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Salsk061 [2.6K]
3 years ago
10

A). Write a number less than 50 that has at least 8 factors. B.) List the number's factors.

Mathematics
1 answer:
Maru [420]3 years ago
6 0

Answer: a. Such number that is less than fifty is 48

b. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 itself.

Step-by-step explanation:

A factor of a number is a number that is capable of dividing another number without leaving any remainder behind. For example, let us consider the number, "12". The factors of 12 refer to other numbers that can divide 12 without leaving any remainder.

Factors of 12 include: 1, 2, 3, 4, 6 and 12 itself. Therefore the number "12" has six factors.

Now, we were asked to write a number that is less than the number "50" and which also has at least 8 factors.

a. One of such numbers that is less than fifty and has at least eight factors is the number, "48".

b. The factors of "48" include:- 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 itself. So, 48 is less than fifty and it has a total of ten factors.

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Samuel orders four DVDs from an online music store. Each DVD costs $10.00. He has a 20% discount code, and sale tax is 6.75%. Wh
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Step-by-step explanation:

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Answer:

0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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}}

Proportion of 0.6

This means that p = 0.6

Sample of 46

This means that n = 46

Mean and standard deviation:

\mu = p = 0.6

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6*0.4}{46}} = 0.0722

Probability of obtaining a sample proportion less than 0.5.

p-value of Z when X = 0.5. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.5 - 0.6}{0.0722}

Z = -1.38

Z = -1.38 has a p-value of 0.0838

0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.

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Answer:

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