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Olin [163]
2 years ago
15

Solve log base 2 of one sixteenth.

Mathematics
1 answer:
irinina [24]2 years ago
8 0

Answer:

-4

Step-by-step explanation:

log (2) (1/16)

2^4=16

fraction is negative exponent

-4

You might be interested in
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t
skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

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 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 CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that \mu = 273, \sigma = 100

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 30, s = \frac{100}{\sqrt{30}}

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

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

By the Central Limit Theorem

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

Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}

Z = 0.88

Z = 0.88 has a p-value of 0.8106

X = 257

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

Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}

Z = -0.88

Z = -0.88 has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 50, s = \frac{100}{\sqrt{50}}

X = 289

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

By the Central Limit Theorem

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

Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}

Z = 1.13

Z = 1.13 has a p-value of 0.8708

X = 257

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

Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}

Z = -1.13

Z = -1.13 has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 100, s = \frac{100}{\sqrt{100}}

X = 289

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

By the Central Limit Theorem

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

Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}

Z = 1.6

Z = 1.6 has a p-value of 0.9452

X = 257

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

Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}

Z = -1.6

Z = -1.6 has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0
2 years ago
Malinda went to the circus and spent $21.10 for admission, $3.25 on a program, and $9.05 on food.
max2010maxim [7]
Assuming you'd like to know about how much malinda spent at the circus,

21.10+3.25+9.05 = 33.4

or about 33 dollars.
7 0
3 years ago
Read 2 more answers
Solve 3/4•1/7 in lowest terms
emmasim [6.3K]

Answer:

3/28

Step-by-step explanation:

\frac{3}{4}*\frac{1}{7}=\frac{3}{4*7}=\frac{3}{28}

that dot is a multiplication sign, right?

3 0
3 years ago
Supervisor: "Because you are working a late shift, you will get an increase in your wage. You will get an additional 10% per hou
rewona [7]

Answer:

I will make <u>$ 13.20</u> per hour

Step-by-step explanation:

Given:

Employee gets money for Working from 2.00 PM to 6.00 PM = \$ 12 per hour

Employee gets money for working from 6.00 PM to 12.00 AM  will get additional 10\%=\frac{10}{100}\times12= \$ 1.2 per hour

Employee gets money for working from 12.00 AM to 01.00 AM will get additional 15\%=\frac{15}{100}\times12= \$ 1.8 per hour

Solution:

Employee works from 2.00 PM to 12.00 AM= Employee gets money for Working from 2.00 PM to 6.00 PM + 10\% extra wage = \$ 12 + \$ 1.2 = \$ 13.2

7 0
3 years ago
The following information is from the December​ 31, 2017 balance sheet of Tudor Corporation.Preferred​ Stock, $100 par $370,000​
Alexeev081 [22]

Answer:

A. $909,000

Step-by-step explanation:

To compute Tudor Corporation’s paid in capital as of December 31, 2017, we must get first the Total Shareholders’ Equity ($991,900) minus Retained earnings as of December 31, 2017 ($82,900) plus treasury shares or any shares reacquired by the company if there is, equals $909,000

or

($991,900 - $82,900 + 0 = $909,000)

7 0
3 years ago
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