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3 years ago

In 3,000 repetitions of an experiment, a random event occurred in 500 cases. The expected probability of this event is?

Mathematics

1 answer:

Veronika [31]3 years ago

3 0

One sixth is the expected probability

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3 years ago

What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to gu

erik [133]

Answer:

4951 students

Step-by-step explanation:

If there was 99 students from each state, that would make the total to be:

99 * 50 = 4950

We can use the pigeon hole principle to make this the minimum number required.

The pigeon hole principle basically tells us that if you have more "pigeons" than "holes" then there must be one hole with multiple objects in it.

So, using this idea, we see that:

we need at least 1 more to ensure this

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2 years ago

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref

hichkok12 [17]

Answer:

P is exactly 3km east from the oil refinery.

Step-by-step explanation:

Let's d be the distance in km from the oil refinery to point P. So the horizontal distance from P to the storage is 3 - d and the vertical distance is 2. Hence the diagonal distance is:

$\sqrt{(3 - d)^2 + 2^2} = \sqrt{(3 - d)^2 + 4}$

So the cost of laying pipe under water with this distance is

$800000\sqrt{(3 - d)^2 + 4}$

And the cost of laying pipe over land from the refinery to point P is 400000d. Hence the total cost:

$800000\sqrt{(3 - d)^2 + 4} + 400000d$

We can find the minimum value of this by taking the 1st derivative and set it to 0

$800000\frac{2*0.5*(3-d)(-1)}{\sqrt{(3 - d)^2 + 4}} + 400000 = 0$

We can move the first term over to the right hand side and divide both sides by 400000

$1 = 2\frac{3 - d}{\sqrt{(3 - d)^2 + 4}}$

$\sqrt{(3 - d)^2 + 4} = 6 - 2d$

From here we can square up both sides

$(3 - d)^2 + 4 = (6 - 2d)^2$

$9 - 6d + d^2 + 4 = 36 - 24d + 4d^2$

$3d^2-18d+27 = 0$

$d^2 - 6d + 9 = 0$

$(d - 3)^2 = 0$

$d -3 = 0$

d = 3

So the cost of pipeline is minimum when P is exactly 3km east from the oil refinery.

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3 years ago