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3 years ago

Rewrite the expression with rational exponents as a radical expression. 7 times x to the two thirds power

Mathematics

2 answers:

Daniel [21]3 years ago

6 0

Answer:

$(7x)^{\frac{2}{3}}$ = $\sqrt[3]{49x^{2} }$

Step-by-step explanation:

We have been given the expression;

7 times x to the two thirds power which can be written mathematically as;

$(7x)^{\frac{2}{3}}$

To express the above expression as a radical, we need to recall that;

$a^{\frac{b}{n}}=\sqrt[n]{a^{b}}$

Therefore;

$(7x)^{\frac{2}{3}}=\sqrt[3]{(7x)^{2} }\\\\=\sqrt[3]{49x^{2} }$

insens350 [35]3 years ago

3 0

Answer:

(7x)^{\frac{2}{3}}=\sqrt[3]{49x^{2} }

Step-by-step explanation:

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The coordinates of one endpoint of a line segment are (4, −12). The length of the segment is 5 units. Determine four coordinate

Nina [5.8K]

Answer:

Four coordinate pairs that could serve as the other endpoint of the given line segment are given by: (9,-12), (-1,-12), (4,-7), (4,-17).

Step-by-step explanation:

One endpoint of (4,-12), length of 5 units.

Four possible pairs:

Add 5 to x, keep y: (4+5,-12) = (9,-12).

Subtract 5 from x, keep y: (4-5,-12) = (-1,-12).

Keep x, add 5 to y: (4,-12+5) = (4,-7)

Keep x, subtract 5 from y: (4,-12-5) = (4,-17)

Four coordinate pairs that could serve as the other endpoint of the given line segment are given by: (9,-12), (-1,-12), (4,-7), (4,-17).

6 0

3 years ago

The amounts of electricity bills for all households in a city have a skewed probability distribution with a mean of $139 and a

ZanzabumX [31]

Answer:

P (within $6 of 4) = 0.9164

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

Mean of $139 and a standard deviation of $30.

This means that $\mu = 139, \sigma = 30$

Random sample of 75 households

This means that $n = 75, s = \frac{30}{\sqrt{75}} = 3.464$

75 > 30, which means that the sampling distribution is approximately normal.

Find the probability that the mean amount of electric bills for a random sample of 75 households selected from this city will be within $6 of the population mean.

This is the pvalue of Z when X = 139 + 6 = 145 subtracted by the pvalue of Z when X = 139 - 6 = 133.

X = 145

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

By the Central Limit Theorem

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