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3 years ago

Area of a regular hexagon with an apothem of 15 cm

Mathematics

1 answer:

Anton [14]3 years ago

8 0

Answer:

area = 779.4 cm²

Step-by-step explanation:

divide it into 6 equal equilateral triangles. Each corner of a triangle will be 60°.

tan 60° = 15/x

1.7321 = 15/x

x = 8.66 (this is one-half of the base of the triangle)

base = 17.32 cm

area of one triangle = 1/2(17.32)(15) = 129.9 cm²

129.9(6) = 779.4 cm² (because 6 triangles make up the hexagon)

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It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate

Hitman42 [59]

Answer:

The minimum sample size is n = 75 so that the desired margin of error is 5 or less.

Step-by-step explanation:

We are given the following in the question:

Population variance = 484

Standard deviation =

$\sigma^2 = 484\\\sigma =\sqrt{484} = 22$

Confidence level = 0.95

Significance level = 0.05

Margin of error = 5

Formula:

Margin of error =

$E = z\times \dfrac{\sigma}{\sqrt{n}}\\\\n = (\dfrac{z\times \sigma}{E})^2$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get

$E\leq 5\\\\1.96\times \dfrac{22}{\sqrt{n}} \leq 5\\\\\sqrt{n} \geq 1.96\times \dfrac{22}{5}\\\\n \geq (1.96\times \dfrac{22}{5})^2\\\\n \geq 74.373$

Thus, the minimum sample size is n = 75 so that the desired margin of error is 5 or less.

3 0

3 years ago

Please help help help help please help will give brainliest if correct

Margarita [4]

Answer:

15 divided by 3 = 5

Step-by-step explanation:

21 divided by 3 = 7

6 divided by 3 = 2

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3 years ago

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3 years ago

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tankabanditka [31]

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3 years ago

The school that Mary goes to is selling tickets to a spring musical. On the first day of ticket sales

andrezito [222]

Answer:

The cost of one adult ticket is $13, and the price of one student ticket is $4.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the cost of an adult ticket

y is the cost of a student ticket.

6 adult tickets and 1 student ticket for a total of $82

This means that

$6x + y = 82$

$y = 82 - 6x$

The school took in $51 on the second day by selling 3 adult tickets and 3 student tickets.

This means that

$3x + 3y = 51$

Simplifying by 3

$x + y = 17$

Since $y = 82 - 6x$

$x + 82 - 6x = 17$

$-5x = -65$

$5x = 65$

$x = \frac{65}{5} = 13$

$y = 82 - 6x = 82 - 6*13 = 82-78 = 4$

The cost of one adult ticket is $13, and the price of one student ticket is $4.

4 0

3 years ago