(1/3) of (14-1/3) = (1/3) x (43/3) = (43/9) = about <em>(4 and 7/9) gallons</em>.
Answer:
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<span>Standard deviation of first data set = 5879.1
Standard deviation of second data set = 14768.78
The second data set is more variable.
The basic definition of standard deviation is the square root of the mean of the squares of the difference from the mean. It's a bit of a mouthful, but easy enough to do. For the first data set, first calculate the mean.
(28995 + 37534 + 31361 + 27087 + 20966 + 37741) / 6 = 30614
Now calculate the square of the differences from the mean
(28995 - 30614)^2 = 2621161
(37534 - 30614)^2 = 47886400
(31361 - 30614)^2 = 558009
(27087 - 30614)^2 = 12439729
(20966 - 30614)^2 = 93083904
(37741 - 30614)^2 = 50794129
And now the average of the squares
(2621161 + 47886400 + 558009 + 12439729 + 93083904 +50794129) / 6 = 34563888.67
And finally, take the square root to get the standard deviation.
sqrt(34563888.67) = 5879.1
Now for the second data set of western states. First, the mean
(72964 + 70763 + 101510 + 62161 + 66625 + 54339) / 6 = 71393.67
Now the squares of the differences
(72964 - 71393.67)^2 = 2465946.778
(70763 - 71393.67)^2 = 397740.4444
(101510 - 71393.67)^2 = 906993533.4
(62161 - 71393.67)^2 = 85242133.78
(66625 - 71393.67)^2 = 22740181.78
(54339 - 71393.67)^2 = 290861655.1
And the average of the squares is 218116865.2
Finally, the square root of the average is 14768.78
So the standard deviation of the 2nd data set is 14768.78
And since the standard deviation of the 2nd data set is larger than the standard deviation of the 1st data set, that means that the 2nd data set is more variable.</span>
Given:
y is directly proportional to x.
when 
To find:
The equation that connects y with x.
Solution:
It is given that, y is directly proportional to x. So,
...(i)
Where, k is the constant of proportionality.
We have, when . Substituting these values in (i), we get
Divide both sides by 5.
Substituting 
in (i), we get
Therefore, the required equation is .
Answer:
n = -2
Step-by-step explanation:
4n + 12 = 4
Subtract 12 from both sides.
4n = -8
Divide both sides by 4.
n = -2
