See the attached picture:
Select three side lengths, in centimeters (cm), that can form a right triangle. Use the Pythagorean Theorem.
1 answer:
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Whenever you face the problem that deals with maxima or minima you should keep in mind that minima/maxima of a function is always a point where it's derivative is equal to zero.
To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).
B(y)=b-c
B(y)=100y-18y²
Now that we have a net benefits function we need find it's derivate with respect to y.
Now we must find at which point this function is equal to zero.
0=100-36y
36y=100
y=2.8
Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.
B(2.8)=100(2.8)-18(2.8)²=138.88≈139.
One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.
To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).
B(y)=b-c
B(y)=100y-18y²
Now that we have a net benefits function we need find it's derivate with respect to y.
Now we must find at which point this function is equal to zero.
0=100-36y
36y=100
y=2.8
Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.
B(2.8)=100(2.8)-18(2.8)²=138.88≈139.
One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.
Answer:
Step-by-step explanation:
The model , the number of planets found up to time
, as a Poisson process. So, the
has distribution of Poison distribution with parameter
a)
The mean for a month is, per month
(Here. t = 24)
For Poisson process mean and variance are same,
(Poisson distribution mean and variance equal)
The standard deviation of the number of planets is,
b)
For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter . The sum of
of these independent exponential has distribution Gamma
.
From the given information, and
Calculate the expected value.
(Here, and
)
C)
Calculate the probability that she will become eligible for the prize within one year.
Here, 1 year is equal to 12 months.
P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)
Hence, the required probability is 0.2149 or 21.49%