How old is Katie if her mother is 3 times as old as her, but was 4 times older than her 4 years ago?
A. 12 years old
B. 8 years old
C. 36 years old
D. 32 years old

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Answer:

Area = x4 + 4x3 + 3x2 - 4x - 4

Length = x3 +5x2 + 8x + 4

Width = Area / Length.

Performing long division with polynomial.

x4 + 4x3 + 3x2 - 4x - 4 / x3 + 5x2 + 8x + 4 = x-1

Width = x-1

Step-by-step explanation:

The value of the width of the rectangle is,

⇒ (x - 1)

We have to given that;

In a rectangle;

Area = x⁴ + 4x³ + 3x² - 4x - 4

Length = x³ +5x² + 8x + 4

We know that;

Width = Area / Length.

Hence, Performing long division with polynomial.

Width = x⁴ + 4x³ + 3x² - 4x - 4 / x³ +5x² + 8x + 4

         = x - 1

Thus, The value of the width of the rectangle is,

⇒ (x - 1)

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Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

Answer:

y = x + 22

Graph is also attached

Step-by-step explanation:

slope-intercept form: y = mx + b

2y - 2x = 44

    + 2x   + 2x

2y = 2x + 44

\(\frac{2y}{2}=\frac{2x+44}{2}\)

y = x + 22

Hope this helps!

The number of students who knows all the 3 languages is 12

Total number of students = 80

Number of students who knows English = 50

Number of students who knows French = 55

Number of students who knows German = 46

Number of students who knows English and French = 37

Number of students who knows French and German = 28

Number of students who knows English and German = 25

Number of students who knows none of the languages = 7

Here we have to use the equation of the union of set

n(E∪F∪G) = n(E) + n(F) + n(G) - n(E∪F) - n(F∪G) - n(E∪G) + n(E∩F∩G)

80 - 7 = 50 + 55 +46 - 37 - 28 -25 + n(E∩F∩G)

n(E∩F∩G) = 73 - 50 -55 -46 +37 +28 +25

n(E∩F∩G) = 12

Hence, the number of students who knows all the 3 languages is 12

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Rotation - Rotation is a plane transformation that rotates every point in a figure through a given angle and direction on a fixed point.

Transformation - Transformation is a process that alters the shape and or position of a point, a line, or a geometric figure.

Translation - Translation occurs when a figure is relocated from one position to another without changing its size, shape, or orientation.

Dilation - Dilation is a transformation that alters the size of a figure, whether enlarging or shrinking it, but it has no effect on the shape of the figure.

Angle of Rotation - Angle of Rotation is the amount that a figure is rotated about a fixed point referred to as the point of rotation.

Line of Reflection - Line of Reflection is a transformation in which each point in a shape appears at an equal distance on the opposite side of a given line.

Hope this helps!!

The engineer should take a sample size of approximately 40 to be 95% confident of being in error by only 0.125 minutes.

To calculate the sample size for estimating the cycle time, the engineer can use the formula for continuous data:

E = (zα/2) * (σ / √n)

where:
E is the maximum allowable error (0.125 minutes),
zα/2 is the z-value for a 95% confidence level (which corresponds to a 0.025 alpha level),
σ is the standard deviation (0.4 minutes), and
n is the sample size (unknown).

Rearranging the formula, we have:

n = (zα/2)^2 * (σ^2 / E^2)

Plugging in the given values, we get:

n = (1.96)^2 * (0.4^2 / 0.125^2)

Simplifying the equation, we have:

n ≈ 3.8416 * (0.16 / 0.015625)

n ≈ 3.8416 * 10.24

n ≈ 39.494

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The simplified form of the given coordinate is (0,7/4) and the points in the coordinate plane given below:

In the given question we have to represent in given point in the coordinate plane.

The given coordinate is (0, 1 3/4).

In the given coordinate we firstly simplify the given coordinate.

We solve 1 3/4 this mixed fraction in the improper fraction.

To convert into improper fraction we multiply 1 with 4 then add with 3.

So simplified form is;

1 3/4 = 7/4

So the simplified form is (0, 7/4).

The point on the coordinate plane is given below:

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Answer:

Solution given:

2y+1=17

subtracting both side by 1

2y+1-1=17-1

2y=16

dividing both side by 2

2y/2=16/2

y=8

Answer:

2S + J = 24000

Step-by-step explanation:

let Susan be S

let Jinan be J

they paid 24000

susan paid twice as muh as jinan did​

2S + J = 24000

therefore equation is

2S + J = 24000

To finding the points on the given surface that are closest to the origin using Lagrange multipliers.

