Kris wanted to understand whether studentstudents at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below:

 
In favor
Opposed
Undecided
Grade 9
6
4
8
Grade 10
10
11
9
Grade 11
12
15
11
Grade 12
15
6
14


If the principal randomly selects a student in grade 10 from this survey, what is the probability that the student is opposed to extending the school day?

If they have a remainder of 4 when divided by six the sequence of terms are: 6n+4

42≤6n+4≤92

subtract 4 from both ends

 38≤6n≤88

divide both ends by 6

 6.3≤n≤14.6

since n must be an integer...

7≤n≤14 so the number of integers is:

14-7+1=8 

they are 6n+4 for n=[7,14]...46,52,58,64,70,76,82,88

There are 8 integers between 42 and 92, inclusive, that have a remainder of 4 when divided by 6. These integers can be expressed in the form of 6n + 4 and can be found by incrementally adding 6, starting from the smallest integer greater than 42 that meets this condition.

To find how many integers from 42 to 92, inclusive, have a remainder of 4 when divided by 6, we need to identify the numbers that fit the condition. These numbers are of the form 6n + 4, where n is an integer. Starting with the smallest number greater than 42 that fits the condition, which is 46 (as 6*7 + 4 = 46), we can find the next by adding 6 to get 52, then 58, and so on, up until we reach the largest number less than or equal to 92 that fits the condition, which is 88 (as 6*14 + 4 = 88).

To find the total count, we calculate (88 - 46) / 6 + 1 = 42 / 6 + 1 = 7 + 1 = 8. Therefore, there are 8 numbers between 42 and 92 that have a remainder of 4 when divided by 6.

42/2 = 21

 21 = w +2w+3

21 = 3w +3

18 =3w

w = 18/3 = 6

 width is 6

 length = 6x2=12+3 = 15

6+6+15+15 = 42

 width = 6 m

 length = 15 m

it fills at 3 gallons per minute, but loses 2 gallons per minute

 3-2 =1, so it fills at 1 gallon per minute

200 gallons at 1 gallon per minute = 200 minutes,

200/60 = 3 hours and 20 minutes

Answer:

Angles are 34.59°, 85.08° and 60.33°

Step-by-step explanation:

Let ABC is a triangle, ( that show the dog park)

In which,

AB = 150 feet

BC = 98 feet

CA = 172 feet,

By the cosine law,

[tex]BC^2=AB^2+AC^2-2(AB)(AC)cos A[/tex]

[tex]2(AB)(AC)cos A=AB^2+AC^2-BC^2[/tex]

[tex]\implies cos A=\frac{AB^2+AC^2-BC^2}{2(AB)(AC)}-----(1)[/tex]

Similarly,

[tex]\implies cos B=\frac{AB^2+BC^2-AC^2}{2(AB)(BC)}-----(2)[/tex]

[tex]\implies cos C=\frac{BC^2+AC^2-AB^2}{2(BC)(AC)}-----(3)[/tex]

By substituting the values in equation (1),

[tex]cos A=\frac{150^2+172^2-98^2}{2\times 150\times 172}[/tex]

[tex]=\frac{22500+29584-9604}{51600}[/tex]

[tex]=\frac{42480}{51600}[/tex]

[tex]\approx 0.8233[/tex]

[tex]\implies m\angle A\approx 34.59^{\circ}[/tex]

Similarly,

From equation (2) and (3),

m∠B ≈ 85.0°, m∠C ≈ 60.33°

Answer: A is the correct answer.

Step-by-step explanation:

Just did the question, followed OP's advice since no one answered. Good luck.

Final answer:

To find the area of a triangle with sides in a given ratio, first find the value of x by setting up and solving an equation using the perimeter. Then, multiply each side by x to find the base and height of the triangle. Finally, substitute the base and height into the formula for the area of a triangle.

Explanation:

To find the area of a triangle, we can use the formula: Area = 1/2 × base × height. In this case, we don't know the base and height directly, but we do know that the sides of the triangle are in the ratio of 11:16:24. Let's assume the sides are 11x, 16x, and 24x. The perimeter of the triangle is 510 ft, which means 11x + 16x + 24x = 510. Simplifying this equation, we get 51x = 510. Therefore, x = 10. Now we can find the base and height of the triangle by multiplying the corresponding sides by 10. The base is 11x * 10 = 110 ft and the height is 16x * 10 = 160 ft.

Now we can substitute these values into the formula to calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 110 ft × 160 ft = 8800 square feet.

Each one of the remaining angles measures 60°.

We know that the sum of the interior angles of a closed figure of n sides is given by:

(n - 2)*180°.

A pentagon has 5 sides, so we use n = 5 and we get:

(5 - 2)*180° = 540°

Now we know that 3 angles add up to 420°.

Then the other two angles must add up to:

540° - 420° = 120°

And those two angles are equal, then each one measures:

120°/2 = 60°.

