You and your friend play a video game. You have a final score of 40 points and your friend has a final score of -21 points. By how many points did you win?

Answer:

yes you are supposed to multiply 3/2. Good luck

Step-by-step explanation:

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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Answer:

1. If x is under a square root then x cannot equal a negative number. If x is in the denominator of a fraction then x cannot equal zero.

2. ax2 + bx + c

Step-by-step explanation: Hope this helps :)

we can conclude that ci = di for 1 ≤ i ≤ k. Therefore, the representation of v as a linear combination of basis vectors is unique.

To show that the representation of a vector v ∈ V as a linear combination of basis vectors is unique, we'll assume that there exist two different sets of coefficients c1, c2, ..., ck and d1, d2, ..., dk such that:

c1v1 + c2v2 + ... + ckvk = v   (Equation 1)

d1v1 + d2v2 + ... + dkvk = v   (Equation 2)

To prove that ci = di for 1 ≤ i ≤ k, we'll subtract Equation 2 from Equation 1:

(c1v1 + c2v2 + ... + ckvk) - (d1v1 + d2v2 + ... + dkvk) = v - v

(c1v1 - d1v1) + (c2v2 - d2v2) + ... + (ckvk - dkk) = 0

Now, we can rewrite the above equation as:

(c1 - d1)v1 + (c2 - d2)v2 + ... + (ck - dk)vk = 0

Since the basis vectors v1, v2, ..., vk are linearly independent, the only way for this equation to hold true is if each coefficient (c1 - d1), (c2 - d2), ..., (ck - dk) is equal to zero:

c1 - d1 = 0

c2 - d2 = 0

...

ck - dk = 0

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Answer:

your answer is -5-4-3-2-11

Step-by-step explanation:

this is because -5-4-3-2-11=-26, and that is the lowest term there

The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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Answer:

1)

Step-by-step explanation:

We just need to find a rate where the ratio of miles to gallons is 13:1

This only works for 1) 26 miles 2 gallons since 26/2 = 13/1

Answer:

I think it would be the first one. 26 miles 2 gallons

Step-by-step explanation:

Every gallon would be 13 miles. If you multiply 13 by 2 and 1 gallon by 2, you'll get 26 miles 2 gallons.

Three trigonometric ratios are Sin C=21/29,Cos C=20/29, Tan C=21/20.

Trigonometric ratios, also known as trigonometric functions, are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:

In the given triangle;

AB=21

BC=20

AC=29

Calculating trigonometric ratios;

Sin C=Perpendicular/Hypotenuse

=AB/AC

=21/29

Cos C=Base/Hypotenuse

=BC/AC

=20/29

Tan C=Perpendicular/Base

=AB/BC

=21/20.

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The rockets are at a height of 83.15 meters after 1.36 seconds. Rounded to the nearest hundred, this is 83 meters.

To find the moment when the rockets are at the same height, set f(x) = g(x) and solve for x:

-4.9x2 +50x = -4.9x2 +25x + 34

50x = 25x + 34

25x = 34

x = 1.36

Therefore, the rockets are at the same height after 1.36 seconds. To calculate the height, plug x = 1.36 into either function:

f(1.36) = -4.9(1.36)2 +50(1.36)

f(1.36) = -4.9(1.85) + 68

f(1.36) = 83.15 meters

Therefore, the rockets are at a height of 83.15 meters after 1.36 seconds. Rounded to the nearest hundred, this is 83 meters.

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Given:

The total number of marbles are 26.

Red marbles=10

Black marbles=8

Green marbles=8

The two marbles are drawn randomly,

To find the probability that both marbles are green,

The probability that first marbles chosen is green,

Condition is given that the first is not returned before the second one is drawn.

Now the we have 7 green marbles and total marbles are 25.

Probability is given by,

The total probability of getting both green marbles without replacement is,

Answer: Probability is 0.08615.

Answer:

A. f(x)=log(x+1)-1, is the correct answer.

Step-by-step explanation:

First, I'm going to state my assumptions.

1. There is only one correct answer

2. 0 cannot be the y-intercept

3. You are not going to use imaginary units.

First, the y-intercept is found when x=0, so we are going to plug that in.

