Not sure why such an old question is showing up on my feed...
Anyway, let
and
. Then we want to find the exact value of
.
Use the angle difference identity:
and right away we find
. By the Pythagorean theorem, we also find
. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
Meanwhile, if
, then (by Pythagorean theorem)
, so
. And from this,
.
So,
They will meet back up in 40 minutes because 8x5=40 and 10x4=40 which 40 is both a multple of 8 and 10 so you're welcome
Answer:
90 g of water should be added and he will make 900 g of solution.
Step-by-step explanation:
Let x g be the amount of salt Ilya add to 810g of water to make 10% solution. Then 810+x g is the amount of new solution. Thus,
810+x - 100%,
x - 10%.
Mathematically,
So 90 g of water should be added and he will make 810+90=900 g of solution.
Total students = 15+21=36, so the probability of choosing a girl is 21/36, which reduces to 7/12.
Total freshmen = 12+15=27, so the probability of choosing a freshman is 27/36, which reduces to 3/4.
