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3 years ago

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A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of tune, an average of 28 pa

rticles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Find the probability that at least one particle arrives m a particular one second period. Round your answer to four decimals. Find the probability that at least two particles arrive in a particular 2 second period. Round your answer to four decimals. The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 19 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes? Give your answer accurate to two decimal places.

1 answer:

patriot [66]3 years ago

6 0

Answer:

<u><em>Part I</em></u>

p(x=1)=0.0000

p(x=2)=0.0000

<u><em>Part II</em></u>

p(x)=0.11

Step-by-step explanation:

For Poisson distribution:

$p(X=x)=e^-m\frac{m^x}{x!}$

Where m=mean, x=number of events

Given x=1, and mean,m=28

$p(X=1)=\frac{e^{-28} *28^1}{1!}\\p(X=1)=0.0000$

For x=2 and mean,m=28

$p(X=2)=\frac{e^{-28} *28^2}{2!}\\p(X=2)=0.0000$

For Uniform Distribution

Time interval 10 and 19 minutes is 9

Time interval between 15 and 16 minutes is 1

Therefore:-

$p(x)=\frac{1}{9}\\p(x)=0.1111\\p(x)=0.11 \ (2d.p)$

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Solve to find X. 1/5(x - 2) = 1/10 (x + 6)

LenaWriter [7]

Answer:

x = 10

Step-by-step explanation:

First, distribute:

$\frac{1}{5} x - \frac{2}{5} =\frac{1}{10} x+\frac{6}{10}$

Next, subtract $\frac{1}{5}x$ from both sides:

$-\frac{2}{5} = \frac{1}{10} x -\frac{1}{5} x+\frac{6}{10}$

(multiply $\frac{1}{5}x$ by 2 to get common denominator, $\frac{2}{10} x$ )

$-\frac{2}{5} =-\frac{1}{10}x +\frac{6}{10}$

Next, subtract $\frac{6}{10}$ from both sides:

$-\frac{2}{5} -\frac{6}{10} =-\frac{1}{10} x$

(multiply $\frac{2}{5}$ by 2 to get common denominator, $\frac{4}{10}$ )

$-\frac{10}{10} =-\frac{1}{10} x$ ⇒ $-1=-\frac{1}{10} x$

Next, multiply both sides by 10:

$-10=-x$

FInally, divide both sides by -1:

x = 10

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2 years ago

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Which equation does NOT graph a line? A) y = 5 B) y = -3x3 C) y = 2 3 x D) y = −8x

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<span>B) y = -3x3

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Explain how to multiply the following whole numbers 21 x 14

Lesechka [4]

Answer:

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

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$\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}$

Step-by-step explanation:

Given

$21\:\times \:14$

Line up the numbers

$\begin{matrix}\space\space&2&1\\ \times \:&1&4\end{matrix}$

Multiply the top number by the bottom number one digit at a time starting with the ones digit left(from right to left right)

Multiply the top number by the bolded digit of the bottom number

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

Multiply the bold numbers: 1×4=4

$\frac{\begin{matrix}\space\space&2&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&4\end{matrix}}$

Multiply the bold numbers: 2×4=8

$\frac{\begin{matrix}\space\space&\textbf{2}&1\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}$

Multiply the top number by the bolded digit of the bottom number

$\frac{\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}$

Multiply the bold numbers: 1×1=1

$\frac{\begin{matrix}\space\space&\space\space&2&\textbf{1}\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&\space\space&1&\space\space\end{matrix}}$

Multiply the bold numbers: 2×1=2

$\frac{\begin{matrix}\space\space&\space\space&\textbf{2}&1\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&2&1&\space\space\end{matrix}}$

Add the rows to get the answer. For simplicity, fill in trailing zeros.

$\frac{\begin{matrix}\space\space&\space\space&2&1\\ \space\space&\times \:&1&4\end{matrix}}{\begin{matrix}\space\space&0&8&4\\ \space\space&2&1&0\end{matrix}}$

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Add the digits of the right-most column: 4+0=4

$\frac{\begin{matrix}\space\space&0&8&\textbf{4}\\ +&2&1&\textbf{0}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&\textbf{4}\end{matrix}}$

Add the digits of the right-most column: 8+1=9

$\frac{\begin{matrix}\space\space&0&\textbf{8}&4\\ +&2&\textbf{1}&0\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{9}&4\end{matrix}}$

Add the digits of the right-most column: 0+2=2

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Therefore,

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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Lyrx [107]

Step-by-step explanation:

1. yes 4+16 = 20

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