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3 years ago

1.

Mathematics

1 answer:

Alecsey [184]3 years ago

8 0

Answer:

Basically we have been provided with a stem and leaf plot, and we have to find three values from it, that are:

1) Median

2) Mode

3) Range

First write all the data in in ascending order.

96 , 98 , 104 , 106 , 106 , 106 , 110 , 113 , 113 , 115 , 124 , 129

1) Median

For even number of values median is the average between 2 middle values.

96 , 98 , 104 , 106 , 106 , 106 , 110 , 113 , 113 , 115 , 124 , 129

Median =( 106+110)/2

Median = 108

2) Mode

The number that appears most

Mode = 106

3) Range

Range = max number - min number

Range = 129 - 96

Range = 33

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Which of the following is the standard equation of the ellipse with vertices at (1,0) and (27,0) and an eccentricity of 5/13?

Dovator [93]

The equation of the elipse is given by:

$\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1$

The equation of an elipse of center $(x_0, y_0)$ is given by:

$\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 0$

Values a and b are found according to the vertices and the eccentricity.

It has vertices at (1,0) and (27,0), thus:

$x_0 = \frac{27 + 1}{2} = 14$

$y_0 = \frac{0 + 0}{2} = 0$

$a = \frac{27 - 1}{2} = 13$

$a^2 = 169$

It has eccentricity of $\frac{5}{13}$ , thus:

$\frac{5}{13} = \frac{c}{a}$

$\frac{5}{13} = \frac{c}{13}$

$c = 13$

Thus, b is given according to the following equation:

$c^2 = a^2 - b^2$

$b^2 = a^2 - c^2$

$b^2 = 169 - 25$

$b = \sqrt{144}$

$b = 12$

The equation of the elipse is:

$\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1$

A similar problem is given at brainly.com/question/21405803

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