The series n=0 to infinity 2^n 3^n /n! is (a) divergent by the root test (b) a series where the ratio test is inconclusive (c) divergent by ratio test (d) convergent by ratio test and its sum is 0 (e) convergent by ratio test and its sum is e^6.

Answer:

1.15x

Step-by-step explanation:

In the given question below, the price of a toy wants to sell for 15% more than the original amount.  1.15x would work because you are multiplying 15% more while other equations would show a decrease in its price.

The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

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Answer:0.351

Step-by-step explanation:

Answer:

(0,−3),(1,3),(2,9) are possible options

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

2/(x+2)≠1/(x+1)

Answer:

a. Please check the explanation for filling of the empty column on the table

b. The mean of the random variable x is 7/11

Step-by-step explanation:

a. Firstly, we are concerned with completing the table.

To do this, we simply need to multiply the values in the column of x by the values in the column of p(x)

Thus, we have the following;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

b. We want to find the mean of the random variable x.

All what we need to do here is add all the values of x•P(x) together, then divide by 11.

Thus, we have

(2/36 + 6/36 + 12/36 + 20/36 + 30/36 + 42/36 + 40/36 + 36/36 + 30/36 + 22/36 + 12/36)/11

Since the denominator is same for all, we simply add all the numerators together;

(252/36) * 11 = 252/396 = 63/99 = 7/11

Step-by-step explanation:

n/6 > 2

x6. x6

n > 12

hope this helps

Answer:

diagonal=13cm

Step-by-step explanation:

a² + b²=c²

(12cm)² + (5cm)²=c²

144cm² + 25cm²=c²

169cm²=c²

√169cm²=√c²

13cm=c

Answer:

92

Step-by-step explanation:

83*4 = 332

And 80*3 = 240

332-240 = 92

So you would need 92

Answer:

i need help

Step-by-step explanation:

A Heaviside step function, frequently known as a step function, is a mathematical function that gives 0 for negative input and 1 for non-negative input. This function is represented by the symbol H(x) or u(x) and is useful in various scientific fields.

The step function was introduced by Oliver Heaviside in the year 1894. The Heaviside step function can be modified, scaled, shifted, and summed with other functions. The first example of the Heaviside step function is H(x) = 0 for x < 0 and H(x) = 1 for x ≥ 0.

The second example of the Heaviside step function is H(x - 2) which is a step function shifted by two units in the negative x-direction. The third example of the Heaviside step function is H((x + 3)/5) which is a step function shifted by three units in the positive x-direction and scaled by a factor of 5.

b) Solve the following differential equation: y'' + y = u(t-2), y(0) = 0 and y'(0) = 2, 0 ≤ t ≤ [infinity]i) The derivative property for Laplace transforms:Initial conditions of the second order differential equation y'' + y = f(t) can be solved by using Laplace transforms. We take the Laplace transform of both sides of the equation:

L(y'' + y) = L(f(t)).

By using the derivative property of Laplace transforms, we can write it as follows:

\(L(y'') + L(y) = L(f(t))s^2Y(s) - sy(0) - y'(0) + Y(s) = F(s).\)

By substituting the given values of initial conditions and the given Heaviside step function, we obtain:

\(s^2Y(s) - 2 = \frac{1}{s}e^{-2s}.\)

Solving this expression for Y(s), we get:

\(Y(s) = \frac{1}{s^3}e^{-2s} + \frac{2}{s^2}e^{-2s}.\)

Applying the inverse Laplace transform to Y(s), we obtain the solution of the given differential equation:

y(t) = \left(\frac{1}{2}t^2 - t + 1\right)u(t-2) - \left(t-2\right)u(t-2) + \left(1-t+e^{2-t}\right)u(t).

ii) The method of undetermined coefficients:In this method, the general solution of the given differential equation is found by assuming the solution of the forced part of the differential equation. For u(t - 2) = 1, we have:y'' + y = 1, y(0) = 0, y'(0) = 2The characteristic equation of the differential equation is:

r^2 + 1 = 0.

Solving this expression for r, we get:r = ±iThe homogeneous solution of the given differential equation is:

y_h(t) = c_1cos(t) + c_2sin(t).

The particular solution of the given differential equation is taken as:

y_p(t) = A.

Differentiating this expression with respect to t, we get:.

y'_p(t) = 0

y''_p(t) = 0.

