Find the volume of the sphere with a radius of 18 cm. Round your answer to the nearest whole
number, and please be sure to include your units.

Answer:

Step-by-step explanation:

rational

Answer:

Rational

Explanation:

18/42 is 4.258 which is a rational number

Answer:

The mean is decreased by 1.25.

The mode  remains the same.

The median is decreased by 2 .

Step-by-step explanation:

Re arranging the data 14, 22, 20, 25, 26, 17, 21, 30, 27, 25, 14, and 29.

Gives

14, 14,17,20,  21, 22, 25,25, 26,  27, 29,30,  

Now the mean = 14, +14,+17, +20, +21,+ 22, +25,+25,+ 26, +  27, +29,+30/12

Mean= 270/12=22.5

The Mode ( the repeated value) = 14,25

Median ( the average of middle value) =  22+25/2= 23.5

When 30 is replaced is by 15

Now the mean = 14, +14, +15,+17, +20, +21,+ 22, +25,+25,+ 26, +  27, +29/12

The  Mean becomes = 255/12=21.25

The Mode ( the repeated value) = 14,25

Median ( the average of the middle value) =  21+22/2= 21.5

The difference between the 2 means  is = 22.5- 21.25= 1.25

The mode  remains the same.

The median is decreased by 2 .

The mean is decreased by 1.25 which is more than 50 % of the value obtained between the ratio of the omitted and added value (30/15=) i.e. 2

Hey there!

2x^3y

= 2(-2)^3(3)

= 2(-3)^9

-2^9

= (-2)^9

= -2 * -2 * -2 * 2 * -2 * -2 * 2 * -2 * -2

= 4 * 4 * 4 * 4 * -2

= 16 * 16 * 2

= 256 * -2

= -512

= -2(-512)

= -1,024

Therefore, your answer is: -1,024

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The angles that make the trigonometric statements true using the relationship of sine and cosine for the value of the angle is 45°.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The angles that make the trigonometric statements true.

Let the angle be x. Then we have

sin(x) = cos(B)

sin(B) = cos(x)

If they are equal then we can apply the sine and cosine relationship.

\(\rm sin (90 - \theta) = cos \ \theta\\\\\rm cos (90 - \theta) = sin \ \theta\)

Then sin x can be written as cos (90 – B). Then we have

cos(90 – B) = cos(B)

       90 – B = B

                B = 45

Similarly, cos x can be written as sin (90 – B). Then we have

sin(90 – B) = sin(B)

      90 – B = B

               B = 45

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Answer:

Both fill in the blanks are A

Step-by-step explanation:

Correct on edge

Answer:

Step-by-step explanation: Find the y-intercept. Write the equation in slope-intercept form. Write an equation of the line that passes through each pair of points. 5. (4, −3), (2, 3)

y=6x+6 is the function representing the line that includes the points (2,18) and (5,36).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are (2,18) and (5,36).

m=36-18/5-2

=18/3=6

slope of line is 6.

Now we need to find the equation of line passing through (2,18) and (5,36).

We need to find the y intercept.

18=6(2)+c

18=12+c

18-12=c

6=c

So y intercept is 6

The equation of line is y=6x+6

Hence y=6x+6 is the function representing the line that includes the points (2,18) and (5,36).

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The equation or system of equations that can be used to determine the number of cats and dogs Bea has in her pet shop is d = 2c - 5 d + 3 = c + 3. We can solve the system of equations using substitution and plug it back into either equation to find the value of d, which is 8 cats and 10 dogs.

The equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop is:

d = 2c - 5

d + 3 = c + 3

No, Bea's Pet Shop could not initially have 15 cats and 20 dogs. This is because the equation or system of equations states that the number of dogs is five less than twice the number of cats, which would mean that 15 cats would result in 25 dogs, which is not equal to 20.

To determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop, we can use the equation or system of equations that we previously created.

d = 2c - 5

d + 3 = c + 3

We can solve the system of equations using substitution:

d = 2c - 5

d + 3 = c + 3

d + 3 = c + 3

d = c + 3

2c - 5 = c + 3

2c = c + 8

c = 8

Once we determine the value of c, we can plug it back into either equation to find the value of d:

d = 2(8) - 5

d = 15 - 5

d = 10

Therefore, Bea initially had 8 cats and 10 dogs in her pet shop.

