find geometric probability​

The height of the water in cylinder after inversion is h = R(2 - √3) cm.

The curved surface of a liquid in a container is known as a meniscus and is created by the intermolecular interactions between the liquid and the material of the container. The type of the liquid and the container, as well as outside variables like temperature and pressure, all affect the meniscus' form. A concave meniscus has a liquid surface that is lower in the middle than it is at the edges, whereas a convex meniscus has a liquid surface that is higher in the middle than it is at the edges. Many scientific and technical applications, such as figuring out a liquid's surface tension or how fluids behave in microfluidic devices, might benefit from understanding the geometry of the meniscus.

Let us suppose the height of the water level after inversion = h.

The volume of the figure 1 is:

V1 = πR²(R-h)

where, (R-h) represents the height of the cylinder filled with water.

When inversion takes place water forms a smaller hemisphere with radius h.

The volume is:

V2 = 2/3 πh³ + πh² (R-h)

Setting the equations:

V2 = 2/3 πh³ + πh² (R-h)

h = R(2 - √3)

Hence, the height of the water after inversion is h = R(2 - √3) cm.

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Answer:

y=2

Step-by-step explanation:

Hey there!

The answer is y=2 because the x-axis is not defined (there's no value for it as the line didn't pass through it)

Answer:

try 594 divided by 16

Step-by-step explanation:

sorry if I'm wrong but hope it helps

In this case, Anika can choose to read the books over the summer in 604800 different orders.

Different orders can be chosen by Anika to read the books over the summer. This can be calculated using the permutation formula.

The formula for permutation is:

P(n,r) = n!/(n-r)!

Where:

P = permutation

n = total number of items

r = number of items taken at a time

In this case, n = 9 (total number of books) and r = 9 (number of books taken at a time).

Therefore,P(9,9) = 9!/(9-9)! = 9!/0! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 = 604800

Hence, Anika can choose to read the books over the summer in 604800 different orders.

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The time restriction faced by ABC Corporation for it to buy back its newly issued shares is 4 weeks

What is share buyback?

Share buyback means that the company would repurchase its own shares in the stock market by paying investors holding the shares, then reduce its number of shares outstanding by the number of shares bought back.

The shares repurchased are known as Treasury stocks, which are held until the company decides to reissue them or cancel them.

The restriction placed on a company before it can repurchase its shares is that the shares must be in issue 4 weeks, in other words, the new issued shares through Initial Public Offer(IPO) must be existence for 4 weeks before being repurchased by the company after having issued an IPO.

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The volume is 63.717 cubic units

The limits of integration for rho are 0 and 4 cos phi, since the sphere has radius 4 cos phi. The limits for phi are π/4 and π/2, since we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of a point. Finally, the limits for theta are 0 and 2π, since theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.

Thus, the volume of the region is given by:

V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos phi) ρ² sin phi dρ dphi dtheta

Simplifying the integral using basic calculus, we get:

V = 8 x (64/3 - 16/3√2π) = 63.717

Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere rho = 4 cos phi is 8(64/3 - 16/3√2π), which is an exact answer using π as needed.

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Answer:

Arrowhead +15

Bone +721

Clay bowl +0

Necklace +462

Woven basket -1200

Step-by-step explanation:

the clay bowl is directly at sea level. so, it's +0 away from sea level.

Answer:

\(2x = 8\)

Step-by-step explanation:

We first need to find the value of 'x'.

This means that we need to solve for 'x' in the equation that is given.

======================================================

\(5x - 3 = 17\\\rule{150}{0.5}\\5x - 3 + 3 = 17 + 3\\\\5x = 20\\\\\frac{5x = 20}{5}\\\\\boxed{x = 4}\)

The value of 'x' is 4.

======================================================

We then need to find the value of '2x' by replacing x with '4' and then evaluating.

\(2x; x= 4\\\rule{150}{0.5}\\2 \times 4\\\\\boxed{8}\)

The value of '2x' is 8.

======================================================

Hope this helps!

Answer

1

\((a + b)^{2} = {a}^{2} + 2ab + {b}^{2} \)

Therefore

Answer:

1

Step-by-step explanation:

SEE IMAGE FOR Solution ...

The probability of getting heads is 31/50.

Number of tosses = 50

Number of heads = 31

The probability of getting heads will be:

= Number of heads / Total number of tosses

= 31/50

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The completed relative frequency table is given by the image shown at the end of the answer.

