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Gekata [30.6K]
3 years ago
6

Abby said that 22.47 ÷ 2.1 equals 0.107.  Is Abby's answer reasonable?   A. Yes, Abby's answer is reasonable.   B. No, Abby's an

swer should be closer to 1.1.   C. No, Abby's answer should be closer to 11.   D. No, Abby's answer should be 110.
Mathematics
1 answer:
wolverine [178]3 years ago
8 0
I would say it is reasonable because none of the other answers are close. the correct answer is should be 10.7...
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a) 1/2

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Step-by-step explanation:

The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for p such that 1000p(1-p) is maximized. Once we have that p, we can easily find the answer to part b.

Finding the value that maximizes 1000p(1-p) is the same as finding the value that maximizes p(1-p), just on a smaller scale. So, we really want to maximize p(1-p). To do this, we will do a trick called completing the square.

p(1-p)=p-p^2=-p^2+p=-(p^2-p)=-(p^2-p+1/4)-(-1/4)=-(p-1/2)^2+1/4.

Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of p such that the inner part of the square term is equal to 0.

p-1/2=0\\p=1/2.

So, the answer to part a is \boxed{1/2}.

We can then plug 1/2 into the equation for p to find the answer to part b.

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So, the answer to part b is \boxed{250}.

And we're done!

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