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3 years ago

Find the mean and the median of this data set: 9, 8, 5, 3, 37, 8, 4, 2. The mean is and the median is .

Mathematics

1 answer:

tatyana61 [14]3 years ago

3 0

Answer:

The mean is 9.5 and the median is 6.5.

Step-by-step explanation:

To find the mean:

Add all numbers given.

9+8+5+3+37+8+4+2= 76

Then divide by the amount of numbers (8).

76/8= 9.5

To find the median:

Re-arrange the order of the numbers from least to greatest.

2, 3, 4, 5, 8, 8, 9, 37

Count towards the middle. If there is no exact middle (like this equation), then take the two middle numbers and add them.

5+8= 13

After, divide by two since there are two numbers being added.

13/2= 6.5

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Find sinϴ and cosϴ if tanϴ=1/4 and sinϴ>0

eduard

If you're using the app, try seeing this answer through your browser: brainly.com/question/2787701

_______________

$\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\
\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\
\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}$

Square both sides:

$\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\
\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\
\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}$

$\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\
\mathsf{17\,sin^2\,\theta=1}\\\\
\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}$

Since $\mathsf{sin\,\theta}$ is positive, you can discard the negative sign. So,

$\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}$

Substitute this value back into $\mathsf{(i)}$ to find $\mathsf{cos\,\theta:}$

$\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}$

I hope this helps. =)

Tags: trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus

7 0

2 years ago

A negatively charged balloon moves close to another balloon. They then repel each other. What can be said about the other balloo

lana66690 [7]

Answer: B: It has a negative charge.

Step-by-step explanation:

According to theory espoused by the French physicist, Charles-Augustin de Coulomb, like charges charges will repel each other and unlike charges will attract one another.

This means that objects with negative charges will repel each other. As the first balloon in the question was negatively charged, it would only repel the other balloon if it was negatively charged as well.

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3 years ago

Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the d

lesya [120]

Answer:

segment EH and segment E prime H prime both pass through the center of dilation.

Step-by-step explanation:

Center of dilation is point (0.1), same as H. Both, E(0,5) and H(0,1) are placed over y-axis, then E' and H' are also located at y-axis.

After dilation, H' is placed at (0,1) because it coincides with the center of dilation

Distance between E and center of dilation is 4 units, then E' should be at 4*3=12 units from the center of dilation and over y-axis. Therefore, E' is placed at (0, 13)

So, segment E'H' goes from (0,1) to (0,13), and pass through the center of dilation, like segment EH.

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3 years ago

Solve T= C(7+AB) for A

Tcecarenko [31]

T= C(7+AB)

T = 7C + ABC

T - 7C = ABC

(T - 7C)/BC = A

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3 years ago

What's the distance between points (2, 2) and (4.1)

Tresset [83]

Answer:

-(1/2)

Step-by-step explanation:

y1-y2/x1-x2

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2 years ago