Answer: The correct option is 1.
Explanation:
The given piecewise function is,
It means if x<0, then
If 
, then
Since the f(x) is defined for x<0 and , therefore the function f(x) is not defined for 
.
From the graph 2, 3 and 4 we can easily noticed that for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.
Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for , hence the first option is correct.
Answer:
The length of the circumference is 
or 
Step-by-step explanation:
<u><em>The question in English is</em></u>
On a court, the central circumference will be painted, which has a diameter of 5 m. What is the length of the circumference?
we know that
The circumference of a circle is given by the formula
we have
substitute
This is the exact value
assume
Answer:
120*2.75*60/5280
= 3.75
Step-by-step explanation:
So James is walking at 120 steps a minute, there are 60 minutes in one hour, and 5,280 feet in a mile. So, to find how quickly James is walking, we multiply how many steps he is taking a minute by how much distance each step is (120 * 2.75) that gives us how much distance in one minute, so we then multiply by 60 because there are 60 minutes in one hour. Then divide the entire equation by how many feet are in one mile (5,280) giving us the answer 3.75 miles per hour. And the equation 120*2.75*60/5280
Answer:
p-value (0.0208) is less than alpha = 0.05 reject H0.
Step-by-step explanation:
we have the following data:
sample size = n = 75
x, the number to evaluate is 45
the sample proportion would be: x / n = 45/75
p * = 0.6
Now, the null and alternative hypotheses are:
H0: P = 0.72
Ha: P no 72
two tailed test
statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)
replacing we have:
z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)
z = -2.31
p-vaule = 2 * p (z <-2.31)
using z table, we get:
p-vaule = 2 * (0.0104)
p-vaule = 0.0208
Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.
A logistic differential equation can be written as follows:
![\frac{dP}{dt} = rP[1- \frac{P}{K}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%20rP%5B1-%20%5Cfrac%7BP%7D%7BK%7D%5D%20)
where r = growth parameter and K = carrying parameter.
In order to write you equation in this form, you have to regroup 2:
![\frac{dP}{dt} = 2P[1- \frac{P}{10000}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%202P%5B1-%20%5Cfrac%7BP%7D%7B10000%7D%5D%20)
Therefore, in you case r = 2 and K = 10000
To solve the logistic differential equation you need to solve:
![\int { \frac{1}{[P(1- \frac{P}{K})] } } \, dP = \int {r} \, dt](https://tex.z-dn.net/?f=%20%5Cint%20%7B%20%5Cfrac%7B1%7D%7B%5BP%281-%20%5Cfrac%7BP%7D%7BK%7D%29%5D%20%7D%20%7D%20%5C%2C%20dP%20%3D%20%20%5Cint%20%7Br%7D%20%5C%2C%20dt%20%20)
The soution will be:
P(t) =
where P(0) is the initial population.
In your case, you'll have:
P(t) = <span>
Now you have to calculate the limit of P(t).
We know that
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hence,
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