All categories

3 years ago

Rewrite the following expression using the properties of logarithms.

1 answer:

8 0

$\bf \textit{logarithm of factors}
\\\\
log_a(xy)\implies log_a(x)+log_a(y)
\\\\\\
\textit{Logarithm of rationals}
\\\\
log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y)
\\\\\\
\textit{Logarithm of exponentials}
\\\\
log_a\left( x^b \right)\implies b\cdot log_a(x)\\\\
-------------------------------$

$\bf log_2(z)+2log_2(x)+4log_9(y)+12log_9(x)-2log_2(y)
\\\\\\
log_2(z)+log_2(x^2)+4log_9(y)+12log_9(x)-2log_2(y)
\\\\\\
log_2(z\cdot x^2)-2log_2(y)+4log_9(y)+12log_9(x)
\\\\\\
log_2(z\cdot x^2)-log_2(y^2)+4log_9(y)+12log_9(x)
\\\\\\
log_2\left( \cfrac{zx^2}{y^2} \right)+4log_9(y)+12log_9(x)
\\\\\\
log_2\left( \cfrac{zx^2}{y^2} \right)+log_9(y^4)+log_9(x^{12})\implies 
log_2\left( \cfrac{zx^2}{y^2} \right)+log_9\left( \cfrac{y^4}{x^{12}} \right)$

You might be interested in

19. A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years

Juliette [100K]

Answer:

a) Approximately normal.

b) The mean is 75 years and the standard deviation is 0.8485 years.

c) 0.9909 = 99.09% probability that the mean age exceeds 73 years

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.

Sample of 50 retirees

This means that $n = 50$

Mean age and standard deviation are 75 and 6 years

This means that $\mu = 75, \sigma = 6$

a. Describe the shape of the sampling distribution of the sample mean in this case

By the Central Limit Theorem, approximately normal.

b. Find the mean and standard error of the sampling distribution of the sample mean.

By the Central Limit Theorem, the mean is 75 and the standard error is $s = \frac{6}{\sqrt{50}} = 0.8485$

c. What is the probability that the mean age exceeds 73 years?

This is 1 subtracted by the pvalue of Z when X = 73.

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

By the Central Limit Theorem

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

$Z = \frac{73 - 75}{0.8485}$

$Z = -2.36$

$Z = -2.36$ has a pvalue of 0.0091

1 - 0.0091 = 0.9909

0.9909 = 99.09% probability that the mean age exceeds 73 years

5 0

3 years ago

B^10/B^2=B^5 True or false

puteri [66]

Answer:

True

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.

kipiarov [429]

Answer:

25 years

Step-by-step explanation:

Solution:-

- Data for the average daily temperature on January 1 from 1900 to 1934 for city A.

- The distribution X has the following parameters:

Mean u = 24°C

standard deviation σ = 4°C

- We will first construct an interval about mean of 1 standard deviation as follows:

Interval for 1 standard deviation ( σ ):

[ u - σ , u + σ ]

[ 24 - 4 , 24 + 4 ]

[ 20 , 28 ] °C

- Now we will use the graph given to determine the number of years the temperature T lied in the above calculated range: [ 20 , 28 ].

T1 = 20 , n1 = 2 years

T2 = 21 , n2 = 3 years

T3 = 22 , n3 = 2 years

T4 = 23 , n4 = 4 years

T5 = 24 , n5 = 3 years

T6 = 25 , n6 = 3 years

T7 = 26 , n7 = 5 years

T8 = 27 , n8 = 2 years

T5 = 28 , n9 = 1 years

- The total number of years:

∑ni = n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9

= 2 + 3 + 2 + 4 + 3 + 3 + 5 + 2 + 1

= 25 years

3 0

3 years ago

Read 2 more answers

Classwork

Andrews [41]

Answer:

Step-by-step explanation:

Each box represents 1/3. 5/3 of white is 2 boxes more so red needs 2 boxes more than white. 5 red and 3 white is the only one that follows the criteria.

6 0

3 years ago

How many three-digit numbers are divisible by 2,3 or 5? plEASe helP I aM DeSpeRatE

frosja888 [35]

Answer:

Step-by-step explanation:

- A number is divisible by 2 if its last digit is 2, 4, 6, 8 or 0

- A number is divisible by 3 if ist sum of digits is divisible by 3.

- A number is divisible by 5 if its last digit is a 5 or a 0.

The least 3 digit number divisible by 30 is 120 and the greatest is 990.

8 0

3 years ago

Read 2 more answers