Please help me! (probability models)

Given a 30-60-90 triangle with a long leg of 9 inches, determine the length of the hypotenuse

lianna [129]

A Quick Guide to the 30-60-90 Degree Triangle

The 30-60-90 degree triangle is in the shape of half an equilateral triangle, cut straight down the middle along its altitude. It has angles of 30°, 60°, and 90°. In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, you can find the long leg by multiplying the short leg by the square root of 3.

Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. The long leg is the leg opposite the 60-degree angle.

Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles. All 30-60-90 triangles, have sides with the same basic ratio. If you look at the 30–60–90-degree triangle in radians, it translates to the following:

30, 60, and 90 degrees expressed in radians.

The figure illustrates the ratio of the sides for the 30-60-90-degree triangle.

A 30-60-90-degree right triangle.

If you know one side of a 30-60-90 triangle, you can find the other two by using shortcuts. Here are the three situations you come across when doing these calculations:

Type 1: You know the short leg (the side across from the 30-degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.

Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.

Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.

Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.

In the triangle TRI in this figure, the hypotenuse is 14 inches long; how long are the other sides?

Because you have the hypotenuse TR = 14, you can divide by 2 to get the short side: RI = 7. Now you multiply this length by the square root of 3 to get the long side:

The long side of a 30-60-90-degree triangle.

6 0

3 years ago

Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP

-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$$\Rightarrow \frac{h}{2}=r$

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

$$\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3$ (formula)

$$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3$

$$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3$

Hence it is true.

Option A, option C and option E are true.

6 0

4 years ago

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How many different 10 person committees can be selected from a pool of 23 people?

Salsk061 [2.6K]

We're going to be using combination since this question is asking how many different combinations of 10 people can be selected from a set of 23.

We would only use permutation if the order of the people in the committee mattered, which it seems it doesn't.

Formula for combination:

$C(n,r)=\dfrac{n!}{(n-r)!r!}$

Where $n$ represents the number of objects/people in the set and $r$ represents the number of objects/people being chosen from the set

There are 23 people in the set and 10 people being chosen from the set

$C(23,10)=\dfrac{23!}{(23-10)!10!}$

$=\dfrac{23!}{13!\times10!}$

Usually I would prefer solving such fractions by hand instead of a calculator, but factorials can result in large numbers and there is too much multiplication. Using a calculator, we get

$=1,144,066$

Thus, there are 1,144,066 different 10 person committees that can be selected from a pool of 23 people. Let me know if you need any clarifications, thanks!

~ Padoru

4 0

3 years ago

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Which number replaces the box to make this a true number sentence?

valkas [14]

Answer:

C. 5

Step-by-step explanation:

first expression 5 × (9-3) = 30

second one 45 - 3x

to make it 30 = 30

x should be = 5

8 0

3 years ago

Which one is higher -33 ft or -92 ft

ahrayia [7]

Answer:

-92

Step-by-step explanation:

because its farther away from 0

8 0

3 years ago

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