3. In how many ways can you fill three different positions by choosing from 15 different people?
A. 3.2.1
B. 15 14 12.3
C. 15-3
D. 15 14 13

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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the answer will be thirty three cm.

Solution is y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))

The differential equations of the given system are: y1′=5y1+3y2y2′=3y1+5y2 The solutions to these equations are:y1(t)=c1e2t+c2e8t y2(t)=−c1e2t+c2e8tNow,

let's rewrite the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t).The vector form of y1(t) and y2(t) is as follows: y1 vector(t) = (1 0) (c1e2t) + (0 1) (c2e8t)y2 vector(t) = (-1 0) (c1e2t) + (0 1) (c2e8t)

Therefore, the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t) is as follows: y(t) = c1((1 0) (c1e2t) + (0 1) (c2e8t)) + c2((-1 0) (c1e2t) + (0 1) (c2e8t))y(t) = (c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1)y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))

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Answer:

Step-by-step explanation:

2x+6 ≤ 10  or  2x + 8 > 20

⇔ 2x ≤ 4  or  2x > 12

⇔ x ≤ 2  or  x > 6

Answer:

d

Step-by-step explanation:anser :d

Answer:

\(\sqrt{x} \int\limits^a_b {x} \, dx \pi\)Step-by-step explanation:

Answer:

To solve the equation 2sinx - sqrt(3) = 0, we can first add sqrt(3) to both sides to get:

2sinx = sqrt(3)

Then, we can divide both sides by 2 to isolate sin(x):

sinx = sqrt(3)/2

Now, we need to find all values of x that satisfy this equation. We can do this by recalling the values of sin(x) for which it equals sqrt(3)/2. These values occur at x = pi/3 and x = 2pi/3, since sin(pi/3) = sqrt(3)/2 and sin(2pi/3) = sqrt(3)/2. We can also note that sin(x) is positive in the first and second quadrants of the unit circle, where x is between 0 and pi.

Since the problem asks for solutions in the interval 0 ≤ x ≤ 2pi, the correct answers are:

b. pi/3

c. 2pi/3

Therefore, the solutions for x are x = pi/3 and x = 2pi/3. Answers a and d, 5pi/3 and 4pi/3 respectively, are not valid solutions since they fall outside the interval 0 ≤ x ≤ 2pi.

\(y > 3 \times 2 \\ solve \: for \: y \\ y > 6 \\ ye \: {6 + \infty }\)

Sorry that's all i know

Answer:

Approximately 0.11 acres can be planted with one pound of seed

Step-by-step explanation:

You use the rule of 3

66 pounds / 7 acres = ? pounds / 1 acre

? = 66 x 1 ÷ 7

? = 66 ÷ 7

? ≈ 9.23 pounds / acre

Now you know how many pounds you have for 1 acre. You reuse the formula from before

9.23 pounds / 1 acre = 1 pound/ ? acres

? = 1x1 ÷ 9.23

? = 1 ÷ 9.23

? = 0.11 acres/pound

Verify the answer:

0.11 x 9.23 ≈ 9.33, which is approximately 1 pound

Answer:

90 pounds per acre

Step-by-step explanation:

Im right

Answer:

false

Step-by-step explanation:

Answer: the answer is 129

Step-by-step explanation: 180 subtract by 51 and it will give u 129

Answer:

129 degrees

Step-by-step explanation:

A straight line measurement is 180 degrees.

180 - 51 = 129 degrees

The dimensions of the box that maximize the volume are x = √700 and h = 100 / √700.

To find the largest possible volume of the box, we need to optimize the dimensions of the box. Let's denote the length of each side of the square base as x and the height of the box as h.

The surface area of the box consists of the area of the square base (x^2) and the four sides of the box (4xh). Since the box has an open top, we do not consider the top surface. The total surface area is given as 2100 square centimeters, so we have:

x^2 + 4xh = 2100

To maximize the volume, we need to express the volume of the box (V) in terms of a single variable. The volume of a rectangular prism is given by V = x^2h.

We can rewrite the equation for the surface area to solve for h:

h = (2100 - x^2) / (4x)

Now we can substitute this expression for h in the volume equation:

V = x^2 * [(2100 - x^2) / (4x)]

Simplifying, we have:

V = (1/4) * (2100x - x^3)

To find the maximum volume, we need to find the critical points of this function. We take the derivative of V with respect to x and set it equal to zero:

dV/dx = 2100/4 - (3/4)x^2 = 0

Solving this equation, we find:

2100/4 = (3/4)x^2

x^2 = 700

x = √700

Substituting this value back into the equation for h, we find:

h = (2100 - 700) / (4 * √700) = 1400 / (4 * √700) = 100 / √700

Therefore, the largest possible volume of the box is:

V = (1/4) * (2100 * √700 - 700 * √700) = 350√700 cubic centimeters.

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X-intercept (5,0),(1,0)

Y-intercept (0,5)

Vertex (3,-4)

Axis of Symmetry x=3

Answer:

Its B

Step-by-step explanation:

0=0

For the full explanation simply copy and paste your equation to your device browser.

