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3 years ago

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82. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value

of each expression when x = 9, y= 8, and z= 16. In each case, the expression evaluates to a rational number.
b. 11√y2z4

1 answer:

HACTEHA [7]3 years ago

7 0

Answer:

11yz² and when evaluating we get 22528

Step-by-step explanation:

We have the expression $11\sqrt{y^{2}z^{4} }$

We know that a square root is a 1/2 exponent, so we're going to multiply the exponents of y and z by 1/2.

$11\sqrt{y^{2}z^{4} }= 11y^{2(1/2)}z^{4(1/2)} } =11yz^{2}$

Therefore the expression is rewritten as $11yz^2$

Now we're going to evaluate this expression for y = 8 and z = 16

$11yz^{2} =11(8)(16)^2=88(256)=22528$

Thus, when evaluated the result is 22528

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3 years ago

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Answer:

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Step-by-step explanation:

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

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

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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This is 1 subtracted by the pvalue of Z when X = 229.5. So

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

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