Given:
The vertices of a triangle are R(3, 7), S(-5, -2), and T(3, -5).
To find:
The vertices of the triangle after a reflection over x = -3 and plot the triangle and its image on the graph.
Solution:
If a figure reflected across the line x=a, then
The triangle after a reflection over x = -3. So, the rule of reflection is
The vertices of triangle after reflection are
Similarly,
And,
Therefore, the vertices of triangle after reflection over x=-3 are R'(-9,7), S'(-1,-2) and T'(-3,-5).
Answer:
Where the mean and
the deviation
Since the distribution for X is normal then we can conclude that the distribution for the sample mean is given by:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where the mean and
the deviation
Since the distribution for X is normal then we can conclude that the distribution for the sample mean is given by: