Let there be x quarts of the 20% salt solution, and (25 - x) quarts of the 80% salt solution.
Then the total amount of salt in the 20% portion would be 0.2x, while that from the 80% portion would be (0.8)(25 - x). This would have to total up to (0.44)(25) in the final solution, so the equation is:
0.2x + 0.8(25 - x) = (0.44)(25)
-0.6x + 20 = 11
x = 15 quarts of the 20% salt solution
25 - x = 10 quarts of the 80% salt solution
Sum/difference:
Let
This means that
Now, assume that 
is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
If the null hypothesis,
is rejected, then we can conclude that the correlation coefficient is significant. This means that there is enough evidence to conclude that a relationship exists between the two (or more) variables involved in the regression.
<h2>
Answer:</h2><h2>
The expected number of people who will attend this concert = 2260</h2>
Step-by-step explanation:
The concert organizers estimate people will attend if it is not raining = 19000
If its raining people will attend = 4000
On the day of the concert, meteorologists predict a 90% chance of rain.
This means 10 % chance of not raining
The expected number of people = 90% (4000) + 10% (19000)
= 360 + 1900
= 2260
The expected number of people who will attend this concert = 2260
