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Goryan [66]
3 years ago
5

Identify the values of the variables. Give your answers in simplest radical form. PLEASE HELP!!

Mathematics
1 answer:
Talja [164]3 years ago
3 0

First question:

By definition of sine and cosine, we have

\sin30^\circ=\dfrac h{\sqrt5}\implies h=\dfrac{\sqrt5}2

\cos30^\circ=\dfrac g{\sqrt5}\implies g=\dfrac{\sqrt{15}}2

Second question:

By definition of tangent, we have

\tan60^\circ=\dfrac{5\sqrt2}x\implies x=\dfrac{5\sqrt2}{\sqrt3}=\dfrac{5\sqrt6}3

Then by Pythagoras' theorem,

(5\sqrt2)^2+x^2=y^2\implies y=\sqrt{(5\sqrt2)^2+\left(\dfrac{5\sqrt6}3\right)^2}=\sqrt{50+\dfrac{50}3}=\sqrt{\dfrac{200}3}=\dfrac{10\sqrt6}3

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18 out of 24 of Emils CDs are country music 5 out of 8 of Imanis CDs are country music. Which is a true statement A Half of each
photoshop1234 [79]
Answer:
The third choice is the correct one : Emily has a greater fraction of country music than Imani.

Explanation:
For Emily:
18 out of 24 of the CDs are country music.
This means that the ratio is 3/4 which greater then 1/2

For Imani:
5 out of 8 of the CDs are country music
This means that the ratio is 5/8 which is also greater than 1/2

Now, let's check the choices:
First choice:
<span>Half of each CD collection consists of country music.
</span>This choice is wrong as we have noted that the ratio for both is greater than 1/2

Second choice:
<span>less than half of each CD collection consists of country music.
</span>This choice is wrong as we have noted that the ratio for both is greater than 1/2

Third choice:
<span>Emily has a greater fraction of country music than Imani.
</span>Emily - Imani = 3/4 - 5/8 = 1/8
This means that Emily has more country music than Imani
Therefore, this choice is correct

Fourth choice:
<span>Imani has greater fraction of country music than Emil.
</span>This choice is wrong as we have noted in the third option that Emily has a larger fraction.

Based on the above:
The third choice is the correct one.

Hope this helps :)
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3 years ago
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