If you want to learn more about angles, you can read:

https://brainly.com/question/17972372

The sine of negative eleven pi divided by twelve is -0.5.

To find the sine of negative eleven pi divided by twelve, we need to determine the exact value of this trigonometric function. The sine function represents the ratio between the length of the side opposite the angle and the hypotenuse in a right triangle. In this case, the angle is negative, which means it lies on the negative y-axis. Remember that the unit circle can help us determine the values of trigonometric functions for any angle. By mapping the angle on the unit circle, we can see that -11π/12 is equivalent to -330 degrees. Since the sine function has a period of 360 degrees, we can find the reference angle by subtracting 360 degrees. So, the reference angle is 30 degrees (360 - 330).The sine of 30 degrees is 0.5. However, the angle is negative, so the sine function is negative. Therefore, the exact value of sine of -11π/12 is -0.5.

Final Answer:

The exact value of [tex]\(\sin\left(-\frac{11\pi}{12}\right)\)[/tex] is:
[tex]\[\frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]

Explanation:

To find the sine of an angle that is not one of the commonly known angles, such as [tex]\(-\frac{11\pi}{12}\)[/tex], we can use sine sum and difference identities. In this case, we know the sine of [tex]\(-\frac{\pi}{12}\)[/tex] is not a standard angle, but we can express it as a sum or difference of angles like [tex]\(-\frac{\pi}{4}\)[/tex] and [tex]\(-\frac{\pi}{3}\)[/tex] whose sines we do know.

The sum identity for sine is:
[tex]\[\sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b)\][/tex]

We can express the angle [tex]\(-\frac{11\pi}{12}\)[/tex] as the sum of two angles for which we do know the sine and cosine values, for example,[tex]\(-\frac{\pi}{4}\)[/tex] and [tex]\(-\frac{2\pi}{3}\)[/tex] because:
[tex]\[-\frac{11\pi}{12} = -\frac{3\pi}{4} - \frac{2\pi}{3}\][/tex]
Using the sum identity for sine, we can find the sine value as follows:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \sin\left(-\frac{3\pi}{4}\right)\cos\left(-\frac{2\pi}{3}\right) + \cos\left(-\frac{3\pi}{4}\right)\sin\left(-\frac{2\pi}{3}\right)\][/tex]

Now, let's find the values of sine and cosine for these angles.
[tex]\(\sin\left(-\frac{3\pi}{4}\right) = -\sin\left(\frac{3\pi}{4}\right) = -\sin\left(\frac{\pi}{2} + \frac{\pi}{4}\right) = -\frac{\sqrt{2}}{2}\)[/tex]since sine is an odd function.

[tex]\(\cos\left(-\frac{2\pi}{3}\right) = \cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2}\)[/tex] since cosine is an even function.

[tex]\(\cos\left(-\frac{3\pi}{4}\right) = \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2}\)[/tex] since cosine is an even function.

[tex]\(\sin\left(-\frac{2\pi}{3}\right) = -\sin\left(\frac{2\pi}{3}\right) = -\frac{\sqrt{3}}{2}\)[/tex] since sine is an odd function.

Substitute these trigonometric values into the sum identity:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \left(-\frac{\sqrt{2}}{2}\right)\left(-\frac{1}{2}\right) + \left(-\frac{\sqrt{2}}{2}\right)\left(-\frac{\sqrt{3}}{2}\right)\][/tex]

Simplify the expression:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\][/tex]
Combine the terms with a common denominator:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]

Therefore, the exact value of [tex]\(\sin\left(-\frac{11\pi}{12}\right)\)[/tex] is:
[tex]\[\frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]

The equation is 180 - x = 9 (90 - x).Then the measure of the angle will be 78.75 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

Let 'x' be the angle. Then the equation is given as,

180 - x = 9 (90 - x)

180 - x = 810 - 9x

8x = 630

x = 78.75 degrees

The measure of the angle will be 78.75 degrees.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ5

Answer:

[tex] \frac{11\sqrt{2}}{2}[/tex]

Step-by-step explanation:

In a 45-45-90 triangle, the length if the hypotenuse is 11

WE use the common ratio of 45-45-90 degree triangle

common ration is x: x: x sqrt(2)

x sqrt(2) is the length of the hypotenuse

[tex]x\sqrt{2} = 11[/tex]

Divide by sqrt(2) on both sides

[tex]x= \frac{11}{\sqrt{2}}[/tex]

To rationalize the denominator, multiply by sqrt(2) at the top and bottom

sqrt(2) * sqrt(2) = 2

[tex]x= \frac{11\sqrt{2}}{2}[/tex]

Answer:

Will’s Wrapping Company needs 7,720 mm of paper to wrap the chocolate bar.

The number that is 10 times less than 0.43 is 0.043, found by dividing 0.43 by 10.

The operation looks like this:

0.43*10^{-1} = 0.043.

Therefore, 0.43 is 10 times as much as 0.043

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

hope this helps!