The set of data 6, 2, 2, 2 will have the least dispersion from its mean.
<h3 /><h3>What will be the mean?</h3>From four sets of data, we take the mean of 6,2,2,2
So the mean will be
So the mean of the data (6,2,2,2) is 3 which has the least dispersion from its every data as compared to the other data
Thus the set of data 6, 2, 2, 2 will have the least dispersion from their mean.
<h3 />To know more about mean follow
The linear equation is y = 4x - 4
And the graph of the linear equation can be seen in the image below.
<h3>How to graph the last line?</h3>
It seems that you already are good at graphing, so I will try to explain how to find the equation more in detail.
Remember that a general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
In this case, we know that the y-intercept is -4, then b = -4, replacing that we get:
y = a*x - 4
Now we also can see that this line passes through the point (2, 4), this means that if we evaluate in x = 2, the outcome should be y = 4, replacing that we get:
4 = a*2 - 4
4 + 4 = a*2
8 = a*2
8/2 = a = 4
Then the slope is 4, and the linear equation is:
y = 4x - 4
The graph is below.
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The partial fraction decomposition is
The fraction is given as:
Split the fraction as follows:
Take the LCM
Cancel the common factors
8x + 19 = Ax - A + Bx + 8B
By comparison, we have:
Ax + Bx = 8x
-A + 8B = 19
This gives
A + B = 8
-A + 8B = 19
Add both equations
9B = 27
Divide by 9
B = 3
Substitute B = 3 in A + B = 8
A + 3 = 8
Solve for A
A = 5
So, we have:
Hence, the partial fraction decomposition is
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