Substituting these expressions in the given differential equation, we get:

y''_p + y_p = 1

0 + A = 1

A = 1.

Therefore, the particular solution of the given differential equation is:

y_p(t) = 1.

The general solution of the given differential equation is:

y(t) = c_1cos(t) + c_2sin(t) + 1.

Using the initial condition y(0) = 0, we get:

c_1 = -1.

Using the initial condition y'(0) = 2, we get:

c_2 = 2.

Therefore, the solution of the given differential equation is:

y(t) = 2sin(t) - cos(t) + 1.

For u(t - 2) = 0, the solution is the homogeneous solution y(t) = c1cos(t) + c2sin(t).

The Heaviside step function is a useful function in mathematics and science fields, and it can be modified, scaled, shifted, and summed with other functions. The Laplace transform and method of undetermined coefficients are used to solve the initial conditions of the given second-order differential equation.

The derivative property of Laplace transforms is used to solve the initial conditions of the differential equation. The method of undetermined coefficients is used to solve the given differential equation by assuming the solution of the forced part of the differential equation.

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Answer:

9.936

Step-by-step explanation:

V = Bh

B = base

base = Lengh x width

base = 4.8 x 2.3

base = 11.04

V = 11.04h

H = height

H = .9

V = .9 x 11.04

V = 9.936

Answer:

9.936 m³

Step-by-step explanation:

Answer:216

Step-by-step explanation:3x9x8

Answer:

12

Step-by-step explanation:

Answer:

x+9x+x+100=1178

11x=1178-100

x=1078/11

x=98

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

12^2 + 9^2 = 225

square root of 225 = 15

Answer:

Product 1, because the function is exponential

Step-by-step explanation:

An exponential function, such as f(x) = 3^x, grows very quickly.

Answer: Product 1, because the function is exponential

Answer:

you need 32.5 cups of red for the same shade of purple

Step-by-step explanation:

2:5

13:32.5

Answer:

32.5 cups of red

Step-by-step explanation:

Lets take it step-by-step.

So to make purple paint you mix 2 parts of blue and 5 parts of red. So if you use 13 cups of blue you need to use 32.5 cups of red because...

13 divided by 2 = 6 1/2, so you would have to multiply 5 x 6 1/2 which is 32.5

Next time you come across a problem like this take the large number you have Ex. 13, and divide it by the smaller number you know Ex. 2, and then multiply the number that you've gotten by dividing Ex. 6 1/2, with the other small number Ex. 5, and then you have your answer.

If you need any more help let me know :)

Mary and Jerry's number will be 39 and 50.The sum of their numbers is 89. Which shows that the obtained answer is correct.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

Let, Mary’s number be x

From the given condition sum of their numbers is 89.

\(\sf x+(x+11)=89\)

\(\sf 2x+11=89\)

\(\sf 2x=89-11\)

\(\sf 2x=78\)

\(\sf \dfrac{2x}{2} =\dfrac{78}{2}\)

\(\sf x=39\)

Jerry's number will be:

\(\sf x+11\)

\(\sf 39+11\)

\(\sf 50\)

Hence the Mary and Jerry's number will be 39 and 50.

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Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

x = - 3, y = - 11

Step-by-step explanation:

Given the 2 equations

y = 7x + 10 → (1)

y = - 4x - 23 → (2)

Substitute y = 7x + 10 into (2)

7x + 10 = - 4x - 23 ( add 4x to both sides )

11x + 10 = - 23 ( subtract 10 from both sides )

11x = - 33 ( divide both sides by 11 )

x = - 3

Substitute x = - 3 into either of the 2 equations and evaluate for y

Substituting into (1)

y = 7(- 3) + 10 = - 21 + 10 = - 11

Answer:

You need to cross multiply 37/45+x/100 which equals 17%

Step-by-step explanation:

The first part represents the 37 dollars out of the original 45 and the second part represents x= the unknown percent out of 100 percent. This would be 17%

Answer:

panomonasabe kumainka ng tae masarap ba gustumupa ha gustu mo gutu mo

x - 3 < 6         {add 3 to both sides}

x < 9

graph

x∈(-∞; 9)

Answer:

y=7/9x+31/9

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-2-5)/(-7-2)

m=-7/-9

m=7/9

y-y1=m(x-x1)

y-5=7/9(x-2)

y=7/9x-14/9+5

y=7/9x-14/9+45/9

y=7/9x+31/9

Among the three variants of the SPI (Specific, Precise, and Impression) model, the Specific model exhibits the best flexibility, while the Impression model demonstrates the best optimization.

