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.
Two angles<span> are </span>Adjacent<span> when they have a common side and a common vertex (corner point) and don't overlap</span>
240,000 = 24 x 10,000 but 10,000 = 10 x 10 x 10 x 10 = 10⁴, then:
240,000 = 24 x 10⁴
Answer: 135 pounds
Step-by-step explanation:
600-60=540
540/4=135
Income of the first account after x years:
Income of the second account after x years:
Equating the above tw values we get the equation:
Solving the above equation for x:
Answer 8 years.
