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3 years ago

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Mathematics

1 answer:

stealth61 [152]3 years ago

8 0

Answer:

See attachment showing the rise and run

Slope = 1

Step-by-step explanation:

In the diagram attached below, the rise is represented by the blue line, while the run is represented by the red line.

Rise = 4 units

Run = 4 units

It's a positive slope because the line slopes upwards from left to right

Slope = rise/run = 4/4

Slope = 1

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How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F

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a) Sample Mean = 79.4

Sample standard deviation = 30.62

b) 90% Confidence interval: (67.56 ,91.24)

Step-by-step explanation:

We are given the following in the question:

Prices for sleeping bags has an approximately normal distribution.

We are given the following sample:

35, 85, 105, 40, 100, 50, 30, 23, 100, 110, 105, 95, 105, 60, 110, 120, 95, 90, 60, 70

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1588}{20} = 79.4$

Sum of squares of differences = 1971.36 + 31.36 + 655.36 + 1552.36 + 424.36 + 864.36 + 2440.36 + 3180.96 + 424.36 + 936.36 + 655.36 + 243.36 + 655.36 + 376.36 + 936.36 + 1648.36 + 243.36 + 112.36 + 376.36 + 88.36 = 17816.8

$S.D = \sqrt{\displaystyle\frac{17816.8}{19}} = 30.62$

b) 90% Confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at degree of freedom 19 and}~\alpha_{0.10} = \pm 1.7291$

$79.4 \pm 1.73(\displaystyle\frac{ 30.62}{\sqrt{20}} ) = 79.4 \pm 11.84 = (67.56 ,91.24)$

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3 years ago