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Likurg_2 [28]
3 years ago
10

Find the measures of the supplementary angles of their measures are in ratio of 22:23

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
8 0

Answer:

  Measures of the supplementary angles = 88° and 92°

Explanation:

 Two angles that add to 180 degrees is called as supplementary angles.

  Angles are in the ration 22:23

  So, we have

               22a + 23a = 180

               45 a = 180

                    a = 4

      Angles are 22 x 4 = 88 ° and 23 x 4 = 92°

  Measures of the supplementary angles = 88° and 92°

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Bogdan [553]

Answer:

1) 80% CI: [3.04; 3.26]gr

d= 0.11

2) n= 28 hummingbirds

Step-by-step explanation:

Hello!

The study variable of this experiment is:

X: the weight of a hummingbird. (gr)

And it has a normal distribution, symbolically: X~N(μ;σ²)

And (I hope I got it correctly) its population standard deviation is σ= 0.33

There was a sample of n= 15 hummingbirds taken, its sample mean X[bar]= 3.15 gr

1) You need to construct an 80% Confidence Interval for the population mean of the hummingbird's weight.

Since the study variable has a normal distribution, you can use either the standard normal distribution or the Student's t distribution. Both are useful to estimate the population mean. Since the population standard variance is known, the best choice is the Standard normal.

Z= <u> X[bar] - μ </u>~ N(0;1)

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2) You need to calculate a sample size for a 80% Confidence interval for the average weight of the hummingbirds with a margin of error of d= 0.08

As I said before, the margin of error is half the amplitude of the interval, the formula you use to estimate the population mean has the following structure:

"point estamator" ± "margin of error"

Then the margin of error is:

d= Z_{1- \alpha /2} * (σ/√n)

Now what you have to do is rewrite the formula based on the sample size

d= Z_{1- \alpha /2} * (σ/√n)

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√n * \frac{d}{Z_{1- \alpha /2}}= σ

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n = (σ * \frac{Z_1- \alpha /2}{d})²

n=  (0.33 * \frac{1.28}{0.08})²

n= 27.8784 ≅ 28 hummingbirds.

I hope it helps!

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