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Aleks04 [339]
3 years ago
10

Rational numbers are _____ natural numbers.

Mathematics
2 answers:
zhannawk [14.2K]3 years ago
4 0
Rational numbers are sometimes natural numbers.
Harrizon [31]3 years ago
4 0

Answer:

sometimessssssss

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It's a reflection over the y-axis

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Which function is graphed below?
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Evaluate 3|-4|<br> 12<br> 4<br> -12
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12

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3 years ago
HELP ASAP!!! Alex bought a notebook containing 96 pages, and numbered them from 1 through 192. Bob tore out 25 pages of Alex’s n
zubka84 [21]
<h3>Answer: No it is not possible</h3>

=====================================================

Explanation:

Page 1 is labeled with 1 and 2, which sum to 1+2 = 3

Page 2 is labeled with 3 and 4 which sum to 3+4 = 7

Page 3 is labeled with 5 and 6 which sum to 5+6 = 11

and so on until we reach

Page 96 is labeled with 191 and 192, which sum to 191+192 = 383

Note how each page has an odd page number label and an even number label (odd on the front side; even on the back side). Adding any odd number to an even number will result in an odd number. We can prove it as such

x = some odd number = 2m+1, m is any integer

y = some even number = 2n, n is an integer

x+y = 2m+1+2n = 2(m+n)+1 = some other odd integer because it is in the form 2p+1 with p = m+n as an integer

This explains why the results 3,7,11,..,383 are all odd.

------------------------

So we effectively have this set of values {3,7,11,...,383}. This is an arithmetic sequence with 3 as the first term and 4 as the common difference.

If we add two odd numbers together, we get an even number (proof is similar to one shown above)

odd + odd = even

But if we add in another odd number, then we'll go back to an odd result

odd + odd + odd = odd

If we have an odd number of odd numbers added up, then the result will be odd. In this case, we're adding 25 values from the set {3,7,11,...,383}. The value 25 is odd, so we have an odd number of values from  {3,7,11,...,383} being added up. Therefore, the result Bob will get will always be odd. There is no way to get a sum of 2012 because this value is even.

3 0
3 years ago
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