175 mL at 25% concentration of alcohol contains 0.25 (175 mL) = 43.75 mL of alcohol. If <em>v</em> is the amount of the 70% solution that you use, then that amount contains 0.7<em>v</em> mL of alcohol.
Mixing these two yields a total volume of 175 mL + <em>v</em>, and it contains 43.75 mL + 0.7<em>v</em> alcohol. You want to end up with a concentration of 45%, which means the ratio of the amount of alcohol to the total volume needs to be 0.45:
(43.75 mL + 0.7<em>v</em>) / (175 mL + <em>v</em>) = 0.45
Solve for <em>v</em> :
43.75 mL + 0.7<em>v</em> = 0.45 (175 mL + <em>v</em>)
43.75 mL + 0.7<em>v</em> = 78.75 mL + 0.45<em>v</em>
0.25<em>v</em> = 35 mL
<em>v</em> = 140 mL
Answer:
It's B
Step-by-step explanation:
"Brainlypatrol" is deleting my answers. >:(
Answer:
a) 1/2
b) 250
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 such that is maximized. Once we have that , we can easily find the answer to part b.
Finding the value that maximizes is the same as finding the value that maximizes , just on a smaller scale. So, we really want to maximize . To do this, we will do a trick called completing the square.
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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 such that the inner part of the square term is equal to .
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So, the answer to part a is .
We can then plug into the equation for p to find the answer to part b.
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So, the answer to part b is .
And we're done!
-9 because 2+7=9 so the negative part oh then must be -9
Answer:
-8f
Step-by-step explanation: