5 subtracted from 3 times a number x gives 7.

​

The value of the integral (9x + 9y) da over the region r is approximately 14.0625.

To evaluate the given integral using a transformation, we can use the concept of a double integral over a region in the xy-plane.

First, let's define the transformation T from the uv-plane to the xy-plane, where x = 9u and y = 9v. This transformation scales the coordinates by a factor of 9.

Next, let's find the Jacobian determinant of the transformation. The Jacobian determinant of T is given by the absolute value of the determinant of the matrix of partial derivatives of x and y with respect to u and v. In this case, the matrix is:

J(T) = |[∂x/∂u  ∂x/∂v]|
           |[∂y/∂u  ∂y/∂v]|

Taking the partial derivatives, we have:

∂x/∂u = 9   and   ∂x/∂v = 0
∂y/∂u = 0   and   ∂y/∂v = 9

Therefore, the Jacobian determinant is:

J(T) = |[9  0]|
           |[0  9]|

Taking the determinant, we have:

J(T) = (9)(9) - (0)(0) = 81

Now, we can evaluate the integral by transforming it into the uv-plane. The integral becomes:

∬(9x + 9y) dA = ∬(9(9u) + 9(9v))(J(T)) dA

Since x = 9u and y = 9v, we can substitute these expressions into the integral:

∬(9(9u) + 9(9v))(J(T)) dA = ∬(81u + 81v)(81) dA

Now, we need to find the limits of integration in the uv-plane. The region r in the xy-plane corresponds to a parallelogram in the uv-plane with vertices (-1/9, 2/9), (1/9, -2/9), (3/9, 0), and (1/9, 4/9).

Using these vertices, we can determine the limits of integration for u and v:

u ranges from -1/9 to 1/9
v ranges from 2/9 to 4/9

Therefore, the integral becomes:

∬(81u + 81v)(81) dA = ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv

Now, we can evaluate this double integral:

∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv = (81)(81) ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (u + v) dudv

Evaluating the inner integral with respect to u, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + vu [v=2/9 to 4/9] dv

Simplifying further, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(2/9) dv

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (4/81)u^2 du

Combining like terms, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2 + 4/81)u^2 du

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du

Now, we can evaluate the integral:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du = (81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du

Integrating u^2 with respect to u, we get:

(81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du = (81)(81)(85/162) [u^3/3] from -1/9 to 1/9

Plugging in the limits of integration, we have:

(81)(81)(85/162) [(1/9)^3/3 - (-1/9)^3/3]

Simplifying further, we get:

(81)(81)(85/162) [(1/729)/3 - (-1/729)/3] = (81)(81)(85/162) [2/729]/3

Now, we can simplify this expression:

(81)(81)(85/162) [2/729]/3 = (81)(81)(85/162) (2/729)(1/3)

Finally, evaluating this expression, we get:

(81)(81)(85/162) (2/729)(1/3) ≈ 14.0625

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Answer:

8

Step-by-step explanation:

1/2(12)=6

Answer:

8

Step-by-step explanation:

1/2(8+4)=6

Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

Answer:

1

Step-by-step explanation:

\((3^{n-1})\cdot(3^{1-n})\\\\=3^{n-1+1-n}\\\\\longrightarrow n-1+1-n=(n-n)+(-1+1)=0+0=0\\\\=3^{0}\\\\=1\)

Answer:

i believe the answer is x= -1.25

bye the question

greatest common factor means which is common factor in all three numbers as 18,36,45

Step-by-step explanation:

here,

therefore the greatest common factor of 18,36 and 45 is 3.

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer: 5 to the power of 2

Step-by-step explanation:

Answer:

\(5^{2}\)

Step-by-step explanation:

\(\frac{5^4 x 5^3}{5^5} = \frac{5^7}{5^5} = 5^2\)

The surface area of the cone is; 68π units² ​

we have to know the formula to calculate the surface area of the cone

Given that

A = area

r = radius  = 4

L = 13

Therefore, the surface area of the cone

A = π*r² + π*L*r

we replace with the known values;

A = π *  (4u)² + π * 13u * 4u

A = 16π u² + 52π u²

A = 68π u²

Thus, surface area of the cone is 68π u²

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Answer:

yes because we are leraning new things

A cross-sectional effect diagram, also known as an axial force-shear force-bending moment diagram or simply an internal force diagram, is a graphical representation that shows the distribution of internal forces (axial force, shear force, and bending moment) along the length of a structural member, such as a beam or column.

To draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure, we need to follow these steps:

Step 1: Identify the type of loadingFor this question, the loading conditions are {N}, {T}, {M}. So, the loading types are axial force, shear force, and bending moment.

Step 2: Draw the cross-sectional diagram of the beam. We need to draw the diagram of the cross-section of the beam in the direction of the forces acting on the beam. In this case, it will be a rectangular beam.

Step 3: Draw the effect diagrams After drawing the cross-sectional diagram, we need to draw the effect diagrams for each loading condition.

The effect diagrams are as follows: 1. Axial force diagram (N):In this case, the axial force is positive (+) which means it is a tensile force. 2. Shear force diagram (T):The shear force is negative (-) from x = 0 to x = 1, which means the shear force is acting downward. It is zero at x = 1 and then becomes positive (+) from x = 1 to x = 2, which means the shear force is acting upward. 3. Bending moment diagram (M):The bending moment is zero at x = 0, becomes negative (-) from x = 0 to x = 1, reaches a minimum at x = 1, and then becomes positive (+) from x = 1 to x = 2.

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The standard deviation of a larger sample will be closer to the standard deviation of the population than the standard deviation of a smaller sample, making it a better estimate of the population standard deviation.

In order to measure the variability or spread of a population, a population standard deviation is utilized. This is frequently unknown and estimated using the standard deviation of a random sample taken from the population. The sample standard deviation is the measure of variability for a set of data values obtained from a sample.The sample standard deviation is preferable to the population standard deviation for samples, particularly large samples. The sample standard deviation, abbreviated as "s", is used to estimate the population standard deviation, represented by the Greek letter sigma, which is unknown in this situation. The sample standard deviation is more likely to accurately reflect the true population standard deviation when it is calculated from a large sample size.Samples from populations that have a normal distribution provide the most precise estimate of the population standard deviation. If the population distribution is not normal, the sample size should be at least 30. However, for smaller samples, it is impossible to estimate the population standard deviation using the sample standard deviation. This is particularly true when the population has an atypical or unusual distribution.

In conclusion, the sample standard deviation (s) is a better estimate of the population standard deviation for large samples.

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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Alright! Let's go step by step. We want to understand how the house size relates to the number of residents. In other words, as the number of residents changes, how does the size of the house change? This relationship can be represented by a linear regression equation. The general form of a linear regression equation is:

y = m*x + b

Here:

- y is the dependent variable (in our case, the house size).

- x is the independent variable (in our case, the number of residents).

- m is the slope of the line (how much y changes for a unit change in x).

- b is the y-intercept (the value of y when x is 0).

We'll use the data you provided to calculate 'm' and 'b'. There are different ways to calculate these values, but I'll use a method that is relatively simple to understand:

m = (N * Σ(xy) - Σx * Σy) / (N * Σ(x^2) - (Σx)^2)

b = (Σy - m * Σx) / N

Where:

- N is the number of data points (in our case, 15).

- Σ stands for summation (sum of all values).

Now, let's calculate 'm' and 'b' using the data you provided:

Number of Residents(x) | House size (Sq. ft)(y) | xy | x^2

------------------------|------------------------|----|-----

3                      | 1992                   |5976|9

3                      | 1754                   |5262|9

3                      | 1766                   |5298|9

5                      | 2060                   |10300|25

6                      | 2293                   |13758|36

6                      | 2139                   |12834|36

3                      | 1836                   |5508|9

4                      | 1924                   |7696|16

6                      | 2321                   |13926|36

4                      | 2060                   |8240|16

3                      | 1769                   |5307|9

4                      | 1955                   |7820|16

5                      | 2309                   |11545|25

4                      | 1857                   |7428|16

4                      | 1972                   |7888|16

Σx = 66

Σy = 30999

Σxy = 120978

Σ(x^2) = 282

Plug these values into our formulas:

m = (15 * 120978 - 66 * 30999) / (15 * 282 - 66^2)

  ≈ 305.91

b = (30999 - 305.91 * 66) / 15

  ≈ 905.27

So our linear regression equation is:

House size = 305.91 * (Number of Residents) + 905.27

Now, let's predict the house size for a family of 5 residents:

House size = 305.91 * 5 + 905.27

           ≈ 2444.82 Sq. ft

This means that, according to our linear regression model, a family of 5 residents would need a house size of approximately 2445 square feet.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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Answer:

x > 3   or   3 < x < infinity

Step-by-step explanation:

Since the circle over 3 is "open" (not filled in), this means that the symbol we use for the inequality is simply "greater than" rather than "greater than/equal to".

