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:
X + 45
X + 12
1 - x
X - 13
Step-by-step explanation:
Using the keywords sum of, more than, and subtracted will help you. (You can also flip the expression since it didn't say how.
Answer:
200+60+4
Step-by-step explanation:
200+60+4=264
12. 1.625 [terminating]; 13. 0.83 [bar notation over 3 (repeating)]; 14. 900 cm = 9 m; 15. 0.23 cm = 2.3 mm
Repeating decimals are parts of decimals that have repetitive digits; terminating decimals are decimals whose digits end.
Whether you are using Metric or Imperial, you have to determine whether you are going from a small unit to a big unit or vice versa. Then perform your operation. So, in exercise 14, the smaller unit is centimeters, so you would be going from big to small. Exercise 15 has you going from small to big.
There are centimeters in one meter, so multiply 9 by to get 900 centimeters.
There are 10 millimeters in one centimeter, so divide 2.3 by 10 simply by moving the decimal point ONCE to the left [Power of 10].
small to BIG → Division
BIG to small → Multiplication
I am joyous to assist you anytime.
