Concentration = [ (mass of sugar)/(mass of solution) ] * 100
=> mass of solution = mass of sugar * 100 / concentration
1) concentration 20%
mass of sugar = 0.5 lbs
=> mass of solution = mass of sugar * 100 / concentration = 0.5 lbs * 100 / 20
mass of solution = 2,5 lbs
mass of water = mass of solution - mass of sugar = 2.5 lbs - 0.5 lbs = 2.0 lbs
Answer: she must add 2.0 lbs of water and will obtain 2.5 lbs of syrup
2) concentration 25%
Follow the same procedure.
mass of solution = 0.5 lbs * 100 / 25 =
mass of solution = 2.0 lbs
mass of water = 2.0 lbs - 0.5 lbs = 1.5lbs
Answer: she has to add 1.5 lbs of water and will obtain 2.0 lbs of syrup
3) Same procedure
mass of solution = mass of sugar * 100 / concentration = 0.5 lbs * 100 / 1.5
mass of solution = 33.33 lbs
mass of water = 33.33 lbs - 0.5 lbs = 32.83 lbs
Answer: she has to add 32.83 lbs of water and will obtain 32.83 lbs of syrup
825 miles because 495 divided by 9 is 55 so 55=1 mile and 15 miles=825
The probability that four of the five digits are the same is 0.036.
There are 10,000 (10*10*10*10) possible sequences. There are 4C3 ways, 4, of having exactly three digits be the same value. The differing digit can be any of the four positions. There are 10P2 ways, 90 (10*9), to choose the digits of the sequence since we have 10 choices for the digit to be repeated, then 9 more options or the differing digit. The product of the combination arrangements and permutation selection, 4*90, shows there are 360 sequences with three of the same digit. Thus the probability is 360/10,000 or 0.036 or 3.6%.
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