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bekas [8.4K]
3 years ago
10

Combinatorics problem. A web site was hit 300 times over a period of 15 days Show that over some period of 3 consecutive days, i

t was hit at least 60 times.
Mathematics
1 answer:
crimeas [40]3 years ago
6 0

Answer:

There is a period of 3 consecutive days in which the website was hits at least 60 times.

Step-by-step explanation:

A web site was hit 300 times over a period of 15 days.

To solve this question we will use the Pigeonhole Principle.

Here, n = 300 and k = 5

We will find \frac{n}{k} to get that there is a hole with at least \frac{300}{5}=60 pigeons.

Hence, there is a period of 3 consecutive days in which the website was hits at least 60 times.

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Solve the system of equations y = 2x + 3 and 4x - 2y = -6 using a graphical method.
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Answer:

-1

Step-by-step explanation:

You are asked to solve this set by substitution. Note that the first equation defines

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in the second equation, the result is:

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2x + 3 = 4x + 7

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Let's set the goal of getting all the terms that contain x isolated on the left side of

the equal sign and all the constants by themselves on the right side. Begin by getting rid

of the +3 on the left side by subtracting 3 from the left side. But if you subtract

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result in the following sequence:

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2x + 3 - 3 = 4x + 7 - 3

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Combining numbers on the left side and on the right side simplifies the equation to:

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2x = 4x + 4

.

Now, in a similar fashion, let's get rid of the 4x on the right side by subtracting

4x from the right side. When we do this subtraction, to keep the equation in balance

we must also subtract 4x from the left side. This results in:

.

 

2x - 4x = 4x - 4x + 4

.

On both sides of the equation combine terms containing x to get:

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-2x = 4

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Finally, solve for x by dividing both sides of the equation by -2 because -2 is the multiplier

of x. This results in:

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x = 4/-2 = -2

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So now that we know x = -2, we can return to either one of the original equations  

in the equation set and substitute -2 for x. Then we can solve for y. Let's return

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y = 2x + 3

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Then substituting -2 for x gives:

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y = 2*(-2) + 3 = -4 + 3 = -1

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3 years ago
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