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The complete question is: At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three more of each, the ratio of cats to dogs will be – Write an equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop. Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning. Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.​

The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

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The value of \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) is \(e^z\cos y\).

The gradient is a vector operation that transforms a scalar function into a vector with a magnitude equal to the highest rate of change of the function at the gradient's point and a direction pointing in the same direction.

To find \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\), we need to calculate the divergence of the gradient of the function ϕ.

The gradient of ϕ is given by:

\(\bar{\nabla} \phi\) = (∂x/∂ϕ​, ∂y/∂ϕ, ∂z/∂ϕ)

Let's calculate the partial derivatives of ϕ with respect to each variable:

\(\frac{\partial \phi}{\partial x}=e^{z}\sin y\)

\(\frac{\partial \phi}{\partial y}=xe^{z}\cos y\)

\(\frac{\partial \phi}{\partial z}=xe^{z}\sin y\)

Now, we can find the divergence of \(\bar{\nabla} \phi\) by taking the sum of the partial derivatives:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) =  \(\frac{\partial}{\partial x}(e^z\sin y)+\frac{\partial}{\partial y}(xe^z\cos y)+\frac{\partial}{\partial z}(xe^z\sin y)\)

Simplifying each partial derivative:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) = \(e^z\cos y\) + \((-xe^z\sin y)\) + \((xe^z\sin y)\)

Combining like terms, we find:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) = \(e^z\cos y\)

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The complete question is:

Given that \(\phi(x, y, z)=x e^{z} \sin y\) Find \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\).

Answer:

c is your answer to the question

Answer:

22 miles

Step-by-step explanation:

Answer:

I answered your last question also

2 log3x – 2 logx3 -3 <0

\(\mathrm{Subtract\:}2\log ^3\left(x\right)\mathrm{\:from\:both\:sides}\)

\(2\log ^3\left(x\right)-2logx^3-3-2\log ^3\left(x\right)<0-2\log ^3\left(x\right)\)

\(\mathrm{Simplify}\)

\(-2logx^3-3<-2\log ^3\left(x\right)\)

\(\mathrm{Add\:}3\mathrm{\:to\:both\:sides}\)

\(-2logx^3-3+3<-2\log ^3\left(x\right)+3\)

\(\mathrm{Simplify}\)

\(-2logx^3<-2\log ^3\left(x\right)+3\)

\(Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)\)

\(\left(-2logx^3\right)\left(-1\right)>-2\log ^3\left(x\right)\left(-1\right)+3\left(-1\right)\)

\(\mathrm{Simplify}\)

\(2lx^3og>2\log ^3\left(x\right)-3\)

\(\mathrm{Divide\:both\:sides\:by\:}2lx^3o;\quad \:l>0\)

\(\frac{2lx^3og}{2lx^3o}>\frac{2\log ^3\left(x\right)}{2lx^3o}-\frac{3}{2lx^3o};\quad \:l>0\\\)

\(\mathrm{Simplify}\)

\(g>\frac{2\log ^3\left(x\right)-3}{2lx^3o};\quad \:l>0\)

Step-by-step explanation:

The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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(a) The absolute extreme values of the function f(x) = -2x^3 + 27x^2 - 84x on the interval [1, 8] are to be determined.
(b) the answer is A. The absolute maximum is 252 at x = 7

To find the absolute extreme values, we need to evaluate the function at the critical points and endpoints of the interval. Critical points occur where the derivative of the function is either zero or undefined.

Taking the derivative of f(x) and setting it equal to zero, we get f'(x) = -6x^2 + 54x - 84. Solving this quadratic equation, we find x = 2 and x = 7 as the critical points.

Next, we evaluate the function at the critical points and endpoints: f(1) = -59, f(2) = 4, f(7) = 252, and f(8) = -400.

The absolute maximum value is 252 at x = 7.

