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2 years ago

What is the angle of depression from the start of a 6-foot-high access ramp that ends at a point 40 feet away along the ground?

Mathematics

1 answer:

NISA [10]2 years ago

5 0

Answer:

8.53°

Step-by-step explanation:

Observe the attached image.

The ramp forms an alpha angle triangle with an opposite side of 6 ft and an adjacent side of 40 ft.

We know that the tangent of an angle is defined as:

$tan(\alpha) = \frac{opposite\ side}{adjacent\ side}$

So:

$tan(\alpha) = \frac{6}{40}$

To clear the angle we apply the inverse of the tangent (arctangent) on both sides of the equation:

$atan(tan(\alpha)) =atan(\frac{6}{40})$

$\alpha= atan(\frac{6}{40})\\\\\alpha = 8.53\°$

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Area of regular polygons

Finger [1]

Hello!

To find the area of a hexagon you do 3 $\frac{3 \sqrt{3} }{2} } a^{2}$ where a is one of the sides

Since the perimeter is 60 we can do 60/ the sides of the shape

60/6 = 10

So one side is equal to 10

you put that into the formula to get the area of a hexagon and you get 259.81

Hope this helps!

8 0

2 years ago

Assume that a simple random sample has been selected from a normally distributed population. State the hypotheses, find the test

BaLLatris [955]

Solution

Hypotheses:

- The population mean is 132. In order to test the claim that the mean is 132, we should check for if the mean is not 132.

- Thus, the Hypotheses are:

$\begin{gathered} H_0:\mu=132 \\ H_1:\mu\ne132 \end{gathered}$

Test statistic:

- The test statistic has to be a t-statistic because the sample size (n) is less than 30.

- The formula for finding the t-statistic is:

$\begin{gathered} t=\frac{\bar{X}-\mu}{\frac{s}{\sqrt{n}}} \\ \\ where, \\ \bar{X}=\text{ Sample mean} \\ \mu=\text{ Population mean} \\ s=\text{ Standard deviation} \\ n=\text{ Sample size} \end{gathered}$

- Applying the formula, we have:

$\begin{gathered} t=\frac{137-132}{\frac{14.2}{\sqrt{20}}} \\ \\ t=\frac{5}{3.1752} \\ \\ t\approx1.5747 \end{gathered}$

Critical value:

- The critical value t-critical, is gotten by reading off the t-distribution table.

- For this, we need the degrees of freedom (df) which is gotten by the formula:

$\begin{gathered} df=n-1 \\ df=20-1=19 \end{gathered}$

- And then we also use the significance level of 0.1 and the fact that it is a two-tailed test to trace out the t-critical. (Note: significance level of 0.1 implies 10% significance level)

- This is done below:

- The critical value is 1.729

P-value:

- To find the p-value, we simply check the table for where the t-statistic falls.

- The t-statistic given is 1.5747. We simply check which values this falls between in the t-distribution table. It falls between 1.328 and 1.729. We can simply choose a value between 0.1 and 0.05 and multiply the result by 2 since it is a two-tailed test.

- However, we can also use a t-distribution calculator, we have:

- Thus, the p-value is 0.13183

Final Conclusion:

- The p-value is 0.13183, and comparing this to the significance level of 0.1, we can see that 0.13183 is outside the rejection region.

- Thus, the result is not significant and we fail to reject the null hypothesis