The second paragraph would typically involve the detailed calculation steps and the final solutions obtained, but without the specific values for the equation y² = 9 + xz, it is not possible to provide the explicit solutions.

To find the points on the given surface that are closest to the origin using Lagrange multipliers, we need to set up the appropriate optimization problem.

Let's denote the variables as x, y, and z. Our objective is to minimize the distance from the origin, which can be expressed as the square of the distance, D² = x² + y² + z². We also have the constraint y² = 9 + xz, which represents the given surface.

To solve this optimization problem, we introduce a Lagrange multiplier λ and set up the Lagrangian function L = D² - λ(y² - 9 - xz). We take the partial derivatives of L with respect to x, y, z, and λ, and set them equal to zero.

Solving the system of equations formed by these partial derivatives, we obtain the values of x, y, z, and λ that satisfy the optimization problem.

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Answer:

curved lines

Step-by-step explanation:

because a linear persctive is a straight line or perspective where in which a curved line isnt

When you trim a video, the start and end markers of the timeline indicate the portion of the video that will play during the slide; the trimmed portion indicates the portion that is removed or excluded from the final playback.

When editing a video, you may want to remove certain parts or shorten its duration. Trimming allows you to specify the exact portion of the video that will be included in the final version. The timeline represents the entire duration of the video, and the start and end markers on the timeline serve as reference points for indicating the selected segment. By adjusting the position of these markers, you can define the beginning and end points of the desired portion. The section of the timeline between the start and end markers represents the portion of the video that will play during the slide or be included in the final output. The remaining parts of the video outside of this selected segment are considered the trimmed portion, which will be excluded from the playback or final edited version of the video.

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The correct choice is A: Exactly one of the eigenspaces has dimension 2 or larger. The eigenspace associated with the eigenvalue λ = ...

Unfortunately, the specific matrix A and its eigenvalues and eigenvectors are not provided in the question. To determine the real eigenvalues and associated eigenvectors of a given matrix A, you would need to find the solutions to the characteristic equation det(A - λI) = 0, where det represents the determinant, A is the matrix, λ is the eigenvalue, and I is the identity matrix.

Once you have found the eigenvalues, you can substitute each eigenvalue back into the equation (A - λI)x = 0 to find the corresponding eigenvectors. The eigenvectors associated with each eigenvalue will form the eigenspace.

The dimension of the eigenspace corresponds to the number of linearly independent eigenvectors associated with a particular eigenvalue. If an eigenspace has a dimension of 2 or larger, it means there are at least 2 linearly independent eigenvectors associated with that eigenvalue.

Without the specific matrix A provided in the question, we cannot determine the eigenvalues, eigenvectors, or the dimensions of the eigenspaces.

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Answer:

-2

Step-by-step explanation:

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

Slope

\( = \frac{14 - 4}{ - 8 - ( - 3)} \)

\( = \frac{10}{ - 8 + 3} \)

\( = \frac{10}{ - 5} \)

= -2

Answer:  

Step-by-step explanation:

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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The distance in kilometers in scientific notation \(2.03 \times 10^3 km\)

Scale factors are values or constants multiplied with a variable

If Alvin and Simon raced a distance of \(2.9 \times 10^2\) kilometers and they need to race 7 times that distance in a kilometer, the distance traveled will be:

Hence the distance in kilometers in scientific notation \(2.03 \times 10^3 km\)

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Answer:

X=8.7 (1dp)

Step-by-step explanation:

X=8.7

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Addition of the given is (a) \(9x^{3} +x^{2}-6x+5\)

Equation given,

Eq 1 = \(7x^{3} - 2x^{2}-5x+6\)

Eq 2 = \(2x^{3}+ 3x^{2}-x-1\)

Adding Eq 1 + Eq 2,

\((7x^{3} - 2x^{2}-5x+6) + (2x^{3}+ 3x^{2}-x-1)\)

\((7x^{3} + 2x^{3}) + (- 2x^{2}+ 3x^{2})+(-5x-x)+(6-1)\)

\(9x^{3}+ x^{2}-6x+5\)

Hence, the answer.

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The value of the given trigonometric expression \(\frac{\sin\theta-\cos\theta}{\tan\theta}\) is \(\frac{279}{1640}\).

We know the trigonometric identities,

The sum of squares of sine and cosine of an angle is unity.
\(\sin^2\theta+\cos^2\theta=1\)

The tangent of any angle is the ratio of the sine and cosine of that angle.
\(\tan\theta=\frac{\sin\theta}{\cos\theta}\)

The cosine of any angle is the ratio base to the hypotenuse of a right triangle.