A. f(x)=log(1)-1 =-1 Correct.

B. f(x)=log(0+1)=0 Incorrect since it is assumed that 0 cannot be the y-intercept.

C. f(x)=log(0-1)+1 Impossible without using imaginary units, therefore, this answer is incorrect.

D. f(x)=log(0-1)-1 Same story as C.

Answer:

A

Step-by-step explanation:

Comment

The best way to find out the answer to this is to graph it. Once you've done that, it will be obvious once you have done that. The question is which way does y = log(x + 1) move? Left or right? Look at the red line. That's the one that has the y intercept. The line is y = log(x+1) - 1

The mean and standard deviation of the z-scores for pulse rates of women can be calculated using the formula z = (x - μ) / σ, where x represents the original pulse rate, μ represents the mean, and σ represents the standard deviation.

In this case, the mean of the original pulse rates is 77.5 beats per minute, and the standard deviation is 11.6 beats per minute. To convert these pulse rates to z-scores, we subtract the mean from each pulse rate and divide by the standard deviation.

The mean of the z-scores will be 0, as subtracting the mean from each value results in a mean of 0. The standard deviation of the z-scores will be 1, as dividing by the standard deviation ensures that the z-scores have a standard deviation of 1.

Therefore, the values of the mean and standard deviation after converting the pulse rates of women to z-scores are a mean of 0 and a standard deviation of 1.

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Because a few extreme scores can create a deceptively large estimate of variation, the (B) range offers only a crude estimate of the variation in a data set.

Therefore, because a few extreme scores can create a deceptively large estimate of variation, the (B) range offers only a crude estimate of the variation in a data set.

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The complete question is given below:

Because a few extreme scores can create a deceptively large estimate of variation, the _________ offers only a crude estimate of the variation in a data set.

(A) standard deviation

(B) range

(C) mode

(D) mean

The mass will reach a maximum height of 0.82 m above its equilibrium position before falling back down due to gravity.

We need to use the principles of Hooke's law and conservation of energy.

Hooke's law states that the force exerted by a spring is proportional to its displacement from equilibrium, and this relationship can be expressed mathematically as F = -kx, where F is the force, k is the spring constant, and x is the displacement.

Given that a mass of 3 kg stretches a spring 5/2, we can determine the spring constant using the formula k = (mg)/x, where m is the mass, g is the acceleration due to gravity, and x is the displacement.

Plugging in the values, we get:
k = (3 kg x 9.8 m/s^2)/(5/2 m) = 58.8 N/m

Now we can use the conservation of energy to find the maximum height that the mass will reach.

At the highest point, all of the potential energy is converted to kinetic energy, and vice versa at the lowest point.

Therefore, we can equate the initial potential energy to the final kinetic energy, using the formulas:
PE = mgh
KE = 1/2 mv^2

where PE is potential energy, KE is kinetic energy, m is the mass, h is the height, and v is the velocity.

Plugging in the values, we get:
PE = (3 kg x 9.8 m/s^2 x 1 m) = 29.4 J
KE = (1/2 x 3 kg x 4 m/s^2) = 6 J

Since energy is conserved, we can equate these two values and solve for h:
PE = KE
mgh = 1/2 mv^2
h = v^2/2g
h = (4 m/s)^2 / (2 x 9.8 m/s^2)
h = 0.82 m

Therefore, the mass will reach a maximum height of 0.82 m above its equilibrium position before falling back down due to gravity.

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Answer:

\( - 30(x + 5) = 7x - 7 \\ - 30x - 150 = 7x - 7 \\ 7x + 30x = - 150 + 7 \\ 37x = - 143 \\ x = \frac{ - 143}{37} \\ x = - 3.864\)

________o____o_____

30–(x+5)=7x-7

30 – x–5 =7x -7

7x+x = 30-5+7

8x = 32

x= 32/8

x=4

I hope I helped you^_^

\(\large\huge\green{\sf{Answer:-}}\)

\( \frac{65 {a}^{3} }{5a} = \frac{65 {a}^{2} }{5} = 13a {}^{2} \)

In a regression equation, the estimated coefficients represent the change in the dependent variable for a one-unit increase in the corresponding independent variable, holding all other independent variables constant.

