I need help with this problem

Messages arrive to a computer server according to a Poisson distribution with a mean rate of 11 per hour. Determine the length o

Zarrin [17]

Answer:

The length of the interval during which no messages arrive is 90 seconds long.

Step-by-step explanation:

Let X = number of messages arriving on a computer server in an hour.

The mean rate of the arrival of messages is, λ = 11/ hour.

The random variable X follows a Poisson distribution with parameter λ = 11.

The probability mass function of X is:

$P(X=x)=\frac{e^{-11}11^{x}}{x!};\ x=0,1,2,3....$

It is provided that in t hours the probability of receiving 0 messages is,

P (X = 0) = 0.76

Compute the value of t as follows:

$P(X=0)=\frac{e^{-11\times t}(11\times t)^{0}}{0!}\\0.76=e^{-11\times t}\\\ln(0.76)=-11\times t\\t=-\frac{\ln(0.76)}{11} \\=0.025\ hours\\\approx90\ seconds$

Thus, the length of the interval during which no messages arrive is 90 seconds long.

6 0

3 years ago

Jennifer has $400. She bought a dress worth $343. She

Anuta_ua [19.1K]

Answer:

hmm i think its dependent!

srry if im wrong tho

8 0

3 years ago

What is the area of a regular heptagon with side length of 6 meters and a distance from the to the vertex of 6 meters? round you

Ahat [919]

Apothem = side length / 2*tan(180 / number of sides)
apothem = side length / 2*tan (180 / 7)
apothem = 6 / (2*tan( 25.7142857143))
apothem = 6 / 2*0.48157
apothem = 6.2296239384 

Polygon area = (# of sides * side length * apothem) / 2
Polygon area = ( 7 * 6 * 6.2296239384) / 2
Polygon area = 130.8221027064

8 0

3 years ago

A real estate company wants to build a parking lot along the side of one of its buildings using 400 feet of fence. If the side a

svetlana [45]

Answer:

1.) Therefore the side parallel to the building is 100 feet.

2.) The side perpendicular to the building is 200 feet.

Step-by-step explanation:

The parking lot, which is rectangular, is built along the side of one of its buildings.

The side of the parking lot which is alongside the building needs no fence,

let us say that this side is of length y.

Let the perpendicular to the building be of length x.

The perimeter of the parking lot that actually needs to be fenced = 2x + y

The amount of fencing available = 400 feet.

Therefore 2x + y = 400 .... (i)

Therefore y = 400 - 2x .... (ii)

The area of the parking lot, A = xy = x ( 400 - 2x) = 400x - $2x^2$ .... (iii)

Therefore $\frac{dA}{dx} = \frac{d(400x - 2x^2}{dx} = 400 - 4x$ .... (iv)

Also we get $\frac{d^2A}{dx^2} = -4$ .... (v)

Hence we will get the maximum value of the parking lot by equating the first order differential of area, A to zero as the second order differential of area, A is negative.

Therefore from (iv) we get 400 - 4x = 0 ∴ x = 100 feet

y = 400 - 2x = 400 - 200 = 200 feet.

1.) Therefore the side parallel to the building is 100 feet.

2.) The side perpendicular to the building is 200 feet.

6 0

3 years ago

Round your answer to the nearest tenth of a cubic centimeter.

Zigmanuir [339]

Answer:

22.1

Step-by-step explanation:

Because of it being a pyramid we must use the equation Bh1/2

B = L + W we assume that the base is a perfect square meaning all sides are the same length B = 4.8 + 4.8 = 9.6 then we multiply by the height

9.6 x 4.6 = 44.16 next you divide by 2 or multiply by .5

44.16/2 = 22.08 then finally rounding to the nearest tenth

making 22.1 cubic inches

8 0

2 years ago