Need the answers to 38-41
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Slope intercept form of a line perpendicular to 3x + y = -8, and passing through (-3,1) is
<u>Solution:</u>
Need to write equation of line perpendicular to 3x+y = -8 and passes through the point (-3,1).
Generic slope intercept form of a line is given by y = mx + c
where m = slope of the line.
Let's first find slope intercept form of 3x + y = -8
3x + y = -8
=> y = -3x - 8
On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c , we can say that for line 3x + y = -8 , slope m = -3
And as the line passing through (-3,1) and is perpendicular to 3x + y = -8, product of slopes of two line will be -1 as lies are perpendicular.
Let required slope = x
So we need to find the equation of a line whose slope is and passing through (-3,1)
Equation of line passing through and having lope of m is given by
Substituting the values we get,
Hence the required equation of line is found using slope intercept form
1) Mean of the set of data: 29.88
2) Mean absolute deviation: 10.13
3) See explanation
Step-by-step explanation:
1)
The mean of a set of data it is calculated as
where
N is the number of data in the set
is the value of each point in the dataset
For the set of data in this problem, we have:
And the number of values is
N = 8
Therefore, we can calculate the mean:
2)
The mean absolute deviation of a set of data is given by
where
N is the number of values in the dataset
are the single values
is the mean of the dataset
The dataset here is
The mean, calculated in part 1), is
And
N = 8
Therefore the mean absolute deviation is
3)
The mean of a dataset is the sum of the single values of the dataset divided by the number of values. The mean represents the value for which, if the dataset would have N values all equal to
, the sum of the values of the dataset would be the same as the sum of the actual values.
The mean absolute deviation for a set of data represents the average of the absolute deviations of the single points from the mean of the dataset. This quantity gives a measure of the "dispersion" of the points around the mean: in fact, the larger the mean absolute deviation is, the more the points are "spread" around the mean of the dataset. Instead, if the mean absolute deviation is small, it means that the points are closer to the mean value.
Learn more about mean and spread of a distribution:
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