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2 years ago

Determine whether or not each of the following is a partition of set N of natural numbers. (With reason)

Mathematics

1 answer:

polet [3.4K]2 years ago

6 0

Only Set B is a partition of set N of natural numbers .

<h3>What are Natural Numbers ?</h3>

Numbers starting from 1 to infinity comes under Natural Numbers.

It is asked in the question that to determine whether or not each of the following is a partition of set N of natural numbers

A ) {{n | n > 5}, {n | n < 5}]

It is not a set of natural numbers as it does not include 5.

B ) [{n | n ≥ 6}, {1, 3,5} , {2, 4}]

{1,3,5} {2,4}and {n|n≥6} include all the natural numbers

Therefore , it forms a partition of N.

C ) {{n | n^2 > 11}, {n | n^2 < 11}

Every natural number n must satisfy either n^2 > 11 or n^2 < 11

This cannot be possible , therefore it is not the partition of Natural Numbers.

To know more about Natural Numbers

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A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40

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Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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.

a. How large was the sample used in this survey?

We have that $s = 25, \sigma = 400$ . We want to find n, so:

$s = \frac{\sigma}{\sqrt{n}}$

$25 = \frac{400}{\sqrt{n}}$

$25\sqrt{n} = 400$

$\sqrt{n} = \frac{400}{25}$

$\sqrt{n} = 16$

$(\sqrt{n})^2 = 16^2[tex][tex]n = 256$

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

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3 years ago

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Step-by-step explanation:

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2 years ago

Which statement explains how the lines 2x + y = 4 and y = one halfx + 4 are related?

KatRina [158]

Answer:

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Step-by-step explanation:

To solve this problem .

we will convert the equations in slope intercept form.

Slope intercept form of equation is y = mx+c

where m is slope of line and c is y intercept.

________________________________

equation 1 is

2x+y = 4

=> y =4 - 2x or y = -2x + 4

comparing it with y = mx + c

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_________________________________________

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so equation is

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Now lets evaluate options

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But here slope are different -2 and 1/2 .

Thus lines are not parallel.

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They are perpendicular. correct option

For lines to be perpendicular, product of slope should be equal to -1.

-2*1/2 = -1

we can see that product of slope should be equal to -1 .

Thus lines are perpendicular

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They are the same line. wrong option

For lines to be same both slope and y intercept should be same.

Y intercept is same but the slopes are different -2 and 1/2 .

Thus lines are not the same line.

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They are not related. wrong option

As we have found that the lines are perpendicular .

So this option is intuitively wrong

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3 years ago