You need a 15% acid solution for a certain test, but your supplier only ships 5% solution and 17.5% solution. If you need 20 lit
2 answers:
Answer:
4 liters of 5% and 16 liters of 17.5%
Step-by-step explanation:
Let quantity of 5% be x liters and of 17.5% be y liters
x+y=20 hence y=20-x
Introducing percentages
0.05x+0.175(20-x)=0.15*20
0.05x+3.5-0.175x=3
-0.125x=-0.5
Therefore, y=20-x=20-4=16
You need 4 liters of 5% and 16 liters of 17.5% to achieve 20 liters of 15% acid solution
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Part A
Since order matters, we use the nPr permutation formula
We use n = 12 and r = 8
There are a little under 20 million different permutations.
<h3>Answer: 19,958,400</h3>Side note: your teacher may not want you to type in the commas
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Part B
In this case, order doesn't matter. We could use the nCr combination formula like so.
We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.
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Another way we can compute the answer is to use the result from part A.
Recall that:
nCr = (nPr)/(r!)
If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320
So,
Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.
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<h3>Answer: 495</h3>