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3 years ago

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

Mathematics

1 answer:

densk [106]3 years ago

7 0

Answer:

The derivative of the function is:

$g'(x) = \frac{1}{1.6094x}$

Step-by-step explanation:

If we have a function in the following format:

$g(x) = \log_{a}{f(x)}$

This function has the following derivative

$g'(x) = \frac{f'(x)}{f(x)*\ln{a}}$

In this problem, we have that:

$g(x) = \log_{5}{x}$

So $f(x) = x, f'(x) = 1, a = 5$

The derivative is

$g'(x) = \frac{f'(x)}{f(x)*\ln{a}}$

$g'(x) = \frac{1}{x*\ln{5}}$

$g'(x) = \frac{1}{1.6094x}$

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3 years ago

Can someone explain how to convert 70kg to lbs? i need to show work on my test.

Jlenok [28]

Answer:

70 kg is 154.3 lbs.

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3 years ago

Which of the following groups are subsrts of rational numbers

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4 years ago

Suppose A and B are dependent events. If P(A) = 0.5 and P(BIA) = 0.6, what is

klasskru [66]

If the probability of independent event A is 0.5, then P(A|B) will be 0.5. Then the correct option is B.

<h3>Which pair of events are called independent events?</h3>

When one event's occurrence or non-occurrence doesn't affect occurrence or non-occurrence of other event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent iff we have:

P(A ∩ B) = P(A)P(B)

Comparing it with chain rule will give

P(A|B) = P(A)

P(B|A) = P(B)

Suppose A and B are dependent events.

If P(A) = 0.5

Then P(A|B) will be

P(A|B) = P(A)

P(A|B) = 0.5

Then the correct option is B.

Learn more about probability here:

brainly.com/question/1210781

#SPJ1

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2 years ago

Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample

fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

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 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 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$