Answer:

2p+15-11p=3(5-3p)

2p-11p+15=15-9p

-9p+9p=15-15

p£R

Answer:

i have made it in pic above

The null hypothesis (H₀) states that people living in rural Idaho communities have an average lifespan of 77 years or less, while the alternative hypothesis (Hₐ) suggests that their average lifespan exceeds 77 years.

In this scenario, the null hypothesis (H₀) assumes that the average lifespan of people in rural Idaho communities is 77 years or lower. On the other hand, the alternative hypothesis (Hₐ) proposes that their average lifespan is greater than 77 years. The random sample of 20 obituaries from rural towns in Idaho provides data with a sample mean (x) of 80.63 and a sample standard deviation (s) of 1.87. To determine if this sample provides evidence to support the alternative hypothesis, further statistical analysis needs to be conducted, such as hypothesis testing or confidence interval estimation.

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Answer:

no se amigos jajajajjajaaa no se

The angles in the triangle are as follows:

m∠1 = 51 degrees

m∠2 = 33 degrees

m∠3 = 123 degrees

m∠4 = 24 degrees

The sum of angles in a triangle is 180 degrees. A right angle triangle is a triangle with one of its angles as 90 degrees.

Therefore, let's find the missing angle of the triangle.

Hence,

m∠1 = 180 - 72 - 57(sum of angles in a triangle)

m∠1 = 51 degrees

m∠2 = 90 - 72

m∠2 = 33 degrees

m∠3 = 180 - 57(sum of angles on a straight line)

m∠3 = 123 degrees

m∠4 = 180 - 123 - 33

m∠4 = 24 degrees

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Answer:  −7

Step-by-step explanation:

The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function.The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

A function creates an output from an input.

The name of the function, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, and the output, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, are all enclosed in parentheses.

x2 -4

(x2 - 2*2)

= (x+2)(x-2)

The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.

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If the eligibility criteria for financial aid for a student is that at most they earn $30,000 per year, then if s is the yearly earnings in dollars, the criteria can be expressed by s ≤ 30,000.

At most earning of $30,000 per year means that the maximum yearly earning to be eligible for financial aid is $30,000. That is the yearly earning can be less than or equal to $30,000. This can be expressed mathematically by

s ≤ 30,000

This is an inequality. As the relationship between the values is not equal, we use an inequality to describe it.

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Answer:

28 pounds of carrots.

Step-by-step explanation:

25+3=28

The percent of slope if there is a rise of 72 metres in 600 metres is given as follows:

12%.

The percent of slope is obtained applying the proportions in the context of this problem.

A proportion is applied because the percent of slope is given by the division of the vertical rise by the horizontal movement, multiplied by 100%.

The parameters for this problem are given as follows:

Hence the percent of slope is obtained as follows:

72/600 x 100 = 12%.

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There are 50,000 odd five-digit counting numbers that can be formed by choosing digits from the set with repetition allowed.

To determine the number of odd five-digit counting numbers that can be formed by choosing digits from a set (with repetition allowed), we need to consider the restrictions and possibilities for each digit position.

1. The leftmost digit:

2. The remaining four digits:

To find the total number of odd five-digit counting numbers, we multiply the possibilities for each digit position:

Total number = (5 options for the leftmost digit) \(\times\) (10 options for each of the remaining four digits)

Total number = \(5 \times 10^4 = 50,000\)

Therefore, there are 50,000 odd five-digit counting numbers that can be formed by choosing digits from the set when repetition is allowed.

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Answer:

To solve this system of equations, we can use the method of substitution.

First, we can solve one of the equations for one of the variables. For example, we can solve the first equation for x:

3x + 2y = 4

3x = 4 - 2y

x = (4 - 2y)/3

Then, we can substitute this expression for x into the second equation to solve for y:

8((4 - 2y)/3) - 3y = -6

8(4) - 8(2y) - 3y = -6

32 - 16y - 3y = -6

19y = 38

y = 2

Finally, we can substitute this value back into either of the original equations to solve for x:

In the first equation:

3x + 2(2) = 4

3x + 4 = 4

3x = 0

x = 0

So the solution to the system of equations is (0,2).

Answer:

graph 1 but im not sure check with someone else.

Step-by-step explanation:

if you divide 10 divided by 2 it gives you 5 and then subtract it by 2.2 = 2.8

there goes your answer.

Answer Each graph below shows a relationship between x and y. For each graph, determine whether x and y are proportional. If x and y are proportional, fill in the blank with a number in simplest form:

Step-by-step explanation:

The Solutions to 12m ² - 4mn-5n² are:

m = n/3 or m = -5n/3

To solve the quadratic equation 12m² - 4mn - 5n² = 0, we can use the quadratic formula:

m = (-b ± √(b^2 - 4ac)) / 2a

where a = 12, b = -4n, and c = -5n².

Substituting these values into the formula, we get:

m = (-(-4n) ± √((-4n)^2 - 4(12)(-5n²))) / 2(12)

Simplifying:

m = (4n ± √(16n² + 240n²)) / 24

m = (4n ± √(256n²)) / 24

m = (4n ± 16n) / 24

So the solutions are:

m = n/3 or m = -5n/3

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