The given expression is \(41\cos\theta=9\)  and we have to find  \(\frac{\sin\theta-\cos\theta}{\tan\theta}\).

\(41\cos\theta=9\\\cos\theta=\frac{9}{41}\)

Now, using the trigonometric identity \(\sin^2\theta+\cos^2\theta=1\), we get

\(\sin^2\theta+\cos^2\theta=1\)

Putting the value of cosθ, and finding the value of sinθ,

\(\sin^2\theta+(\frac{9}{41})^{2} =1\\\sin^2\theta+\frac{81}{1681} =1\\\sin^2\theta=1-\frac{81}{1681}\\\sin^2\theta=\frac{1681-81}{1681}\\\\\sin^2\theta=\frac{1600}{1681}\\\\\sin\theta=\sqrt{ \frac{1600}{1681}}\\\sin\theta=\frac{40}{41}\)

Now, finding the value of tanθ, as tangent is the ratio of sine and cosine of theta,

\(\tan\theta=\frac{\sin\theta}{\cos\theta}\\\\\tan\theta=\frac{\frac{40}{41} }{\frac{9}{41}}\\\\\tan\theta=\frac{40}{9}\)

Now, Putting the values in the expression and simplifying,

\(\frac{\sin\theta-\cos\theta}{\tan\theta}=\frac{\frac{40}{41}-\frac{9}{41} }{\frac{40}{9}}\\\\=\frac{\frac{40-9}{41} }{\frac{40}{9} } \\\\=\frac{31}{41}\times\frac{9}{40}\\\\=\frac{279}{1640}\)

Therefore, the value of the given trigonometric expression \(\frac{\sin\theta-\cos\theta}{\tan\theta}\) is \(\frac{279}{1640}\).

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Answer:

$60

Step-by-step explanation:

Profit = revenue - total cost

cost is total expenses incurred in running the business

total cost =  cost of rent and the expensive saws and equipment + cost of wood + amount paid to worker

50 + 30 + 10 = 90

revenue is the amount earned from selling the chairs. it is equal to 150

Profit = 150 - 90 = 60

Answer:

sina = cosb = \(\frac{3}{5}\)

Step-by-step explanation:

sina = \(\frac{opposite}{hypotenuse}\) = \(\frac{9}{15}\) = \(\frac{3}{5}\)

cosb = \(\frac{adjacent}{hypotenuse}\) = \(\frac{9}{15}\) = \(\frac{3}{5}\)

Answer/Step-by-step explanation:

Given:

When Jada took 8 steps, Noah took 10 steps

When Jada took 12 steps, Noah took 15 steps

a. The following table can be created as follows given that x = steps taken by Jada, and y = steps taken by Noah:

From the info given, the ratio of Noah's steps to Jada's steps is 15 : 12 = 10 : 8 = 5 : 4 = ⁵/4.

Use this ratio to create a table of 3 pairs of values as shown below.

Jada's Steps (x) ===> Noah's steps (y)

4 ===> 5

8 ==> 10

12 ==> 15

b. The graph of that shows this relationship has been attached below. Check the attachment.

c. Constant of proportionality can be calculated in each representation as follows: y/x = k. Where y is steps taken by Noah, x is for steps taken by Jada, and I is constant of proportionality.

Thus,

Constant of proportionality (k) = 15/12 = ⁵/4

This means, for every 5 steps taken by Noah, Jada takes 4 steps.

This relationship is represented by the equation, y = ⁵/4x.

The ⁵/4 in the equation is the constant of proportionality of their relationship.

d. The equation, description, graph, and table all represent the same situation because they all show the same constant of proportionality between x and y.

In the equation, ⁵/4 represents the constant of proportionality. In the graph, the slope is ⁵/4, which is also the same last constant of proportionality.

In the table, the constant of change in each pair is ⁵/4 all through.

Answer:

1/81

Step-by-step explanation:

You just tap the calculator

Refer to the image attached.

Answer:

4

Step-by-step explanation:

Because you use trial and error to see what x is and it says integet meaning 1,2,3,4,5,6... and their opposites.

Answer:

x ≈ 5 using math and x ≈ 4 using trial and error

Step-by-step explanation:

\(6^x = 3800\)

\(x = log_{6}*3800\)

x ≈ 4.6 ≈ 5

Hope this helped!

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Trial and Error:

6 ^ 4 = 1276

6 ^ 5 = 7776

3800 is closer to 1276, so x = 4