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3 years ago

Rewrite the expression using the properties of exponents.

Mathematics

1 answer:

Alexxx [7]3 years ago

7 0

Answer:

$\sqrt[3]{\frac{x^5}{x^4}}$

$\sqrt[3]{x}$

This would be the answer, but you're actually looking for:

$\frac{x^{\frac{5}{3}}}{x^{\frac{4}{3}}}$

Use the property:

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

Therefore, the answer is E

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Step-by-step explanation:

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Read 2 more answers

A particular type of 4th grade Achievement Test provides overall scores that are normally distributed with a mean of 50 and a st

GuDViN [60]

Answer:

a) The minimum score required to be admitted into this program will be 68.8.

b) The minimum score required to be admitted into this program will be 53.05.

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.

In this problem, we have that:

$\mu = 50, \sigma = 10$

a. What will be the minimum score required to be admitted into this program?

Top 3%, so the minimum score is X when Z has a pvalue of 1-0.03 = 0.97. So X when Z = 1.88.

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

$1.88 = \frac{X - 50}{10}$

$X - 50 = 10*1.88$

$X = 68.8$

The minimum score required to be admitted into this program will be 68.8.

b. One state wants to allow all students with scores in the top 38 into a special advanced program. What will be the minimum score required to be admitted into this program?

Top 38%, so the minimum score is X when Z has a pvalue of 1-0.32 = 0.68. So X when Z = 0.305.

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

$0.305 = \frac{X - 50}{10}$