Graph the System $121 x ^ { 2 } + 225 y ^ { 2 } = 27,225$

question 18

Multiple Choice

Graph the system.
-A bridge has an arch in the shape of half an ellipse. If the equation of the ellipse, measured in feet, is $121 x ^ { 2 } + 225 y ^ { 2 } = 27,225$ , find the height of the arch from the road and the width of the arch.

• A) height: \(11 \mathrm { ft }\); width: \(30 \mathrm { ft }\)
• B) height: \(11 \mathrm { ft }\); width: \(15 \mathrm { ft }\)
• C) height: \(15 \mathrm { ft }\); width: \(22 \mathrm { ft }\)
• D) height: \(22 \mathrm { ft }\); width: \(30 \mathrm { ft }\)

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Definitions:

Standard Deviation

An indicator of the degree of variability or spread within a dataset, reflecting the extent to which the data points diverge from the average value.

Variance

An index of variability in a set of data, established by taking the average squared deviation from the mean.

Tchebysheff's Theorem

A theorem that states for any real numbers k > 1, at least (1-1/k^2) of the data values fall within k standard deviations of the mean for any distribution.

Empirical Rule

A statistical rule stating that for a normally distributed dataset, about 68% of values fall within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.