For example, if the estimated coefficient for television advertising is 0.5, then we can interpret it as a $0.5 increase in the dependent variable (such as sales) for every one-unit increase in television advertising expenditure, holding newspaper advertising constant.

Whether the interpretations of the estimated coefficients are reasonable depends on the data and the research question being investigated. It is important to examine the statistical significance, magnitude, and direction of the estimated coefficients, as well as their practical relevance and theoretical soundness, to evaluate the validity and usefulness of the regression model.

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1. The inequality that can be used to determine d, the maximum number of days Melanie can afford to rent a car while staying within her budget is 33.27d + 3.5 ≤ 120.

2. For the second question, the correct inequality is D. 440 ≥ 25 + 62.12d.

Inequality is a mathematical expression that states that two values are not equal.

Inequality expressions employ one of these signs:  less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠).

Rental charge per day = $33.27

Rental charge per mile = $0.07

The number of miles Melanie intends to drive = 50 miles

The total rental charge for 50 miles = $3.50 ($0.07 x 50)

Melanie's budget for the rental = $120

33.27d = total rental charge for d days.

0.07m = total rental charge for m miles.

0.07m = 0.07 x 50 = 3.5

Budget constant: ≤ 120

Therefore, the inequality is:

= 33.27d + 3.5  ≤ 120

Thus, the inequality that can be used to determine d, the maximum number of days is 33.27d + 3.5 ≤ 120.

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A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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To find a polynomial function with integer coefficients that has the given zeros, we can use the factor theorem and the zero-product property. Therefore, the function is f(x) = (x + 2)(x - 1)(x - 3) = x^3 - 2x^2 - 5x + 6 .

In summary, to find a polynomial function with integer coefficients that has the given zeros, we can use the factor theorem and the zero-product property to obtain the factors of the polynomial, and then multiply them together to get the polynomial function.

For example, suppose we want to find a polynomial function with integer coefficients that has zeros at -2, 1, and 3. We can start by using the factor theorem to obtain the factors of the polynomial:

(x + 2)(x - 1)(x - 3)

We can then multiply these factors together to obtain the polynomial function:

f(x) = (x + 2)(x - 1)(x - 3) = x^3 - 2x^2 - 5x + 6

This is a polynomial function with integer coefficients that has zeros at -2, 1, and 3. Note that we can also check this by using the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero. We can plug in each of the zeros (-2, 1, and 3) into the polynomial function and verify that the result is zero, which confirms that these are indeed the zeros of the polynomial.

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The slope of the line above include the following: 1/5.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (3 - 0)/(7 + 8)

Slope (m) = (3)/(15)

Slope (m) = 1/5.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/5.

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The length of the segment will be 4.8 units.

What is a chord of a circle ?

Chords of a circle are the line segments which has two endpoints onto the circumference of a circle.A diameter is also a chord which passes through the center of a circle and it it the biggest chord of a given circle.

According to the given data

Here we can see a circle with two intersecting chords.

We know that when two chords inside a circle intersect each other the product of their segments are equal.

The chords given are AC and BD

∴ AE×EC = BE × ED

 6 × 8 = x × 10

10x = 48

    x = 4.8.

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It is more convenient to integrate with respect to y.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

To sketch the region enclosed by the curves y = 3x² and y = 5x - 2x² and determine whether to integrate with respect to x or y, we can analyze the intersection points and the shape of the curves.

First, let's find the intersection points by setting the equations equal to each other:

3x² = 5x - 2x²

Combining like terms:

5x² - 5x = 0

Factoring out x:

x(5x - 5) = 0

Solving for x:

x = 0 or x = 1

So the curves intersect at x = 0 and x = 1.

Next, we can analyze the behavior of the curves to determine the orientation of the region.

For y = 3x², we have a parabola that opens upwards. This curve lies below the x-axis and is symmetric with respect to the y-axis.

For y = 5x - 2x², we have a downward-opening parabola. This curve lies above the x-axis and is symmetric with respect to the y-axis.

