(50 Points)

Mathematics

2 answers:

Yanka [14]3 years ago

5 0

C
If you plug in the values in that equation, it works.

Assoli18 [71]3 years ago

5 0

To find the other system, since we know already that x = 3 and y = 9, we just have to input the value of x and y in each of the equations and see if they work.

4x + 6y = 64

4 (3) + 6(9) = 64

12 + 54 = 64
66 = 64

That doesn't work, so we move on.

2x + y = 36

2 (3) + 9 = 36

6 + 9 = 36

15 = 36

Once again, we move on.

4x + y = 21

4 (3) + 9 = 21

12 + 9 = 21

21 = 21

Since we're only looking for one answer, we have found it, meaning that the answer to this question is 4x + y = 21.

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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

bezimeni [28]

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