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3 years ago

Two angles in a triangle measure 1020 and 670. What is the measure of the third angle?

Mathematics

1 answer:

Brilliant_brown [7]3 years ago

3 0

Answer:

A) 11°

Step-by-step explanation:

All triangles equal 180, so:

102 + 67 + x = 180

169 + x = 180

x = 11

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Researchers at the National Cancer Institute released the results of a study that investigated the effect of weed-killing herbic

jolli1 [7]

Answer:

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.

This means that:

$p_h = \frac{230}{400} = 0.575, s_h = \sqrt{\frac{0.575*0.425}{400}} = 0.0247$

Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.

This means that:

$p_n = \frac{25}{200} = 0.125, s_n = \sqrt{\frac{0.125*0.875}{200}} = 0.0234$

Distribution of the difference:

$p = p_h - p_n = 0.575 - 0.125 = 0.45$

$s = \sqrt{s_h^2+s_n^2} = \sqrt{0.0247^2 + 0.0234^2} = 0.034$

Confidence interval:

The confidence interval is:

$p \pm zs$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower bound is $0.45 - 1.96(0.034) = 0.3834$

The upper bound is $0.45 + 1.96(0.034) = 0.5166$

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

3 0

3 years ago

The perimeter of this shape is 30 feet. what is the length of the missing side

soldier1979 [14.2K]

30/2 = 15

it could be any positive number that is smaller than 15

6 0

3 years ago

A warden meets with 23 prisoners. He tells them the following:

Sedbober [7]

The prisoners could do a pattern that could signal who has already been in the room. So for example, one light off, both lights off, one light on, both lights off. But with left and right lights to make the sequence last as long as possible. Then after that sequence to have the last one be the signal that everyone has been in there. I dunno this is tricky lol

7 0

3 years ago

Is this true the product of 3/5 + 4 is less than 3/5

galben [10]

No this is not true because 3/5 + 4 equals 4.6 and 3/5 is 0.6

7 0

3 years ago

A football is about how long?

Amanda [17]

Answer:

"Big Game's competitive footballs are the exact dimensions set down by the NCAA – approximately 10.5 to 11.5 inches in length, with a circumference of roughly 28 inches on the long side of the ball and 21 inches on the short side."

Step-by-step explanation:

Hope this helps

6 0

3 years ago