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Yakvenalex [24]

3 years ago

15

The expression log1/3/log2 is the result of applying the change of base formula to a logarithmic expression. Which could be the

original expression?

2 answers:

nasty-shy [4]3 years ago

7 0

Answer:

C

Step-by-step explanation:

given $log_{b}$ a, then the change of base is

$\frac{loga}{logb}$

For the given expression a = $\frac{1}{3}$ and b = 2, hence

The original expression is therefore

$log_{2}$ $\frac{1}{3}$ → C

Dovator [93]3 years ago

5 0

Answer:

Option C. $log_{2}\frac{1}{3}$

Step-by-step explanation:

The given logarithmic expression is $\frac{log(\frac{1}{3} )}{log2}$

Rule of logarithm says

$\frac{log_{e}a }{log_{e}b}=log_{b}a$

So by this rule,

expression $\frac{log(\frac{1}{3} )}{log2}$ will become $log_{2}\frac{1}{3}$

Therefore, Option C. $log_{2}\frac{1}{3}$ will be the answer.

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An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon

salantis [7]

Answer:

(a) The standard error of the mean in this experiment is $0.052.

(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The information provided is:

$n=40\\\mu=\$3.82\\\sigma=\$0.33$

As <em>n</em> = 40 > 30, the distribution of sample mean is $\bar X\sim N(3.82,\ 0.052^{2})$ .

(a)

The standard error is the standard deviation of the sampling distribution of sample mean.

Compute the standard deviation of the sampling distribution of sample mean as follows:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

$=\frac{0.33}{\sqrt{40}}\\\\=0.052178\\\\\approx 0.052$

Thus, the standard error of the mean in this experiment is $0.052.

(b)

Compute the probability that the sample mean is between $3.78 and $3.86 as follows:

$P(3.78$

$=P(-0.77$

Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c)

If the difference between the sample mean and the population mean is less than $0.01 then:

$\bar X-\mu_{\bar x}$

Compute the value of $P(\bar X$ as follows:

$P(\bar X$

$=P(Z$

Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d)

Compute the probability that the sample mean is greater than $3.92 as follows:

$P(\bar X>3.92)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{3.92-3.82}{0.052})$

$=P(Z$

Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.

3 0

3 years ago

There are 150 visitors on the first day of a exhibition The number of visitors increases by 10% on the second day on the third d

Sliva [168]

Answer:

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Step-by-step explanation:

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7 0

3 years ago

Help pls look at the picture

Alika [10]

Answer:

Option A: $-\frac{4}{3}$ is the correct answer.

Step-by-step explanation:

Given that:

Slope of the line = $\frac{3}{4}$

Let,

m be the slope of the line perpendicular to the line with slope $\frac{3}{4}$

We know that,

The product of slopes of two perpendicular lines is equals to -1.

Therefore,

$\frac{3}{4}.m=-1\\$

Multiplying both sides by $\frac{4}{3}$

$\frac{4}{3}*\frac{3}{4}m=-1*\frac{4}{3}\\$

m = $-\frac{4}{3}$

$-\frac{4}{3}$ is the slope of the line perpendicular to the line having slope $\frac{3}{4}$

Hence,

Option A: $-\frac{4}{3}$ is the correct answer.

3 0

3 years ago

When the mountain was last measured, its height was 3,570 meters. Now it is 3,927 meters. What is the percent of increase in the

Elina [12.6K]

Answer:

110%

Step-by-step explanation:

3,927/3,570

=1.1

=110%

6 0

3 years ago

A singles tennis court is a rectangle 27 feet wide and 78 feet long. Suppose a player at corner A hits the ball to her opponent

Sav [38]

Basically, you just have to find the length of the rectangle that is 27 x 78 feet.
The equation for the diagonal:
d = sqrt(l^2+w^2)
l = 27
w = 78
plug them in and solve
d = sqrt ( (27^2) + (78^2) )
d = sqrt ( 729 + 6084 )
d = sqrt ( 6813 )
d <span>≈ 82.5

The ball traveled approximately 82.5 feet from one corner of the rectangular 27 x 78 foot field, diagonally to the other side.

Hope this helps</span>

6 0

3 years ago