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4 years ago

What is the domain of validity for csc theta = 1 / sin theta?

1 answer:

4 0

$De finition\ of\ csc\theta=\frac{1}{sin\theta}\\-----------------------\\therefore\ csc\theta=\frac{1}{sin\theta}\to\frac{1}{sin\theta}=\frac{1}{sin\theta}\\\\the\ denominator\ must\ be\ different\ from\ zero,\ therefore\\\\sin\theta\neq0\iff\theta\neq k\pi\ where\ k\in\mathbb{Z}\\\\Answer:\boxed{D}$

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2. The cone has a radius of 30 mm and slant height of 34 mm. What is the height h for this cone?

Flura [38]

Answer:

h = 16

Step-by-step explanation:

By applying the Pythagorean Theorem, the slant height is given by the formula:

$\sqrt{r^2+h^2}$

34 = $\sqrt{30^2 + h^2}$

$34^2 = 30^2 + h^2$

$1156 = 900 + h^2$

$256 = h^2$

$h = \sqrt{256}$

$h = 16$

6 0

3 years ago

In a study of 775 randomly selected medical malpracticelawsuits, it was found that 502 of them were dropped or dismissed. Use a

bulgar [2K]

By using a 0.05 significance level, we can conclude that there is sufficient evidence that most medical malpractice lawsuits are dropped or dismissed.

<h3>How to test the claim for the medical malpractice lawsuits?</h3>

Since we have to compare whether the sample proportion is greater than or lesser than the population proportion, a one-tailed test would be used. Also, we would calculate the sample proportion of medical malpractice lawsuits that are dropped or dismissed as follows:

Sample proportion, p = x/n

Sample proportion, p = 502/775

Sample proportion, p = 0.6477

Mathematically, the null and alternative hypothesis is given by:

H₀: p = 0.5

H₁: p > 0.5

For the test statistic can be calculated by using this mathematical expression:

$z=\frac{\hat{p}\;-\;p_o}{\sqrt{\frac{p_o(1-p_o)}{n }} }$

Where:

$\hat{p}$ represents the sample mean.
$p_o$ represents the mean.
n represents the number of subjects.

Substituting the given parameters into the formula, we have;

z = (0.6477 - 0.5)/√(0.5(1 - 0.5)/775)

z = 0.1477/√(0.25/775)

z = 0.1477/0.01796

z = 8.224.

For the p-value, we have:

p(z>8.224) = 0.0000

Therefore, the p-value (0.000) is less than the significance level α = 0.05. Based on this, we would reject the null hypothesis.

Read more on malpractice lawsuits here: brainly.com/question/13032617

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5 0

1 year ago

What equation best represents the following sentence?

nikdorinn [45]

Answer: n + 2 = 2n

Step-by-step explanation:

sum = add

number and two = n, 2

twice the number = 2 x n

4 0

3 years ago

Use the drop-down menus to complete each statement about the functions f and g

andre [41]

Answer:24

Step-by-step explanation:Exponential functions are of the form f(x) = ab^x

8 0

3 years ago

Read 2 more answers

Which of the following are important properties of the arithmetic mean? Check all that apply. Multiple select question. The mean

vovikov84 [41]

Answer:

All of the values in the data are used in calculating the mean.

The sum of the deviations is zero.

There is only one mean for a set of data.

Step-by-step explanation:

Required

True statement about arithmetic mean

(a) False

The mean can be equal to, greater than or less than the median

(b) True

The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.

(c) True

All mean literally represent the distance of each value from the average; so, when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e. $\sum(x - \bar x) = 0$

(d) True

The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.

(e) False

Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.

3 0

3 years ago