Answer:
0.048 is the probability that more than 950 message arrive in one minute.
Step-by-step explanation:
We are given the following information in the question:
The number of messages arriving at a multiplexer is a Poisson random variable with mean 15 messages/second.
Let X be the number of messages arriving at a multiplexer.
Mean = 15
For poison distribution,
Mean = Variance = 15
From central limit theorem, we have:
where n is the sample size.
Here, n = 1 minute = 60 seconds
P(x > 950)
Calculation the value from standard normal z table, we have,
0.048 is the probability that more than 950 message arrive in one minute.
The perimeter of a rectangle restaurant kitchen is 40 meters. the area is 96 square meters. what are the dimensions of the kitchen?
Answer:
√3
Step-by-step explanation:
From the formula used in calculating Friction, we have:
Frictional Force = coefficient of Friction × Reaction
i.e Fr = μ × R
Resolving Frictional Force and Reaction of a body moving with on an Inclined plane,
Frictional Force = mass × g × sin a
where a = to the angle given
Reaction = mass × g × cos a
Therefore,
mass × g × sin a = μ × mass × g × cos a
mass and g cancels out on both sides.
Therefore,
sin a = μ × cos a
make "μ" subject.
μ = sin a/cos a
(recall: tan a = sin a /cos a)
μ = tan a
recall a = angle given = 60°
μ = tan 60°
μ = √3
or simply recall that
μ = tan a
μ = tan 60°
μ = √3
Given, y varies directly as the cube of x.
So, [tex] y=kx^3 [/tex]
By using the order pair (4, 16) we can get x=4 and y=16.
Now plug in these values in the above equation.
So, 16=k*4^3
16 = k *64
16/64 = k (By dividing each sides by 64).
So, k=1/4
So, the equation for this variation is y= 1/4*x^3
Now we need to find the value of y for x=2.
So, plug in x=2 in the above equation. Hence,
y=1/4* 2^3
=1/4*8
=8/4
=2
So, y=2
