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3 years ago

Use the definition of the logarithmic function to find x. log4 0.25=x x=?

1 answer:

5 0

The answer is -1.

$log_4(0.25) =log_4( \frac{1}{4})= log_4(4^{-1} ) \\ \\ 
log(x^{a} ) = a*log(x) \\ \\ 
log_4(4^{-1} )= -1 *log_4(4) \\ \\ 
log_y(x) = \frac{log(x)}{log(y)} \\ \\ 
-1 *log_4(4) = -1* \frac{log(4)}{log(4)} = -1$

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stiv31 [10]

is it -2 ?

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3 years ago

Pentagon DEFGH is translated 4 units to the right to create pentagon UVXYZ. DE is 5cm long. What is the length of UV?

Semmy [17]

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3 years ago

Determine if each of the following pairs of rates are proportional

Afina-wow [57]

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3 years ago

PLZ I WILL PUT YOU AS BRAINYEST 29<(m^2+9)/2<45

denis23 [38]

Answer:

M=4

Step-by-step explanation:

29-25=4

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That’s where the 25 comes from

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With the 25, m = 4

5 0

3 years ago

A population of values has a normal distribution with μ = 149.8 μ=149.8 and σ = 68.2 σ=68.2. You intend to draw a random sample

Len [333]

Answer:

There is a 49.20% probability that a single randomly selected value is less than 148.3.

There is a 38.21% probability that a sample of size n = 186 n=186 is randomly selected with a mean less than 148.3.

Step-by-step explanation:

Problems of normally distributed samples 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.

In this problem, we have that:

A population of values has a normal distribution with $\mu = 149.8$ and $σ=68.2$ .

Find the probability that a single randomly selected value is less than 148.3

This is the pvalue of Z when $X = 148.3$ .

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

$Z = \frac{148.3 - 149.8}{68.2}$

$Z = -0.02$

$Z = -0.02$ has a pvalue of 0.4920

There is a 49.20% probability that a single randomly selected value is less than 148.3.

Find the probability that a sample of size n = 186 n=186 is randomly selected with a mean less than 148.3.

We want to find the mean of the sample, so we have to find the standard deviation of the population. That is

$s = \frac{68.2}{\sqrt{186}} = 5$

Now, we have to find the pvalue of Z when $X = 148.3$ .

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

$Z = \frac{148.3 - 149.8}{5}$

$Z = -0.3$

$Z = -0.3$ has a pvalue of 0.3821

There is a 38.21% probability that a sample of size n = 186 n=186 is randomly selected with a mean less than 148.3.

8 0

3 years ago