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Elanso [62]
3 years ago
10

When studying radioactive​ material, a nuclear engineer found that over 365​ days, 1,000,000 radioactive atoms decayed to 972 co

mma 737 radioactive​ atoms, so 27 comma 263 atoms decayed during 365 days.
a. Find the mean number of radioactive atoms that decayed in a day.

b. Find the probability that on a given​ day, 51 radioactive atoms decayed.
Mathematics
1 answer:
disa [49]3 years ago
8 0

Answer:

a) 74.69

b) 0.08% probability that on a given​ day, 51 radioactive atoms decayed.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

a. Find the mean number of radioactive atoms that decayed in a day.

27,263 atoms in 365 days. The mean is

\mu = \frac{27263}{365} = 74.69

b. Find the probability that on a given​ day, 51 radioactive atoms decayed.

This is P(X = 51).

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = x) = \frac{e^{-74.69}*(74.69)^{51}}{(51)!} = 0.0008

0.08% probability that on a given​ day, 51 radioactive atoms decayed.

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NARA [144]

Ans(a):

Given function is f(x)=\frac{3x-1}{x+4}

we know that any rational function is not defined when denominator is 0 so that means denominator x+4 can't be 0

so let's solve

x+4≠0 for x

x≠0-4

x≠-4

Hence at x=4, function can't have solution.


Ans(b):

We know that vertical shift occurs when we add something on the right side of function so vertical shift by 4 units means add 4 to f(x)

so we get:

g(x)=f(x)+4

g(x)=\frac{3x-1}{x+4}+4

We may simplify this equation but that is not compulsory.

Comparision:  

Graph of g(x) will be just 4 unit upward than graph of f(x).


Ans(c):

To find value of x when g(x)=8, just plug g(x)=8 in previous equation

8=\frac{3x-1}{x+4}+4


8-4=\frac{3x-1}{x+4}


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4x-3x=-1-16

x=-17

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Answer:

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