Round each number to the nearest 100 <br> 976

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

2 years ago

A survey of 80 randomly selected companies asked them to report the annual income of their presidents. Assuming that incomes are

Artyom0805 [142]

Answer:

The 90% confidence interval estimate of the mean annual income of all company presidents is ($579,545, $590,580).

Step-by-step explanation:

The information provided is:

$n=80\\\sigma=30,000\\\bar x=585062.50\\\text{Confidence level} = 90\%$

The critical value of <em>z</em> for 90% confidence level is, 1.645.

Compute the 90% confidence interval estimate of the mean annual income of all company presidents as follows:

$CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\\\\=585062.50\pm 1.645\times\frac{30000}{\sqrt{80}}\\\\=585062.50\pm5517.50\\\\=(579545, 590580)$

Thus, the 90% confidence interval estimate of the mean annual income of all company presidents is ($579,545, $590,580).

This interval implies that there is 90% probability that the true mean annual income of all company presidents is within this interval.

4 0

2 years ago

28:solve: PLEASE HELP -0.25x+1.75x<-1.75+2.5x. (round your answer to the nearest hundredth)

Lena [83]

Answer:

Step-by-step explanation:

-0.25x+1.75x<-1.75+2.5 x

sift terms containing x to right and constant term to left

1.75<2.5 x+0.25x-1.75 x

1.75<2.75x-1.75x

1.75<1.00 x

or 1.75 <x

or x>1.75

7 0

2 years ago

Use the figure below to complete the following problem Given : R,S,T are midpoints of AC, AB, and CB.

Nikolay [14]

Answer:

answer=RT

Step-by-step explanation:

because

3 0

2 years ago

Read 2 more answers

Noah started with a number, x. He took the difference of four times the number and three and cubed the result. Write the express

Oksi-84 [34.3K]

Answer:

The expression representing Noah’s new number is $(4x-3)^3.$

Step-by-step explanation:

Noah started with a number, x.

Four times the number x is 4x

The difference of four times the number and three is 4x - 3

The difference of four times the number and three cubed is $(4x-3)^3$

Thus, the expression representing Noah’s new number is $(4x-3)^3.$

4 0

3 years ago

Round each number to the nearest 100 976