(b) A graphing utility can be used to visualize the function and confirm our conclusions. The graph shows that the function has a local maximum at x = 2, but the absolute maximum occurs at x = 7 with a value of 252. Thus, the answer is A. The absolute maximum is 252 at x = 7.


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A conic section is the set of all points (x, y) in a plane where the difference of the distances from two distinct fixed points is a positive constant. This geometric shape is known as an ellipse.

An ellipse can be defined as the locus of points in a plane such that the sum of the distances from two fixed points, called foci, to any point on the ellipse is constant. The first paragraph provides a concise summary of the answer.

The concept of an ellipse can be understood through its definition and properties. When considering two fixed points, known as foci, in a plane, the set of all points where the difference of the distances from these foci is constant forms an ellipse.

The distance between the foci determines the elongation and shape of the ellipse. If the distance between the foci is larger, the ellipse becomes more elongated, while a smaller distance results in a more circular shape. The constant difference of distances from the foci is known as the major axis of the ellipse, and it represents the longest chord that passes through the center of the ellipse.

The minor axis, perpendicular to the major axis, represents the shortest chord passing through the center. The shape, size, and orientation of an ellipse can be determined by its foci and the distance between them, making it a fundamental concept in mathematics and geometry.

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The probability that the mean score of the 49 seniors is greater than 20 is 0.0516. To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with any distribution will approach a normal distribution as the sample size increases.

First, we need to find the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. We can use the formula SEM = σ / √n, where σ is the population standard deviation, and n is the sample size.

In this case, σ = 6.0 and n = 49, so SEM = 6.0 / √49 = 0.857.

Next, we need to standardize the sample mean using the z-score formula: z = (x - μ) / SEM, where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

In this case, x = 20, μ = 18.6, and SEM = 0.857, so z = (20 - 18.6) / 0.857 = 1.63.

Finally, we need to find the probability that a standard normal distribution is greater than 1.63, which is 0.0516 when rounded to 4 decimal places.

Therefore, the probability that the mean score of the 49 seniors is greater than 20 is 0.0516.

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To evaluate the given integrals using polar coordinates, from Cartesian coordinates to polar coordinates. In each case, given regions or curves in polar form and apply the appropriate limits of integration to compute the integral.

7. To evaluate the integral ∫∫R x dA, where R is the top half of the disk with center at the origin and radius r, we convert to polar coordinates. In polar form, the region R is defined by 0 ≤ r ≤ r and 0 ≤ θ ≤ π. The integral becomes ∫∫R x dA = ∫₀ʳ ∫₀ᴨ x r dr dθ. Evaluating this integral gives the desired result.

8. The integral ∫∫R x dA, where R is the region in the first quadrant enclosed by the circle x² + y² = r² and the lines y = x and x = 0, can be evaluated using polar coordinates. Converting the equations to polar form gives r² = r²cos²θ + r²sin²θ and θ = π/4 and θ = 0 as the limits of integration. The integral becomes ∫∫R x dA = ∫₀ʳ ∫₀ᴨ/₄ x r dr dθ. Evaluating this integral gives the desired result.

9. The integral ∫∫R x dA, where R is the region in the first quadrant between the circles x² + y² = a² and x² + y² = b² (where a < b), can be evaluated using polar coordinates. In polar form, the region R is defined by a ≤ r ≤ b and 0 ≤ θ ≤ π/2. The integral becomes ∫∫R x dA = ∫ₐᵇ ∫₀ᴨ/₂ x r dr dθ. Evaluating this integral gives the desired result.

10. The integral ∫∫R x dA, where R is the region that lies between the circles x² + y² = a² and x² + y² = b² (where a < b), can be evaluated using polar coordinates. In polar form, the region R is defined by a ≤ r ≤ b and 0 ≤ θ ≤ 2π. The integral becomes ∫∫R x dA = ∫ₐᵇ ∫₀²ᴨ x r dr dθ. Evaluating this integral gives the desired result.

11. The integral ∫∫R x dA, where R is the region bounded by the semi-circle x = √(r² - y²) and the x-axis, can be evaluated using polar coordinates. Converting the equations to polar form gives r = rcosθ and θ = -π/2 and θ = π/2 as the limits of integration. The integral becomes ∫∫R x dA = ∫₋ᴨ/₂ᴨ/₂ ∫₀ʳ x r dr dθ. Evaluating this integral gives the desired result.