Additionally, there is no point on the right side; it is an infinite arrow. This means that x is equivalent to anything above 3.

Therefore, x is greater than 3 is the correct inequality. Depending on the answer your teacher is looking for, however, it could also be 3 < x < infinity. this is because there is no visible end to the arrow.

*As I don't know what you're focusing on, I cannot tell you which answer your teacher is looking for. Base your answer off the form of the answers of the lesson you are focusing on.

A check or quadrangle is defined by the intersection of pairs of diagonals of a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides are parallel and have the same length. The opposite angles of a parallelogram are equal. A parallelogram is a unique type of quadrilateral with specific characteristics.

A quadrangle or check is defined as the intersection of pairs of diagonals of a parallelogram. In other words, it is the area inside the parallelogram that is divided into four triangles, each of which shares a common vertex in the center of the parallelogram.

The diagonals of a parallelogram are the line segments that connect the opposite vertices of a parallelogram. When these diagonals intersect, they form four triangles, which are also known as the parallelogram's "sub-triangles." The point where the diagonals intersect is called the center of the parallelogram, and it divides each diagonal into two equal parts.

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It's impossible to answer this without the table...

Answer:

12

Step-by-step explanation:

set up your proportion 80/200=X/30 and cross multiply.
200X=2400 then isolate the variable by dividing 2400 by 200. This gives you 12 and that is your answer.

The nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

Given the 13th unit requires 87 minutes and 26th unit requires 64 minutes.To find the estimated time required by the 50th unit, we need to use the equation of the linear equation of the line.Let's find the value of m (slope).`m = (64 - 87)/(26 - 13)m = -23/13`Let's find the value of b (y-intercept).`b = 87 - (-23/13) × 13b = 87 + 23b = 110`

Therefore, the equation of the line can be written as:y = -23/13 x + 110Let's substitute the value of x as 50 and find the value of y (time required by the 50th unit).`y = -23/13 × 50 + 110y = 47.31`Rounded to the nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

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The unknown angle x in the triangle is 80 degrees

From the question, we have the following parameters that can be used in our computation:

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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This segment consists of (insert characteristics of the target audience, such as demographics, interests, or behaviors).

The basic customer needs that are being satisfied in this segment include [insert specific customer needs, such as convenience, affordability, or quality]. For example, customers in this segment may value [insert specific need, such as time-saving solutions, personalized experiences, or innovative features].
Developing a buyer persona for this segment involves creating a fictional representation of the ideal customer. This includes information such as their age, gender, occupation, interests, and goals. By understanding this buyer persona, businesses can tailor their marketing strategies and offerings to meet the needs of their target audience effectively.
In conclusion, the chosen product/service is marketed towards [specific market segment]. This segment's basic customer needs, such as [specific needs], are being satisfied.

Creating a buyer persona allows businesses to better understand their target audience and tailor their marketing efforts accordingly. [Insert any additional relevant information if needed to reach the word count requirement].

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The sum of the deviations is -60.

To find the deviation from the mean for each data item, we subtract the mean from each individual data point.

Given data: 9, 15, 21, 36, 54, 81

Mean: 36

a. Deviation from the mean for each data item:

Deviation of 9 from the mean: 9 - 36 = -27

Deviation of 15 from the mean: 15 - 36 = -21

Deviation of 21 from the mean: 21 - 36 = -15

Deviation of 36 from the mean: 36 - 36 = 0

Deviation of 54 from the mean: 54 - 36 = 18

Deviation of 81 from the mean: 81 - 36 = 45

Therefore, the deviations from the mean for each data item are:

-27, -21, -15, 0, 18, 45

b. Sum of the deviations:

Sum of the deviations = (-27) + (-21) + (-15) + 0 + 18 + 45

= -60

The sum of the deviations is -60.

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Using midpoint theorem the value of DE is 4.

What is midpoint theorem?

 According to the midpoint theorem, "The line segment of a triangle linking the midpoint of its two sides is said to be parallel to its third side and is also half the length of the third side."

Here using midpoint theorem we know that ,

=> DE = 1/2 AB

Here DE=34-6x and AB=28-4x.

=> 34-6x=1/2(28-4x)

=>68-12x=28-4x

=> 12x-4x=68-28

=> 8x = 40

=> x =5.

Now put x=5 into DE then,

=> DE=34-6(5)=34-30 = 4.

Therefore using midpoint theorem value of DE is 4.

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Answer:when you're working hard for 4 year graduation and will cost you, 10177.84 for whole 4 year

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

C because 5 times any of the numbers do not equal the y value

Step-by-step explanation: