A stained glass window is in the shape of an equilateral triangle. what is the measure of one interior angle of the triangle

Answer:

V = 216 pi cm^3.

Step-by-step explanation:

The number pi relates the diameter of a circle to its circumference. Therefore, the correct option to fill in the blank is:

a. circumference

The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The sum of the two numbers is 45. One number is 4 times as large as the other.

Let the two numbers be x and y. Then the equation is given as,

x + y = 45      ...1

y = 4x            ...2

From equations 1 and 2, then we have

x + 4x = 45

5x = 45

x = 9

Then the value of y will be

y = 4(9)

y = 36

The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.

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Final answer:

By dividing the total minutes (72) by the minutes per problem (6), we find that the student can solve 12 algebra problems in 72 minutes.

Explanation:

The student asking how many algebra problems can be solved in 72 minutes if each problem takes 6 minutes can be answered with a simple division operation. You divide the total available time by the time taken for each problem to find the number of problems that can be solved. In this case, 72 minutes ÷ 6 minutes per problem equals 12 problems.

To find the value of X in a rectangle with width X and length 2X, we can use the area formula. By solving the equation, we find X = 9, making the width of the rectangle 9 units.

To find the value of X, we need to use the given information about the length and width of the rectangle. Let's assume the width of the rectangle is X. Since the length is double the width, it is 2X. The area of the rectangle is given as 162, so we can set up the equation:

Width × Length = Area

X × 2X = 162

Simplifying the equation, we get:

2X^2 = 162

Dividing both sides by 2, we have:

X^2 = 81

Taking the square root of both sides, we find:

X = ±9

Since the width cannot be negative, the value of X is 9. Therefore, the width of the rectangle is 9 units.

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The width of the rectangle is 9 units.

To find the width of the rectangle, we can set up the equation for the area. The width of the rectangle is X, and the length is twice the width, meaning the length is 2X. The formula for the area is length times width, so we have X * 2X = 162. Simplifying this equation gives us 2X^2 = 162. Dividing both sides by 2 gives us X^2 = 81. Taking the square root of both sides gives us X = 9. Therefore, the width of the rectangle is 9 units.

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The correct answer is [tex]\frac{1}{2}[/tex].

To find the exact value of [tex]\cos(5\pi/12)[/tex] using a half-angle formula, we can follow these steps:

[tex]\cos(2\theta) = 2\cos^2(\theta/2) - 1[/tex]

Substituting [tex]\theta = 5\pi/6[/tex], we get:

[tex]\cos(5\pi/3) = 2\cos^2(5\pi/12) - 1[/tex]

[tex]\cos^2(5\pi/12) = \frac{\cos(5\pi/3) + 1}{2}[/tex]

[tex]\cos(5\pi/3) = \cos(\pi/3 + \pi) = -\cos(\pi/3)[/tex]

[tex]\cos(\pi/3) = \frac{1}{2}[/tex]

[tex]\cos(5\pi/3) = -\frac{1}{2}[/tex]

[tex]\cos^2(5\pi/12) = \frac{-\frac{1}{2} + 1}{2} = \frac{1}{4}[/tex]

[tex]\cos(5\pi/12) = \pm\sqrt{\frac{1}{4}} = \pm\frac{1}{2}[/tex]

Since cosine is an even function, we take the positive value.

[tex]\cos(5\pi/12) = \frac{1}{2}[/tex]

Therefore, the exact value of [tex]\cos(5\pi/12)$ is $\frac{1}{2}[/tex].

Complete question:

Use a half angle formula to find the exact value of the expression?

[tex]\cos(5\pi/12)[/tex]

Answer:

The answer is "120"

Step-by-step explanation:

I did it myself, and this is the answer i got :) I made sure it was correct but let me know if you have problems!

Answer:

Her probability to win the prize quilt is 0.06, or she has a 6% probability of winning it.

Step-by-step explanation:

In statistics, a probability of 100% is represented with a 1. In this case, if Sarah would have bought the 250 tickets, she would have a probability of 1 to win the prize, as

[tex]\frac{250}{250}=1[/tex]

then, if this expression is multiplied by 100, we could say that the precentage of probability would have been 100%...

But Sarah didn't buy the 250 tickets, instead she bought 15, therefore

[tex]\frac{15}{250}=\frac{3}{50}=0.06[/tex]

which means that the probability of her winning the prize quilt is 0.06, or, if multiplied by 100, she has a 6% probability of winning the prize quilt.

Real Question:

You Make A Table To Use AS A Quick Reference Guide. [tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]

Use The Table Tool To Answer The Question:

[tex]\left[\begin{array}{ccc}-8&-104\\-9&-92\\-10&-80\\-11&-68\\-12&-56\end{array}\right][/tex]

What is the y-value when x equals -11?  

[tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]

Step-By-Step Explanation:

Plug In The X-Value [tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\end{array}\right][/tex]

Then You'll Multiply [tex]\left[\begin{array}{ccc}-12(x) Or -12(-11)\\132\end{array}\right][/tex]

To Find The Y-Value Simplify [tex]\left[\begin{array}{ccc}y=-200+132\\y=-68\end{array}\right][/tex]

Answer:

[tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\\y=-200+132\\ y=-68\end{array}\right][/tex]

Answer with explanation:

it is given that ,6.8% of standard normal curve lies to left of z.

6.8% [tex]=\frac{6.8}{100}\\\\=0.068[/tex]

We will use z table to calculate the value of z.

First we will go on y axis in z table to see value of 0.06 and then on 0.08 on x axis.Their point of intersection will give value of z at 0.068, which is equal to 0.2483.

Value of Z ,at 6.8% ,when the curve is normal = 0.25

⇒0.25 represents area in the left of ,z=0.068.

The z-score corresponding to 6.8% in the standard normal distribution is approximately -1.48, rounding to two decimal places, ensuring 6.8% lies to the left.

To find the z-score such that 6.8% of the standard normal curve lies to the left of it,

use a standard normal distribution calculator.

For the z-score corresponding to the cumulative probability of 0.068 (6.8%).

Using a standard normal distribution calculator:

The cumulative probability of 0.068 (or 6.8%) in the standard normal distribution calculator.

find the z-score associated with this probability.

The z-score corresponding to a cumulative probability of 0.068 is approximately -1.48 (rounded to two decimal places).

Therefore, the z-score z such that 6.8% of the standard normal curve lies to the left of it is approximately -1.48.

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