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3 years ago

Please answer this correctly

Mathematics

1 answer:

olga2289 [7]3 years ago

3 0

Answer:

3.14

Step-by-step explanation:

A quarter circle is just 1/4 of an entire circle's area. Since you know the radius is two, simply find the area of the entire circle and divide by 4.

4pi/4 = pi

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The mean number of words per minute (WPM) read by sixth graders is 8888 with a standard deviation of 1414 WPM. If 137137 sixth g

Bingel [31]

Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.

Answer:

"The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

Step-by-step explanation:

This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 $\\ n \geq 30$ . Mathematically

$\\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.

Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean $\\ \mu = 0$ and a population standard deviation $\\ \sigma = 1$ .

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

From the question, we know that

The population mean is $\\ \mu = 88$ WPM
The population standard deviation is $\\ \sigma = 14$ WPM

We also know the size of the sample for this case: $\\ n = 137$ sixth graders.

We need to estimate the probability that a sample mean being greater than $\\ \overline{X} = 89.87$ WPM in the distribution of sample means. We can use the formula [2] to find this question.

The probability that the sample mean would be greater than 89.87 WPM

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}$

$\\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}$

$\\ Z = 1.5634 \approx 1.56$

This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.

We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that $\\ P(\overline{X} < 89.87)$ . Then

$\\ P(z$

However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore

$\\ P(z>1.56) = 1 - P(z$

$\\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594$

Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

5 0

3 years ago

Please help What is the domain of the following function?

enot [183]

Answer:

Let's use these two sets given to explain what is the domain.

Each value from the left set is x, and from the right is f(x).

If we plug any x from the left set in the function, we'll get f(x) that corresponds to it and that's exactly what the arrows are showing.

Domain of the function is, basically, a set of all values x can have.

In this case, it's easy to see, those are all members of the left set (-6, 1, 5, 8), but sometimes this set can have lots and lots of members, even infinity.

8 0

3 years ago

Which of the following equations can be used to find the length of BC in the

ycow [4]

Answer:

BC² = 10² + 30²

the answer is D

4 0

3 years ago

Caitlin makes candles and sells them in her online shop. Tall candles cost $8 each and short candles cost $5 each. last month, s

snow_tiger [21]

Answer:

tall candles = 39

Short candles = 52

Step-by-step explanation:

let tall candles be x

and short candles be y

No. Of candles sold = x + y =91

Money made from candles will be equal to = 8x + 5y = $572

These both are simultaneous linear equations.

x + y =91 ( multiply by 5)

5x + 5y = 455

8x + 5y = $572

Subtract them:

-3x = -117

x = -117/3

x = 39

put value of x in

x + y = 91

39 + y = 91

y = 91 - 39

y = 52

x shows tall candles so they are 39

y shows short candles so they are 52

3 0

2 years ago

W + 4 = (-6) This is an algebra question and I don't get the negative

Arada [10]

Answer:

w = -10

Step-by-step explanation:

w + 4 = (-6)

Subtract 4 from each side

w+4-4 = -6-4

w = -10

7 0

2 years ago

Read 2 more answers