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:
1/4
Step-by-step explanation:
625^x = 5
x = 1/4
Mercury: 87 24/25
Venus 224 7/10
Mars 686 49/50
All we need to do is to convert fractions so they have a denominator of 10, 100, 1000 etc.
87 24/25 = 87 96/100
224 7/10 stays the same
686 49/50 = 686 98/100
Now we can easily convert them into decimals:
Mercury: 87.96
Venus: 224.7
<span>Mars: 686.98</span>
Answer: did you get the answer??????
Step-by-step explanation:
Answer:
galaxies.
Step-by-step explanation:
There are about 
stars in the universe.
The Milky Way galaxy
stars.
All we need to do to find the number of galaxies is to divide the total number of stars in the universe by the number of stars in the Milky Way:
Number of galaxies = (Number of stars in the universe) / (Number of stars in the Milky Way)
Number of galaxies = 
N = 
N = 
The number of galaxies in the universe is approximately .
