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3 years ago

Which logarithmic equation is equivalent to 8^2=64

Mathematics

2 answers:

NISA [10]3 years ago

7 0

Answer:

$2=log_{8}64$

Step-by-step explanation:

We are given a equation:

8²=64

We have to convert this into a logarithmic equation:

Taking log base 8 on both sides, we get

$log_{8}8^{2}=log_{8}64$

$2log_{8}8=log_{8}64$ (since, $log_{a}m^n=nlog_{a}m$ )

$2=log_{8}64$ (since, $log_{a}a=1$ )

Hence, option first is true

adell [148]3 years ago

5 0

Answer:

The answer will be the first one...

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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.

The mean number of words per minute (WPM) read by sixth graders is 84 with a standard deviation of 15 WPM.

This means that $\mu = 84, \sigma = 15$

Sample of 188

This means that $n = 188, s = \frac{15}{\sqrt{188}}$

What is the probability that the sample mean would differ from the population mean by greater than 1.46 WPM?

Greater than 84 + 1.46 = 85.46 or less than 84 - 1.46 = 82.54. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability is is less than 82.54.

P-value of Z when X = 82.54. So

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