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The given function is

First, we make x = 0.

Second, we make g(x) = 0.

Third, we graph the points (0, 4) and (-16, 0).

At last, we draw the line through the points to get the line.

Answer:

K^2 - 100 = (K + 10)(K - 10)

16p^2 - 36 = 4(4p^2 - 9) = 4(2p + 3)(2p - 3)

9d^2 - 32 = (3d - 4)(3d + 4)

24a^2 - 54b^2 = 6(4a^2 - 9b^2) = 6(2a + 3b)(2a - 3b)

100b^3 - 36b = 4b(25b^2 - 9) = 4b(5b - 3)(5b + 3)

Table A doesn't represent the constant of proportionality.

Table B doesn't represent the proportional relationship.

Treat the values in table as (x,y) values. The result is a linear function

For A, 85/5 = 17 while 79 / 10 = 7.9. This doesn't illustrate a constant.

For B, 1.49/16 and 1.59/20 have different values. In this case, 1.49/16 = 0.093 and 1.59/20 = 0.0795.

Therefore. they don't have a constant of proportionality. This was because the values that were gotten for both A and B aren't equal.

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Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?

1. How loud a sound is depending on how far away you are

5 85

10 79

20 73

40 67

b. The fountain drinks at hot dog hut.

16 1.49$

20 1.59$

30 1.89$

Answer:

247/7 = 35 2/7

247/7 = 35 reminder 2

247/7 = 35.2857142857...

Step-by-step explanation:

             35      

          ----------------------------------

   7    |   247

             21

          -----------

               37

               35

             ---------

                 2

247/7 = 35 2/7

247/7 = 35 reminder 2

247/7 = 35.2857142857...

Answer:

350

Step-by-step explanation:

Answer:

Decimal to Fraction Number calculator - online basic math function tool to convert decimal point number 2.4343 to fraction equivalent

Step-by-step explanation:

Answer:

Look Below

Step-by-step explanation:

y=1/16x^2

multiplying both sides by 16 we get:

16y=x^2

The general form of a parabola is:

(x-h)^2=4p(y-k)

thus

4p=16

p=4

The parabola opens upwrd:

Focus: (h,k-p)

(0,0-4)

=(0,-4)

Directrix: y=-4

Answer:

108

Step-by-step explanation:

Answer:135

Step-by-step explanation:

bcs 45x60 is 2700 ÷20= 135

The missing premise is "all dogs are non-cats." Therefore, the argument is true.

The given information and analyze the argument step-by-step.

1. Some non-poodles are not non-cats: This statement means that there are some animals that are not poodles and are also cats.

2. No cats are dogs: This statement means that there is no overlap between cats and dogs.

Now, let's try to determine if "some poodles are dogs" can be concluded from these premises:
Since no cats are dogs, it doesn't matter whether some non-poodles are not non-cats. Poodles are a breed of dog, so it's already a fact that poodles are dogs.

So, the answer is True: some poodles are dogs.

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The general solution to the differential system x' = (3 -2; 1 1)x is x(t) = c₁e^(3t) + c₂e^(-2t), where c₁ and c₂ are real constants.

To find the general solution, we first need to diagonalize the matrix (3 -2; 1 1).

The eigenvalues of this matrix are λ₁ = 2 and λ₂ = 2, with corresponding eigenvectors v₁ = (1; 1) and v₂ = (-2; 1). Using these eigenvectors, we construct the matrix P = (v₁ | v₂) = (1 -2; 1 1).

The inverse of P is P^(-1) = (1/3 2/3; -1/3 1/3). Now, we can write the solution as x(t) = P(Dt)P^(-1)x₀, where Dt = diag(e^(3t), e^(-2t)) is the diagonal matrix of eigenvalues and x₀ is the initial condition vector.

Simplifying this expression gives x(t) = c₁e^(3t) + c₂e^(-2t), where c₁ and c₂ are real constants.

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Answer:

Step-by-step explanation:

3