The Specific model excels in flexibility because it focuses on generating highly specific responses. It tends to produce detailed and accurate information based on the given input.

This flexibility allows users to obtain precise answers to their queries, making it particularly useful for tasks requiring specific knowledge, such as providing instructions, explaining concepts, or offering specific recommendations.

The Specific model's ability to generate focused responses enhances its flexibility for various use cases.

On the other hand, the Impression model stands out in optimization. It excels at generating responses that are more creative, imaginative, and subjective.

It has been optimized to prioritize generating impressive or entertaining output. This model is particularly suited for tasks that require engaging and captivating content, such as storytelling, generating ideas, or creative writing.

The Impression model's optimization focuses on generating outputs that leave a lasting impression on the audience, making it the best choice for such scenarios.

In summary, while the Specific model offers the best flexibility by providing specific and detailed information, the Impression model shines in optimization, generating impressive and captivating responses.

The choice between the two depends on the specific requirements of the task at hand, whether it demands precision or creativity.

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The given equation, 5r^2 + z^2 = 1, represents a surface called an ellipsoid. An ellipsoid is a three-dimensional shape resembling a stretched or compressed sphere.

To explain further, this equation represents a specific type of ellipsoid known as a prolate spheroid. It has a major axis along the z-axis and a minor axis along the r-axis. The equation states that the sum of the squares of the distances from any point on the surface to the r-axis and z-axis is equal to 1.

In simple terms, imagine a three-dimensional shape that is stretched or compressed in such a way that its cross-sections in the r-z plane are ellipses. This is what the equation 5r^2 + z^2 = 1 represents.

To summarize, the given equation represents an ellipsoid, specifically a prolate spheroid, where the sum of the squares of the distances from any point on the surface to the r-axis and z-axis is equal to 1.

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Answer:

400 boys : 200 girls

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of a circle:

(a, b) - the center of a circle

r - the radius of a circle

x² - 8x + 16 + y² + 10y + 25 = 81

(x² - 2(x)(4) + 4²) + (y² + 2(y)(5) + 5²) = 81

use: (a - b)² = a² - 2ab + b² and (a + b)² = a² - 2ab + b²

(x - 4)² + (y + 5)² = 9²

Therefore

the radius: r = 9

the center: (4, -5)

The radius is 9 and the center of the circle  (4, -5)

A circle's center is a point throughout the circle that is equally spaced from every other point on the circumference. The line of refraction symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry surrounding the centre.

The equation of a circle:

(x - a)² + (y - b)² = r²

The center of a circle will be (a, b)

The radius of a circle will be r

x² - 8x + 16 + y² + 10y + 25 = 81

Solving the above equation on the basis of the Equation of a circle.

(x² - 2(x)(4) + 4²) + (y² + 2(y)(5) + 5²) = 81

Using the identity in the above-given equation.

(a - b)² = a² - 2ab + b² and (a + b)² = a² - 2ab + b²

(x - 4)² + (y + 5)² = 9²

The center of the circle will be at coordinates 4 and 5. And the radius of the circle derived is 9.

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For the matrix the true statement is given by option d. Both A and B are false.

Let's analyze each statement of the matrix as follow,

A) If A is a 3 times 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R⁵.

This statement is false.

The domain of the transformation T is not R⁵.

The domain of T is determined by the dimensionality of the vectors x that can be input into the transformation.

Here, the matrix A is a 3 times 5 matrix, which means the transformation T(x) = Ax can only accept vectors x that have 5 elements.

Therefore, the domain of T is R⁵, but rather a subspace of R⁵.

B) If A is a 3 times 2 matrix, then the transformation x right arrow Ax cannot be onto.

This statement is also false.

The transformation x → Ax can still be onto (surjective) even if A is a 3 times 2 matrix.

The surjectivity of a transformation depends on the rank of the matrix A and the dimensionality of the vector space it maps to.

It is possible for a 3 times 2 matrix to have a rank of 2,

and if the codomain is a vector space of dimension 3 or higher, then the transformation can be onto.

Therefore, as per the matrix both statements are false, the correct answer is d. Both A and B are false.

