Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
Answer:
20.
Given, complex number is 10+5i .
We need to find sum of the given complex number and its conjugate. The conjugate of 10+5i is 10-5i. Therefore, the sum will be 10+5i+10−5i=20.
The sample is 200 randomly selected students.
The following things should be considered:
- Let us assume the no of siblings for each student be x.
- Now for determining the mean no of siblings she choose 200 students.
So, here the sample should be 200 randomly selected students.
Therefore the other options should be incorrect.
Thus we can conclude that the sample is 200 randomly selected students.
Learn more about the sample here: brainly.com/question/13287171
Answer:
since we are not given the options, I will write down a few equations that represent the number of French bread loaves and bagels:
- a = number of loaves of French bread
- b = number of bagels
- available amount of flour = 38
2a + b ≤ 38
2a ≤ 38 - b
a ≤ (38 - b) / 2
a ≤ 19 - 0.5b
b ≤ 38 - 2a
b ≤ 2(19 - a)
Hopefully one of these equations is one of the choices given to you.
Answer:
x= 0
Step-by-step explanation:
Because it scale factor