First we look at the row total of people who like to fly, which is of 70%, hence:

Amount those who can drive, we have that:

Amount those who cannot drive, we have that:

Thus the total frequency of the second row is given as follows:

0.17 + 0.13 = 0.30.

The table is given by the image shown at the end of the answer. I don't know if the values are the same but you will have to follow the same procedure to obtain the missing values.

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Answer:

I took the test

the answer is in the image below

Step-by-step explanation:

Theresa uses 14.81 inches of fabrics on an headband and 8.54 inches on a wristband for each player.  

She uses 533.16 inches of fabric on  headbands for 33 players and 3 coaches.

let

x = fabric use for each headbands

Therefore,

33x + 3x = 533.16

36x = 533.16

x = 533.16 / 36

x = 14.81 inches

let

y = fabrics use for each wristband for players

33y = 281.82

y = 281.82 / 33

y = 8.54 inches

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Answer:

(0,-4)

Step-by-step explanation:

The x coordinate comes first in the ordered pair

We do not move left or right from the origin so the x coordinate is zero

The y coordinate is second, we move 4 units down so the y coordinate is negative 4

The ordered pair is (0,-4)

Answer:  brainliest please

Part 1) Option D

Part 2) Option C

Step-by-step explanation:

we know that

In a Rhombus

Opposite angles are congruent, and consecutive angles are supplementary. All sides are congruent by definition. The diagonals bisect the angles

Part 1) What is the measure of angle  ?

-----> remember that the diagonals bisect the angles

Part 2) What is the measure of angle  ?

Remember that

In a rhombus consecutive angles are supplementary

so

The measure of angle  is equal to the measure of angle T divided by

Step-by-step explanation:

Answer:

___________________________________________________________

FACTS TO KNOW BEFORE SOLVING :-

___________________________________________________________

According to the question ,

a) \(\sqrt{18} =\sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}\)

b) \(\sqrt{12} =\sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}\)

c) \(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}\)

Answer:

B. Square

Step-by-step explanation:

Finding the side lengths :

Side 1

⇒ d₁ = √(-4 - 0)² + (8 - 8)²

⇒ d₁ = √16

⇒ d₁ = 4

=============================================================

Side 2

⇒ d₂ = √(-4 + 4)² + (8 - 4)²

⇒ d₂ = √16

⇒ d₂ = 4

===========================================================

Side 3

⇒ d₃ = √(-4 - 0)² + (4 - 4)²

⇒ d₃ = √16

⇒ d₃ = 4

============================================================

Side 4

⇒ d₄ = √(0 - 0)² + (8 - 4)²

⇒ d₄ = √16

⇒ d₄ = 4

As all sides of the figure are equal, and it creates 4 right angles, it is a square.

Answer:

It says or, so you can answer any however the answer to time would be 4 years or so

Step-by-step explanation:

10x5 = 50

50x50 = 2500

2500x.4= 1000

1000/250=4

4

The first five terms of the given sequence are:

a1 = -2

a2 = -5/11

a3 = 0

a4 = 7/67

a5 = 1/8

Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

For given question,

We have been given a sequence \(a_n=\frac{n^2-9}{n^3+3}\)

We need to find the first five terms, a1, a2, a3, a4, a5, of the sequence.

For n = 1,

\(a_1=\frac{1^2-9}{1^3+3} \\\\a_1=\frac{-8}{4} \\\\a_1=-2\)

For n = 2,

\(a_2=\frac{2^2-9}{2^3+3}\\\\ a_2=\frac{-5}{11}\)

For n = 3,

\(a_3=\frac{3^2-9}{3^3+3} \\\\a_3=\frac{0}{30}\\\\ a_3=0\)

For n = 4,

\(a_4=\frac{4^2-9}{4^3+3} \\\\a_4=\frac{7}{67}\)

For n = 5,

\(a_5=\frac{5^2-9}{5^3+3} \\\\a_5=\frac{16}{128}\\\\ a_5=\frac{1}{8}\)

Given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

Therefore, the first five terms of the given sequence are:

a1 = -2

a2 = -5/11

a3 = 0

a4 = 7/67

a5 = 1/8

Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

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Answer:

a is 5 and b is 6 but I am not sure but I hope it helps

Answer:

x = 72

Step-by-step explanation:

\(\frac{x}{16}=\frac{9}{2} \\\\\)

Start by multiplying 16 to both sides

\((\frac{16}{1}) * \frac{x}{16} = (\frac{16}{1}) * \frac{9}{2}\)

16s on the left-hand cancel

\(x =(\frac{16}{1}) * (\frac{9}{2})\)

\(x =( \frac{144}{2} )\)

we can simplify that expression

\(x = 72\)

Answer:

20 feet up

Step-by-step explanation:

its quite simple really, just add 15+5 and you get 20

To find the surface area of a pyramid with an equal side length base, you need to know the length of one side of the base and the slant height of the pyramid. Let's call the side length of the base "s" and the slant height "l".