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The above question is incomplete, the complete question is:

Which of the following best characterizes the following statements:

A) If A is a 3 times 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R^5

B) If A is a 3 times 2 matrix, then the transformation x right arrow Ax cannot be onto

a. Only A is true

b. Only B is true

c. Both A and B are true

d. Both A and B are false

The limit sizes of the populations are \(lim x(t) = 2 and lim y(t) = 1.5.\)

There is no value of a for which this critical point is a spiral sink.

(a) For a=1, we have the following system of equations:

x' = 6x - 2x^2 - 4xy

y' = -4y + 2xy

To find the critical points, we set x' and y' equal to zero and solve for x and y:

6x - 2x^2 - 4xy = 0

-4y + 2xy = 0

From the second equation, we have y(2-x) = 0, so either y=0 or x=2.

Case 1: y = 0

Substituting y=0 into the first equation, we get \(6x - 2x^2 = 0\), which gives us two critical points: (0,0) and (3,0).

Case 2: x=2

Substituting x=2 into the first equation, we get 12 - 8y = 0, which gives us one critical point: (2,3/2).

Now, we compute the Jacobian matrix of the system:

\(J = [6-4y-4x, -4x][2y, -4+2x]\)

At (0,0), we have J = [6, 0; 0, -4], which has eigenvalues \(λ1=6 and λ2=-4.\)Since λ1 is positive and λ2 is negative, this critical point is a saddle.

At (3,0), we have J = [0, -12; 0, -4], which has eigenvalues\(λ1=0 and λ2=-4.\)Since λ1 is zero, this critical point is a degenerate case and we need to look at higher order terms in the Taylor expansion to determine its type.

At (2,3/2), we have J = [0, -8; 3, 0], which has eigenvalues\(λ1=3i and λ2=-3i\). Since the eigenvalues are purely imaginary and non-zero, this critical point is a center or a spiral.

To find the directions of the saddle separatrices, we look at the sign of x' and y' near the critical point (3,0). From x' = -2x^2, we know that x' is negative to the left of (3,0) and positive to the right of (3,0). From y' = 2xy, we know that y' is positive in the upper half-plane and negative in the lower half-plane. Therefore, the saddle separatrices are the x-axis and the y-axis.

From the phase portrait, we see that the critical point (2,3/2) is a spiral sink, which means that both species can coexist in the long-term. The limit sizes of the populations are \(lim x(t) = 2 and lim y(t) = 1.5\).

(c) At the critical point (x=2, y=0.5), the Jacobian matrix is J = [2, -4; 1, 0], which has eigenvalues\(λ1=1+i√3 and λ2=1-i√3\). Since the eigenvalues have non-zero real parts, this critical point is not a center or a spiral sink. Therefore, there is no value of a for which this critical point is a spiral sink.

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Answer:7/97 or 0.072165

Step-by-step explanation:

In response to the given question, we can state that we know that sum of all angles in a triangle is 180. m∠C = 4*11.67+43 = 89.68 = =90

A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.

we know that sum of all angles in a triangle is 180.

2x - 12 + 4x + 43 + 9x - 26 = 180

15x  + 5 = 180

15x = 175

x = 11.67

m∠C = 4*11.67+43 = 89.68 = =90

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Answer:

m∠C = 119°

Step-by-step explanation:

According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

From inspection of the given triangle, the exterior angle is (9x - 26)° and the two non-adjacent interior angles are ∠B and ∠C.

Equate the sum of the two non-adjacent angles to the exterior angle and solve for x:

⇒ (2x - 12)° + (4x + 43)° = (9x - 26)°

⇒ 2x - 12 + 4x + 43 = 9x - 26

⇒ 6x + 31 = 9x - 26

⇒ 57 = 3x

⇒ x = 19

To calculate the measure of angle C, substitute the found value of x into the expression for the angle:

⇒ m∠C = (4x + 43)°

⇒ m∠C = (4(19) + 43)°

⇒ m∠C = (76 + 43)°

⇒ m∠C = 119°

Answer:

Step-by-step explanation:

630

Answer:

789 to nearest whole number.

Step-by-step explanation:

In 4 years its increased from 220 to 350.

350 = 220(e)^4k  where k is some constant.

e^4k = 350/220

4k = ln (350/220) = 0.4643

k = 0.1161

The equation  of growth is therefore

P = 220e^0.1161t)

So  in 2011 ( t = 11 years) the

Population = 220 * e^(11*0.1161)

= 789.