Answer:
<h2>x=12</h2>
Step-by-step explanation:
according to the question
the equation is
Answer:
A and B are not independent events because P(A|B)≠P(A)
is the correct answer.
Step-by-step explanation:
If A and B are independent then we must have
P(AB) = P(A) P(B) and also
P(A/B) = P(A)
We are given that
A and B are two events.
Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .
P(A/B) = P(AB)/P(B) = 0.15/0.5 = 0.3
i.e. P(A/B) is not equal P(A)
Similarly P(B/A) = P(AB)/P(A) = 0.15/0.25 = 0.6 not equal to P(B)
Hence A and B are not independent.
First you solve for X then substitute the number you got for X and then solve for Y.
X= # gallons of pure water that should be evaporated
The total amount of salt must be equal before and after evaporation.
STEP 1
BEFORE EVAPORATION: multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% * 160 gallonsconvert 12% to decimal form (12% ÷ 100)
= 0.12 * 60
STEP 2
AFTER EVAPORATION: subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation
= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)
STEP 3
Set the before & after evaporation equations equal to one another to solve for x.
0.12 * 160= 0.20(160 - x)multiply 0.20 by each term in parentheses
19.2= (0.20 * 160) + (0.20 * -x)multiply in parentheses
19.2 = 32 - 0.20xsubtract 32 from both sides
-12.8= -0.20xdivide both sides by -0.20
64 gallons= x
CHECK:substitute x= 64 into the step 3 equation
0.12 * 160= 0.20(160 - x)19.2= 0.20(160 - 64)subtract in parentheses19.2= 0.20(96)19.2= 19.2
ANSWER: 64 gallons of pure water should be evaporated.
Hope this helps! :)