The surface area of a pyramid can be calculated using the formula:

Surface Area = (1/2) * perimeter of base * slant height + base area

The perimeter of the base of the pyramid is simply 4s (since all sides are equal). The base area can be found by using the formula for the area of a square, which is s^2. Putting this all together, we get:

Surface Area = (1/2) * 4s * l + s^2

Simplifying this expression gives us:

Surface Area = 2sl + s^2

Therefore, the surface area of a pyramid with an equal side length base is given by the formula 2sl + s^2.

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Answer:It is given b the x2 of the anwserr fot the firghjt angle

Step-by-step explanation:

Answer:

The question is unclear, but yes, if you plug in x as 7, then y does equal 3

Step-by-step explanation:

y = x - 3

Now, if x =7, then:

y = 7 - 3,

so y=4

System of Equations

Given the system of equations:

x + z = 6

2x + 4z = 1

To solve the system by the elimination method, we must make the coefficients of one variable opposite.

It's required to eliminate the z-term which means we must make the coefficients of z opposite on both equations.

The coefficient of z is 4 in the second equation, so to eliminate the variable, we must multiply the first equation by -4 as follows:

-4x - 4z = -24

Now when we add both equations, the z is eliminated.

Answer: Multiply equation A by −4.

Answer:

If Ally and Bo share evenly, Bo will get 30$, so will Ally. The half of 60 is 30.

Answer:

  $3846.87

Step-by-step explanation:

Assuming the interest is compounded annually, the value in 3 years is ...

  FV = P(1 +r)^t

  FV = $3500(1.032^3) ≈ $3846.87

Sarah's account will be worth about $3846.87.

Answer:

- 4

Step-by-step explanation:

The absolute value of a number renders a number positive regardless of the preceeding sign. Therefore, either a number is positive or negative, the absolute value of such number will be positive.

In a number line, 0 is the midpoint and values to the left of 0 are negative, while those to the right are positive.

For the scenario, above, the bug is to the left of 0 and has an absolute value of 4 ;

The current position of the number line will be 4 (absolute value) places to the left of 0 which is - 4 (negative numbers are in the left).

The measure of PRS is 70°, So correct option is D.

A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, away from a given central point. Circles are unique among shapes because they have no corners, sides, or edges and are continuous, meaning that they have no gaps or breaks. The circumference of a circle is the distance around its outer edge and is equal to 2π times the radius. The area of a circle is the amount of space contained within its circumference and is equal to π times the square of the radius. Circles are used in a variety of applications, from mathematics and science to engineering, design, and art. In mathematics, circles are used to understand concepts such as angles, arc lengths, and curvature. In science and engineering, they are used to model physical phenomena, such as the motion of planets and the flow of fluids. In design and art, circles are used to create visually appealing patterns, logos, and symbols. The circle is considered a symbol of unity, wholeness, and completeness.

In triangle QRS, angle SQR is 20°, so angle QSR is 180° - 20° = 160°. Since point P is the midpoint of side QR, angle QRP is equal to half of angle QSR, or 160° / 2 = 80°. Therefore, angle PRS = 180° - 80° = 100°. So the measure of angle PRS is 100°, making the answer D. 70°.

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The correct equation regarding the measure of angle 1 is m∠1 = one-half(b - d). (Option c)

According to the given information, the measure of angle 1 is half the difference between b and d. We can represent this information using the equation:

m∠1 = one-half(b - d)

We can simplify this equation by distributing the one-half term, which gives:

m∠1 = 1/2 * b - 1/2 * d

Therefore, the correct equation regarding the measure of angle 1 is m∠1 = one-half(b - d). This equation tells us that the measure of angle 1 is equal to half the difference between b and d. We can use this equation to find the measure of angle 1 if we are given the values of b and d.

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Complete Question:

Which equation is correct regarding m∠1?

m∠1 = one-half(a - c)

m∠1= one-half(a + c)

m∠1 = one-half(b - d)

m∠1 = one-half(b + d)