I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
Check the picture below.
so, a cone, that fits inside the cylinder, will have the same height "h" and radius "r". Thus
Answer:
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1. You have that two sides of a triangle have lengths of 6 and 13. Then, by the <span>Triangle Inequality Theorem, you have:
a+b>c
a+c>b
b+c>a
3. Therefore, you have:
a=6
b=13
c<a+b
c<6+13
c<19
4. The difference between a and b should be lesser that c. Then
a-b<c
13-6<c
7<c
5. Therefore:
c=x
7<x<19
The correct answer is the option B: </span>
B. 7<x<19<span>
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