Based on this information, we can sketch the region enclosed by the curves.

The region enclosed by the curves is bounded by the curves themselves and the x-axis. It is the area between the curves from x = 0 to x = 1.

To determine whether to integrate with respect to x or y, we can observe that the region is vertically oriented, meaning it extends vertically between the curves.

Therefore, it is more convenient to integrate with respect to y.

To draw a typical approximating rectangle, we can choose a small interval along the y-axis and draw a rectangle that spans between the curves for that particular y-interval. This rectangle will represent an approximation of the region's area.

Hence, it is more convenient to integrate with respect to y.

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The value of p is 2 and q is either 7 or 13 and their sum is either 9 or 15.

It is given that the value of p and q is a prime number, and p<q.

But it is also given that the value of both should be less than 18 as well as a prime number.

Therefore the value of both should be 2, 3, 5, 7, 11, 13, and 17.

And it is also given that p<q.

Now we have to find the value of p + q which is odd but not a prime number.

To have a sum as an odd number one number should be even and as it is given that p<q, therefore p=2, and q = 3, 5, 7, 11, 13, 17.

So

p + q = 2 + 5 = 7, which is odd but it is prime

Now again, q = 7

p + q = 2 + 7 = 9 , which is odd as well as not prime.

Again take q = 11

p + q = 2 + 11 = 13, which is odd but prime

Now take q = 13

p + q =  2 + 13 = 15, which is odd as well as not prime.

Now take q = 17

p + q = 2 + 17 = 19, which is odd and prime.

Therefore we have p =2 and q = 7 or 13 and sum p + q =9 or 15 which is odd but not prime.

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The probability is 0.3845.The probability of anything occurring is known as probability.

Explanation:

2/52 * 10/52  = 20/52 = 0.3845.

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Answer:

Work shown below!

Step-by-step explanation:

(a + 3)(a + 5) = \(a^{2} +5a+3a+15=a^{2}+8a+15\)

f′(5) ≈ -3.845

The given function is f(x) = 4 cos (8 ln x).

We need to find f′(x) and f′(5).

The chain rule states that the derivative of a composite function is the product of the derivative of the outside function and the derivative of the inside function.

So we can find the derivative of f(x) as follows:

f(x) = 4 cos (8 ln x)

f′(x) = -4 sin (8 ln x) * d/dx [8 ln x]where d/dx [8 ln x] is the derivative of the inside function 8 ln x with respect to x.

We know that d/dx [ln x] = 1/x.

Therefore, d/dx [8 ln x] = d/dx [ln (x^8)] = 8/x.f′(x) = -4 sin (8 ln x) * (8/x)

So the derivative of f(x) is:f′(x) = -32 sin (8 ln x) / x

To find f′(5), we substitute x = 5 in the expression we got for f′(x):

f′(x) = -32 sin (8 ln x) / x f′(5) = -32 sin (8 ln 5) / 5 f′(5) ≈ -3.845

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Answer:

Step-by-step explanation:

Conclusion:

Hence, 1 pendant costed $2.1.

Hoped this helped.

\(BrainiacUser1357\)

The correct answer is:  d. Can't tell how big A is.

Based on the given information, can we determine the size of the subset A in the real numbers?

No, we cannot determine the size of subset A in the real numbers based on the given information. The size of A could be countably infinite, uncountable, finite, or we may not have enough information to determine its size.

To determine the size of subset A in the real numbers, we can consider the given options.

a. A is countably infinite:

This means that A can be put in a one-to-one correspondence with the set of natural numbers (counting numbers). In other words, A has the same cardinality as the set of natural numbers.

b. A is uncountable:

This means that A cannot be put in a one-to-one correspondence with the set of natural numbers. A set is uncountable if its cardinality is greater than that of the natural numbers.

c. A is finite:

This means that A contains a finite number of elements.

d. Can't tell how big A is:

This indicates that we do not have enough information to determine the size of A based on the given information.

Without any specific information about the subset A, we cannot determine its size.

Therefore, the correct answer is d. Can't tell how big A is.  

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