Richard works from 11:00am to 3:00am dinner break is 75% of the way though work shift what time is his dinner break

A square is inscribed in a circle with an area of 10 pi square inches. what is the area of the square

Naddik [55]

We need to determine the radius and diameter of the circle. If the area of the circle is 10 pi in^2, then, according to the formula for the area of a circle,

A = 10 pi in^2 = pi*r^2. Thus, 10 in^2 = r^2, and r = radius of circle = sqrt(10) in.

Thus, the diam. of the circle is 2sqrt(10) in. This diam. has the same length as does the hypotenuse of one of the triangles making up the square.

Thus, [ 2*sqrt(10) ]^2 = x^2 + x^2, where x represents the length of one side of the square. So, 4(10) in^2 = 2x^2. Then:
40 in^2 = 2x^2, or 20 in^2 = x^2, and so the length x of one side of the square is sqrt(20). The area of the square is the square of this result:

Area of the square = x^2 = [ sqrt(20) ]^2 = 20 in^2 (answer). Compare that to the 10 pi sq in area of the circle (31.42 in^2).

8 0

3 years ago

12, 9, 15, 19, 20, 15<br><br> Mean <br><br> Median <br><br> Mode

Ede4ka [16]

Answer:

Mean: 15

Median: 15

Mode: 15

Step-by-step explanation:

<h2>Definitions:</h2>

<u>Mean</u>: It represents the average value of a given data set. The formula for finding the mean of a given set of numbers by taking the quotient of all numbers and the number of values. In other words:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

<u>Median:</u> It represents the middle value in a given set of numbers. In order to determine the median, it is essential to arrange the given data either in <em>ascending</em> or <em>descending</em> order (although it is customary to arrange the numbers into ascending order).

If there is an odd number of values in a given set, then the <u>middle number</u> is the median of that set.

If a given list comprises of an even number of items, then we must take the <em>average</em> of the two middle numbers.

<u>Mode</u>: It represents the number that <u>occurs most often</u> on a list of items or data.

<h2>Solution:</h2><h3><u>Find the Mean:</u></h3>

Using the formula provided in the previous section for finding the mean:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

$\displaystyle\mathsf{Mean\:=\:\frac{12+9+15+19+20+15}{6}\:=\:\frac{90}{6}\:=\:15}$

<h3><u>Find the Median:</u></h3>

Arrange the given data set in <u><em>ascending order</em></u>:

12, 9, 15, 19, 20, 15 ⇒ 9, 12, <u>15</u>, <u>15</u>, 19, 20

Next, since there is an even number of items on our given data set, we must <u>take the average of the</u><u> two middle numbers</u> (which are 15 and 15):

$\displaystyle\mathsf{Median\:=\:\frac{15+15}{2}\:=\:\frac{30}{2}\:=\:15}$

Therefore, the median is 15.

As described in the previous section of this post, the mode is the number that occurs most often on our given data. The only repeating number on our list is 15, hence it is the mode.

Therefore, the <em>mean</em>, <em>median</em>, and <em>mode</em> of the given data set is <u>15</u>.