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3 years ago

find the circumference of a circle that has an area of 452.16 square meters. (Use 3.1416 as the value of π.)

1 answer:

3 0

(1) circumference of a circle = 2π.R
(2) area of a circle = π.R²

Area = 452.16 m² (given), so we can calculate the radius:
452.16 = π.R²
452.16/π = R²

143.92 = R² → R =√143.92 ≈ 12 m
Having R = 12, now we can calculate the circumference :

circumference of a circle = 2π.R = 2.π.12 = 75.41 m

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Orders arrive at a Web site according to a Poisson process with a mean of 11 per hour. Determine the following: a) Probability o

Nataliya [291]

Answer:

a) 0.39984 = 39.984% probability of no orders in five minutes.

b) 0.06563 = 6.563% probability of 3 or more orders in five minutes.

c) The length of time is 0.63 hours

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Orders arrive at a Web site according to a Poisson process with a mean of 11 per hour.

This means that $\mu = 11h$ , in which h is the number of hours.

a) Probability of no orders in five minutes.

Five minutes means that $h = \frac{5}{60} = \frac{1}{12}$ , so $\mu = \frac{11}{12} = 0.9167$

This probability is P(X = 0). So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.9167}*(0.9167)^{0}}{(0)!} = 0.39984$

0.39984 = 39.984% probability of no orders in five minutes.

b) Probability of 3 or more orders in five minutes.

This is:

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.9167}*(0.9167)^{0}}{(0)!} = 0.39984$

$P(X = 1) = \frac{e^{-0.9167}*(0.9167)^{1}}{(1)!} = 0.36653$

$P(X = 2) = \frac{e^{-0.9167}*(0.9167)^{2}}{(2)!} = 0.168$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.39984 + 0.36653 + 0.168 = 0.93437$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.93437 = 0.06563$

0.06563 = 6.563% probability of 3 or more orders in five minutes.

c) Length of a time interval such that the probability of no orders in an interval of this length is 0.001.

This is h for which:

$P(X = 0) = 0.001$

We have that:

$P(X = 0) = e^{-\mu}$

And

$\mu = 11h$

$P(X = 0) = 0.001$

$e^{-11h} = 0.001$

$\ln{e^{-11h}} = \ln{0.001}$

$-11h = \ln{0.001}$

$h =-\frac{\ln{0.001}}{11}$

$h = 0.63$

The length of time is 0.63 hours

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3 years ago

Two machines can complete 5 tasks every 4 days. Let t represent

Gennadij [26K]

Answer:

you alrady got the answer

Step-by-step explanation:

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3 years ago

Please answer this question with how do work it out?

BartSMP [9]

Answer:

Point B coordinates' are: (3.2, 1.6)

Step-by-step explanation:

Since this is a rhomboid the diagonals AC and OB, must be perpendicular to each other. Then we can find first the equation of the line where segment AC lies, seeing that this line will cross the y axis at the point (0,4), and the x axis at the point (2, 0). The line can then be obtained by calculating the slope of the segment that joins the two points, and then using that the line's y-intercept must be at the point (0, 4):

$slope=\frac{0-4}{2-0} =-2$

then the equation of the line for segment AC must be:

$y=-2x+4$

Next, we calculate the equation of a perpendicular line to the previous one, and that passes through the point (0, 0) to determine the equation of the line that contains the segment OB. Recall that the perpendicular line to one of slope m must have a slope given by: -1/m (the opposite of the reciprocal of "m". Then this new perpendicular line passing through (0, 0) must be given by:

$y=\frac{1}{2} x+0\\y=\frac{1}{2} x$

Now we can find the point at which both lines intersect:

$\frac{1}{2} x=-2x+4\\\frac{1}{2} x+2x=4\\\frac{5}{2} x = 4\\x=\frac{8}{5}$

and therefore the y value of the intersection point can be calculated via:

$y=\frac{1}{2} x\\y=\frac{1}{2} (\frac{8}{5} )\\y=\frac{4}{5}$

Then, point point B must be located at an x value that doubles the x value of the intersecting point, and similarly the y value of point B must be at the double of the value of the intersection point we just calculated. That is:

Point B = $(2\,*\frac{8}{5} ,\,2\,*\frac{4}{5} )=(\frac{16}{5} ,\frac{8}{5}) =(3.2,1.6)$

We can see the coordinates of point B and the lines we just generated in the attached image.

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3 years ago

The second number in an ordered pair of numbers that corresponds to a point on a coordinate system is the ?

Ksivusya [100]

Answer:

See below.

Step-by-step explanation:

The y-coordinate , giving the value of the function at this point. It is a part of the range of the function.

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