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lana66690 [7]
3 years ago
7

To form 3 adjacent squares (as in the figure), 10 toothpicks are required. How many toothpicks are required to form 100 adjacent

squares? ...?
Mathematics
1 answer:
Sonja [21]3 years ago
7 0
<span>Let's say in general you want "n" adjacent squares. Each one needs a top, so that's n toothpicks. Each one needs a bottom, so that's another n toothpicks, and we're up to 2n total. You need one on the far left, and one on the far right, which brings us up to 2n + 2 toothpicks. Now we need to worry about the middle ones. But notice that you don't need n toothpicks for the interior because adjacent squares share. It turns out that you only need n-1. That brings us up to a grand total of 3n + 1 toothpicks, which would be 301 for n = 100.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
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Answer:

Below in bold.

Step-by-step explanation:

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iii) Amount = 100000(1 + 0.04/4)^(3)

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Step-by-step explanation:

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In a city with 40000 people, each person has a 0.00020 probability of committing a crime each hour. What is the probability that
galina1969 [7]

Answer:

2.86% probability that there are exactly 3 crimes during the next hour

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 time interval.

In a city with 40000 people, each person has a 0.00020 probability of committing a crime each hour.

So \mu = 40000*0.0002 = 8

What is the probability that there are exactly 3 crimes during the next hour

This is P(X = 3).

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

P(X = 3) = \frac{e^{-8}*(8)^{3}}{(3)!} = 0.0286

2.86% probability that there are exactly 3 crimes during the next hour

8 0
3 years ago
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Point B is the center of the circle shown, and the length of arc AC is 8π. What is the area of the circle?
Gwar [14]

Answer:

A=324\pi \text{ units}^2\approx1017.88\text{ units}^2

Step-by-step explanation:

The formula for arc length is:

\stackrel{\frown}{A}=2\pi r(\frac{\theta}{360}})

Where Θ is measured in degrees.

We know that the arc length is 8π when the degree is 80. So, substitute 8π for A and 80 for Θ:

8\pi=2\pi r(\frac{80}{360})

Divide both sides by 2π:

4=r\frac{80}{360}

Simplify the fraction:

4=\frac{2}{9}r

Multiply both sides by 9/2:

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So, the radius is 18.

Now, we can find the area of the circle. The formula for the area of a circle is:

A=\pi r^2

Substitute 18 into r:

A=\pi (18)^2

Simplify:

A=324\pi \text{ units}^2\approx1017.88\text{ units}^2

And we're done!

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3 years ago
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