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Harman [31]
3 years ago
9

A 70 meter path surrounds a rectangular garden. the width of the garden is two thirds it's length. Find its area

Mathematics
1 answer:
AlladinOne [14]3 years ago
6 0
You can set up an equation.
Let x = measure of the length.

Width: 2/3x
Length: x

From the question, we know that the perimeter is 70 and based on our prior knowledge, we know that for a rectangle, the perimeter is equal to 2 times the length added to two times the width.

2(2/3x + x) = 70
4/3x + 2x = 70
10/3x = 70
x = 21

So the length is 21 meters.
And since the width is 2/3 the length, 2/3 x 21 is 14.
So the width is 14 meters.

And if you add 21 + 21 + 14 + 14, it will equal 70 meters.

Now let's find the area.
21 x 14 = 294 square meters.
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The arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per hour.

This means that \mu = 2

What is the probability that in one hour more than 5 clients arrive

Either 5 or less clients arrive, or more than 5 do. The sum of the probabilities of these events is decimal 1. So

P(X \leq 5) + P(X > 5) = 1

We want P(X > 5). So

P(X > 5) = 1 - P(X \leq 5)

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P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

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

P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353

P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707

P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707

P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804

P(X = 4) = \frac{e^{-2}*2^{4}}{(4)!} = 0.0902

P(X = 5) = \frac{e^{-2}*2^{5}}{(5)!} = 0.0361

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P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9824 = 0.0176

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