answer is sixteenths.
Step-by-step explanation:
If you count every tick on the line, you can get the number sixteenths. Hope this helped :)
Answer:
Step-by-step explanation:
3 coins make for 8 possible outcomes {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
4 Possible outcomes conatin 2 or more heads.
Probability (At least 2 Heads) = Favourable outcomes/Total possible outcomes
= 4/8 = 1/2 = 0.5 (50%)
I believe the answer is 2, the 3 large circles are filled with 5 dots each, the total number of dots is 17. 15 is the number closest to 17 that can be divided by 3 therefore there would be 2 left over (the 2 dots on the outside)
