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3 years ago

5

A reflecting telescope contains a mirror shaped like a parabola of revolution. If the mirror is 16 inches across at its opening

and is 2 feet deep, where will the light be concentrated?

1 answer:

choli [55]3 years ago

5 0

Answer:

18

Step-by-step explanation:

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Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 450 elementary s

tigry1 [53]

<h2>Answer with explanation:</h2>

The confidence interval for population mean is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ is the sample proportion, n is the sample size , $z_{\alpha/2}$ is the critical z-value.

The values needed to calculate a confidence interval at the 99% confidence level are :

Given : Significance level : $\alpha:1-0.99=0.01$

Sample size : n=450

Critical value : $z_{\alpha/2}=2.576$

Sample proportion: $\hat{p}=\dfrac{280}{450}\approx0.62$

Now, the 99% confidence level will be :

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.62\pm(2.576)\sqrt{\dfrac{0.62(1-0.62)}{450}}\\\\\approx0.62\pm0.023\\\\=(0.62-0.023,\ 0.62+0.023)=(0.597,\ 0.643)$

Hence, the 99% confidence interval is $(0.597,\ 0.643)$

6 0

3 years ago

If the sequence 2, 4, 6, 10, 16, ... were to follow the same pattern as the Fibonacci sequence, what are the next three terms?

AleksandrR [38]

Answer:

10 + 16 = 26

16 + 26 = 42

26 + 42 = 68

(C) the next three terms are 26, 42, 68

8 0

3 years ago

In the middle of the page, draw a small oval oriented vertically.

Phantasy [73]

Answer – A spoon

A small oval oriented vertically would represent the bowl of the spoon, while the small rectangle oriented vertically which is connected to the bottom of the oval would represent the handle of the spoon. The point where the oval connects with the rectangle is the neck of the spoon.

3 0

4 years ago

The same couple, what is the probability that if they have three children, two will be boys and one will be a

cricket20 [7]

3/8 would be the correct answer.

8 0

3 years ago

single die is rolled twice. Find the probability of rolling an oddodd number the first time and a number greater than 33 the sec

givi [52]

Answer:

$\frac{1}{4}$

Step-by-step explanation:

A single die is rolled twice, we have to find the probability of rolling an odd number in first throw and a number greater than 3 in the second throw.

a) Rolling an Odd number in first throw

A die has total 6 possible outcomes, out of which 3 are odd numbers i.e. 1,3 and 5

So, total number of possible outcomes = 6

Total Favorable outcomes (Odd numbers) = 3

Probability is defined as the ratio of favorable outcomes to total number of outcomes. So,

The probability of rolling an odd number would be = $\frac{3}{6} = \frac{1}{2}$

b) Rolling a number greater than 3 in second throw

Here again total possible outcomes = 6

Favorable outcomes (Numbers greater than 3 are 4, 5 and 6) = 3

So,

The probability of rolling a number greater than 3 = $\frac{3}{6} = \frac{1}{2}$

These two events(rolls) are independent of each other, so the overall probability of both events occurring would be the product of individual probabilities.

So,

Probability of rolling an odd number the first time and a number greater than 3 the second time = $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

6 0

3 years ago