The correct answers for this question would be A), B), and C) or the first, second, and third options.
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:
6:12
Step-by-step explanation:
Add 1+2=3
18/3=6
6x1=6
6x2=12
Out it back in the ratio
6:12
Answer:
V = 71944000pi
Step-by-step explanation:
V = 226,018,741.869864
The approximate volume of this cylindrical sub is 226,018,741.869864 cubic meters
Correct answer is Option A: 18/48 = 21/56
You’ll have to divide the numerator by the denominator of each fraction to see whether they have the same quotient:
18/48 = 0.375
21/56 = 0.375
The other options are not proportional.
B) 20/28 = 15/18:
20/28 = 0.714
15/18 = 0.833
Thus, 20/28 ≠ 15/18
C). 3/5 = 13/10
3/5 = 0.6
13/10 = 1.3
Hence, 3/5 ≠ 13/10
D) 7/10 = 10/7
7/10 = 0.7
10/7 = 1.43
Thus, 7/10 ≠ 10/7
These solutions prove that the correct answer is A) 18/48 = 21/56
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