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Answer:
Step-by-step explanation:
Given : Vertices of Triangle ,
and
To find : Centroid of a triangle
The centroid of a triangle is the point of intersection of the three medians of the triangle.
The formula to calculate the centroid of a triangle is:
Where, are the coordinates of the centroid
Substituting the values in the formula gives us:
Therefore,
Answer:
The degrees of freedom is 11.
The proportion in a t-distribution less than -1.4 is 0.095.
Step-by-step explanation:
The complete question is:
Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used. Find the proportion in a t-distribution less than -1.4 if the samples have sizes 1 = 12 and n 2 = 12 . Enter the exact answer for the degrees of freedom and round your answer for the area to three decimal places. degrees of freedom = Enter your answer; degrees of freedom proportion = Enter your answer; proportion
Solution:
The information provided is:
Compute the degrees of freedom as follows:
Thus, the degrees of freedom is 11.
Compute the proportion in a t-distribution less than -1.4 as follows:
*Use a <em>t</em>-table.
Thus, the proportion in a t-distribution less than -1.4 is 0.095.
Make a change of coordinates:
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
to 
. To do this, notice that
we need to take the reciprocal of the Jacobian above.
The integral then changes to
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
we need to take the reciprocal of the Jacobian above.
The integral then changes to