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2 years ago

The sine of the complimentary angle to 75° a. 0.65 c. 0.34 b. 0.57 d. 0.26

Mathematics

2 answers:

netineya [11]2 years ago

7 0

The complementary angle to 75 degrees is 25 degrees.
The sine of 15 degrees is .2588
LETTER D

emmainna [20.7K]2 years ago

3 0

Answer:

d. 0.26

Step-by-step explanation:

We are asked to find the value of the The sine of the complimentary angle to 75°.

Since we know that complementary angles add up-to 90 degrees, so let us find the measure of complementary angle of 75° angle by subtracting 75° from 90°.

$\text{Measure of complementary angle}=90^o-75^0$

$\text{Measure of complementary angle}=15^0$

Now let us find the sine of 15 degree angle. Using a calculator we will get,

$sin(15^o)=0.258819045103$

Upon rounding our answer to nearest hundredth we will get,

$sin(15^o)\approx 0.26$

Therefore, the sine of complementary angle to 75° is 0.26 and option 'd' is the correct choice.

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2) n=298

3) n=426

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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The population proportion have the following distribution

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Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

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The margin of error for the proportion interval is given by this formula:

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And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

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And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

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$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

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And rounded up we have that n=426

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