The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This dist
1 answer:
<h3>Answer: 83.85%</h3>
This value is approximate.
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Explanation:
Let's compute the z score for x = 40
z = (x-mu)/sigma
z = (40-47)/7
z = -1
We're exactly one standard deviation below the mean.
Repeat these steps for x = 68
z = (x-mu)/sigma
z = (68-47)/7
z = 3
This score is exactly three standard deviations above the mean.
Now refer to the Empirical Rule chart below. We'll add up the percentages that are between z = -1 and z = 3. This consists of the two pink regions (each 34%), the right blue region (13.5%) and the right green region (2.35%). These percentages are approximate.
34+34+13.5+2.35 = 83.85
<u>Roughly 83.85%</u> of the one-mile roadways have between 40 and 68 potholes.
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Answer:
a) . It does not have a steady state
b) . It has a steady state.
Step-by-step explanation:
a)
The first step is finding . So:
We have to find the eigenvalues of this differential equation, which are the roots of this equation:
So:
Since this differential equation has a positive eigenvalue, it does not have a steady state.
Now as for the particular solution.
Since the differential equation is equaled to a constant, the particular solution is going to have the following format:
So
C is a constant, so (C)' = 0.
The solution in the form is
b)
The first step is finding . So:
We have to find the eigenvalues of this differential equation, which are the roots of this equation:
So:
Since this differential equation does not have a positive eigenvalue, it has a steady state.
Now as for the particular solution.
Since the differential equation is equaled to a constant, the particular solution is going to have the following format:
So
C is a constant, so (C)' = 0.
The solution in the form is