Your answer is 160 i had this on a test hope this helps
In this question, the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Parameter of 5.2 per square yard:
This means that
, in which r is the radius.
How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?
We want:
![P(X \geq 1) = 1 - P(X = 0) = 0.99](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29%20%3D%200.99)
Thus:
![P(X = 0) = 1 - 0.99 = 0.01](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%201%20-%200.99%20%3D%200.01)
We have that:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-5.2r}*(5.2r)^{0}}{(0)!} = e^{-5.2r}](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-5.2r%7D%2A%285.2r%29%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%20e%5E%7B-5.2r%7D)
Then
![e^{-5.2r} = 0.01](https://tex.z-dn.net/?f=e%5E%7B-5.2r%7D%20%3D%200.01)
![\ln{e^{-5.2r}} = \ln{0.01}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-5.2r%7D%7D%20%3D%20%5Cln%7B0.01%7D)
![-5.2r = \ln{0.01}](https://tex.z-dn.net/?f=-5.2r%20%3D%20%5Cln%7B0.01%7D)
![r = -\frac{\ln{0.01}}{5.2}](https://tex.z-dn.net/?f=r%20%3D%20-%5Cfrac%7B%5Cln%7B0.01%7D%7D%7B5.2%7D)
![r = 0.89](https://tex.z-dn.net/?f=r%20%3D%200.89)
Thus, the radius should be of at least 0.89.
Another example of a Poisson distribution is found at brainly.com/question/24098004
Answer:
it can not go any more
Step-by-step explanation:
7/45 is the simplified terms
Find the area of the top, which is a circle.
Area of a circle = pi x r^2
Area = 3.14 x 1.5^2 = 7.065
Now for the volume multiply the area of the top by the height:
7.065 x 12 = 84.78 cubic inches
Round to the nearest tenth: 84.8 cubic inches
Answer:
![c=18.90-2.1r](https://tex.z-dn.net/?f=c%3D18.90-2.1r)
Step-by-step explanation:
<u><em>The complete question is</em></u>
A chef bought $17.01 worth of ribs and chicken. Ribs cost 1.89 per pound and chicken costs 0.90 per pound. The equation 0.90 +1.89r = 17.01 represents the relationship between the quantities in this situation.
Show that each of the following equations is equivalent to 0.9c + 1.89r = 17.01.
Then, explain when it might be helpful to write the equation in these forms.
a. c=18.9-2.1r. b. r= -10÷2c+9
we have that
The linear equation in standard form is
![0.90c+1.89r=17.01](https://tex.z-dn.net/?f=0.90c%2B1.89r%3D17.01)
where
c is the pounds of chicken
r is the pounds of ribs
step 1
Solve the equation for c
That means ----> isolate the variable c
Subtract 1.89r both sides
![0.90c=17.01-1.89r](https://tex.z-dn.net/?f=0.90c%3D17.01-1.89r)
Divide by 0.90 both sides
![c=(17.01-1.89r)/0.90](https://tex.z-dn.net/?f=c%3D%2817.01-1.89r%29%2F0.90)
Simplify
![c=18.90-2.1r](https://tex.z-dn.net/?f=c%3D18.90-2.1r)
step 2
Solve the equation for r
That means ----> isolate the variable r
Subtract 0.90c both sides
![1.89r=17.01-0.90c](https://tex.z-dn.net/?f=1.89r%3D17.01-0.90c)
Divide by 1.89 both sides
![r=(17.01-0.90c)/1.89](https://tex.z-dn.net/?f=r%3D%2817.01-0.90c%29%2F1.89)
Simplify
![r=9-0.48c](https://tex.z-dn.net/?f=r%3D9-0.48c)
therefore
The equation
is equivalent
The equation is helpful, because if I want to know the number of pounds of chicken, I just need to substitute the number of pounds of ribs in the equation to get the result.