A Railroad Tunnel Is Shaped Like a Semi-Ellipse $\frac { x ^ { 2 } } { 300 } + \frac { y ^ { 2 } } { 100 } = 1$

question 185

Multiple Choice

A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 20 ft and the vertical clearance must be 10 ft at a point 15 ft from the center. Find an equation for the ellipse.

• A) \(\frac { x ^ { 2 } } { 300 } + \frac { y ^ { 2 } } { 100 } = 1\)
• B) \(\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 400 } = 1\)
• C) \(\frac { x ^ { 2 } } { 300 } + \frac { y ^ { 2 } } { 400 } = 1\)
• D) \(\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 300 } = 1\)

Identify and explain key theories and theorists of social change, including cyclical and technological perspectives.

Understand the concept of social change and its impacts on social interactions and institutions.

Describe and compare the features of population structures in different types of societies.

Explain the Malthusian theory of population growth and its criticisms.

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Definitions:

Test Statistic

A calculated value used in a statistical test to decide whether to support or reject the null hypothesis.

One-sample T Test

A statistical test used to compare the mean of a single sample to a known mean or expected value, to see if there is a significant difference.

Normal Population

A population with a distribution that follows the normal (Gaussian) curve, where most measurements are centered around the mean.

Sample Mean

The average value calculated from a sample of data, often used as an estimate of the population mean.