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Mnenie [13.5K]
3 years ago
6

A salad recipe that serves 10 people requires 1 1/2 cups of celery. To serve 5 people, the amount of celery required is

Mathematics
1 answer:
Annette [7]3 years ago
8 0
Well this is a one step equation, just take 1.5 cups of salad and divide it buy 2 because you are only serving half of the people.

1.5 / 2 = .75 cups of celery
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Find the HCF of 2^120-1 and 2^100-1
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There may be more brilliant solution than the following, but here are my thoughts.

We make use of Euclid's algorithm to help us out.
Consider finding the hcf of A=2^(n+x)-1 and B=2^(n)-1.

If we repeated subtract B from A until the difference C is less than B (smaller number), the hcf between A and B is the same as the hcf between B and C.

For example, we would subtract 2^x times B from A, or
C=A-2^xB=2^(n+x)-2^x(2^n-1)=2^(n+x)-2^(n+x)+2^n-1=2^n-1
By the Euclidean algorithm, 
hcf(A,B)=hcf(B,C)=hcf(2^n-1,2^x-1)
If n is a multiple of x, then by repetition, we will end up with
hcf(A,B)=hcf(2^x-1,2^x-1)=2^x-1

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