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Tanzania [10]
3 years ago
11

. Write each number in terms of natural logarithms, and then use the properties of logarithms to show that it is a

Mathematics
1 answer:
siniylev [52]3 years ago
4 0

Answer:

The answer is 3/4

Step-by-step explanation:

Hi, we need to change the base of the logarithm, for that we need to use the following formula.

Log_{b} (a)=\frac{Ln(a)}{Ln(b)}

In our case, this is:

Log_{9} (\sqrt{27} )=\frac{Ln(\sqrt{27} )}{Ln(9)}

Which is the same as:

\frac{Ln(27)^{\frac{1}{2} }}{Ln(9)}

Now, let´s solve this using the log properties

\frac{1}{2} (\frac{Ln(27)}{Ln(9)} )

\frac{1}{2} (\frac{Ln(9*3)}{Ln(9)} )

\frac{1}{2} (\frac{Ln(9)+Ln(3)}{Ln(9)} )

\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(3)}{Ln(9)}  )\\

We can change 3 for 9^(1/2)

\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(9^{\frac{1}{2} } )}{Ln(9)}  )\\

\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(9 )}{2*Ln(9)}  )\\

Since Ln(9) / Ln(9) =1, we get.

\frac{1}{2} (1+\frac{1}{2} )

\frac{1}{2} (\frac{3}{2} )=\frac{3}{4}

Best of luck.

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The equation is of the form

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62.93%

Step-by-step explanation:

We have to solve it by a Poisson distribution, where:

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Now, we have p (x> 3) and that is equal to:

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So, we calculate the probability from 0 to 3:

 p (x = 0) = 2.72 ^ (- 4.33) * 4.33 ^ (0) / 0! = 0.01313

p (x = 1) = 2.72 ^ (- 4.33) * 4.33 ^ (1) / 1! = 0.0568

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