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3 years ago

Factor the expression by taking out the GCF. 3x - 9x3

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

Consider the expression $3x-9x^3.$ It consists of two terms:

$3x=3\cdot x$

and

$-9x^3=-3\cdot 3\cdot x\cdot x\cdot x.$

The common factors in these terms are $3$ and $x.$ Then

$GCF(3x,-9x^3)=3x.$

Taking out the GCF, you obtain

$3x-9x^3=3x(1-3x^2).$

Answer: correct choice is B.

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For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of sc

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Answer:

a) The percentage of bone density scores that are significantly high is 2.28%

b) The percentage of bone density scores that are significantly low is 2.28%

c) The percentage of bone density scores that are not significant is 95.44%

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

a. significantly high (or at least 2 standard deviations above the mean).

This is 1 subtracted by the pvalue of Z = 2.

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% of scores are signifcantly high

b. significantly low (or at least 2 standard deviations below the mean).

pvalue of Z = -2

Z = -2 has a pvalue of 0.0228

2.28% of scores are signicantly low.

c. not significant (or less than 2 standard deviations away from the mean).

pvalue of Z = 2 subtracted by the pvalue of Z = -2.

Z = 2 has a pvalue of 0.9772

Z = -2 has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

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3 years ago

Using the concepts of marginal social benefit and marginal social cost, explain how the optimal combination of goods can be dete

PtichkaEL [24]

Answer:

Optimal combination of goods can be determined in an economy that produces only two goods, with production of extra units of the two goods at a minimal marginal social cost. The consumption of the additional units of the two goods being produced will be benefitted by the consumers. This is known as marginal social benefit.

Step-by-step explanation:

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