The answer is D. The ones on the left are the domain. The ones on the right which the arrows point to are the range
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>=0
Step-by-step explanation:
From the equation, we can see that x must be greater or equal to 0. This is true because every answer to an absolute value is positive or equal to 0. That is your answer.
Answer:
-4/5.
Step-by-step explanation:
The 2 marked points are (-3, 2) and (2, -2)
So the slope = (-2-2)/(2- -3)
= -4/5.
Answer:
<u>The correct answer is 5/24 or 0.21</u>
Step-by-step explanation:
1. Let's review all the information given to answer the question correctly:
Science class in seventh grade = 4 girls and 4 boys
Science class in eighth grade = 5 girls and 7 boys
2. What is the probability that both students selected for the competition are girls, a seventh grader and an eighth grader?
These are independent events, therefore:
Probability of two independent events = Probability of A * Probability of B
Probability of both students selected for the competition are girls = 4/8 * 5/12
Probability of both students selected for the competition are girls = 20/96 = 5/24
<u>The correct answer is 5/24 or 0.21</u>