Answer:
1
Step-by-step explanation:
1/(1+p+q^-1)+1/(1+q+r^-1)+1/(1+r+p^-1) = 1.
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
Answer:
3/8
Step-by-step explanation:
1/8+1/4=1/8+2/8=3/8
Median: middle number
Mean: average
How to calculate the median:
1) line the numbers in order from least to greatest
0 1 2 4 5 24
(you do not need to write all the fours or fives, one four or five is enough to represent it)
2) Next, take one number off each end at a time until you have one number in the middle left (if there are two numbers left in the middle, add them together, than divide them by two)
3) The median is 4 becuase it is in the middle.
How to calculate the mean:
1) Add all the numbers together
0+24+1+4+5+2+5+4 = 45
2) Now we divide 45 by 8 because there are eight numbers in the list
45/8 = 5
3) The mean is 5.
Answer: Median = 4, Mean = 5
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