Answer:
95% Confidence interval: (96.06,103.94)
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 85
Sample mean, = 100
Sample size, n = 30
Alpha, α = 0.05
Population standard deviation, σ = 11
95% Confidence interval:
Putting the values, we get,
(96.06,103.94) is the 95% confidence interval for the population mean test score.
Answer:
Part A
The rotation of the point (x, y) 180° about the origin gives the point (-x, -y)
Therefore, we have the points, ΔLMN, L(1, 1), and M(2, 2), and N(3, 3)
The coordinates of the vertices of the image, ΔL'M'N' are L'(-1, -1), and M'(-2, -2), and N'(-3, -3)
Please find attached the graph of triangle ΔLMN and ΔL'M'N'
Part B
The lines drawn through L and L' and through M and M' are colinear
Part C
A line is defined by two points, such as <em>L </em>and <em>M.</em> Rotation of a line through 180° about the origin will give an image location on the same path as the extension of the original line.
The third point, <em>N</em>, however, defines a plane, and the rotation of a plane by 180° will give an image which is turned upside down with regards to the preimage
Therefore, a trough in the preimage becomes a peak in the image and the lines drawn through N and N' crosses the colinear lines drawn throgh M and M' and L and L'
Step-by-step explanation:
