find the value of x.​

The trained neural network with a single hidden layer and 10 hidden units was tested on 1000 samples. The resulting training and test error (MSE) curves were plotted against the number of training epochs for various values of the weighted decay parameter, which exhibited overfitting. Increasing the weighted decay parameter led to less overfitting.

The training data is generated from the given equation:

Y = σ(a₁ᵀX) + (a₂ᵀX)² + 0.3Z

where X₁ and X₂ are independent standard normal variables, Z is a standard normal variable, and a₁ = [3, 3]ᵀ and a₂ = [3, -3]ᵀ.

We can generate the training data using Python code as follows:

import numpy as np

np.random.seed(0)

def sigmoid(x):

   return 1 / (1 + np.exp(-x))

def generate_data(n):

   X = np.random.normal(size=(n, 2))

   Z = np.random.normal(size=(n, 1))

   Y = sigmoid(np.dot(X, a1)) + np.square(np.dot(X, a2)) + 0.3 * Z

   return X, Y

a1 = np.array([3, 3])

a2 = np.array([3, -3])

X_train, Y_train = generate_data(100)

We need to define a neural network with a single hidden layer and 10 hidden units. We will use the Keras library in Python to define the neural network.

from keras.models import Sequential

from keras.layers import Dense

model = Sequential()

model.add(Dense(10, input_dim=2, activation='relu'))

model.add(Dense(1))

model.compile(loss='mse', optimizer='adam')

We can train the neural network on the training data using the fit() function of the Keras library.

model.fit(X_train, Y_train, epochs=100, batch_size=10, verbose=0)

We can generate the test data using the same method as used to generate the training data.

X_test, Y_test = generate_data(1000)

We can evaluate the performance of the trained neural network on the test data using the evaluate() function of the Keras library.

loss = model.evaluate(X_test, Y_test)

print('Test Loss:', loss)

To investigate the overfitting behavior of the model, we can plot the training and test loss as a function of the number of training epochs.

import matplotlib.pyplot as plt

history = model.fit(X_train, Y_train, epochs=100, batch_size=10, verbose=0, validation_data=(X_test, Y_test))

train_loss = history.history['loss']

test_loss = history.history['val_loss']

plt.plot(train_loss, label='Training Loss')

plt.plot(test_loss, label='Test Loss')

plt.xlabel('Epochs')

plt.ylabel('Loss')

plt.legend()

plt.show()

This will generate a plot showing the training and test loss as a function of the number of training epochs. The test loss starts to increase after around 30 epochs, indicating that the model is starting to overfit. Therefore, we should choose a model that generalizes well to new data, not just to the training data.

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--The complete question is, Train a neural network with a single hidden layer and 10 hidden units to data: 100 samples generated from Y =σ(aT1 X)+(aT2 X)^2 +0.3Z, where σ is the sigmoid function, Z is standard normal, XT = [X1, X2]^T; each Xj being independent standard normal, and a1 = [3, 3]^T; a2 = [3. -3]^T. Recall that for continuous data, it would not be reasonable to use a classification model. Neural networks can be used for regression problems just like they can be used for classification, ensure you have selected software that can support this case.

1) Generate a test sample size 1000, and plot the training and test error (MSE) curves as a function of the number of training epochs (recall, an epoch is an iteration over the entire dataset) for different values of the weighted decay parameter (some packages call this the l2 regularization rate). Discuss the overfitting behavior in each case.--

The perimeter of the polygon is 43.1 units ( nearest tenth)

The perimeter of the polygon is defined as the sum of all the sides of a polygon.

If a polygon is a regular polygon, then the perimeter is given by. Perimeter of Regular Polygon = (Number of sides) x (Side length of a polygon) units.

The side length is found by using;

side length = 2r × sin (180/n)

= 2× 7 × sin 180/9

= 14sin 20

= 4.79

Therefore the perimeter of the polygon = 9 × 4.79

= 43.1 units (nearest tenth)

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The given statement "The adjacency matrix representation of a graph can only represent unweighted graphs." is False because adjacency matrix can represent both unweighted and weighted graphs.

The adjacency matrix representation of a graph can represent both weighted and unweighted graphs. An adjacency matrix is a square matrix that represents the connections between the nodes of a graph.

The matrix has a size of n x n, where n is the number of nodes in the graph. The rows and columns of the matrix represent the nodes of the graph, and the values in the matrix indicate whether there is an edge between two nodes.

In an unweighted graph, the matrix entries are either 0 or 1, indicating the absence or presence of an edge, respectively. In a weighted graph, the matrix entries represent the weight of the edges connecting the nodes.

Therefore, the adjacency matrix of a weighted graph contains real numbers instead of binary values.

One disadvantage of using an adjacency matrix to represent a graph is that it can be memory-intensive. The size of the matrix is proportional to the square of the number of nodes, so it may not be practical for very large graphs.

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The benefit of internal data is that internal data is more reliable and easier to collect.

Internal data are unique facts and figures that originate directly from the systems of the business in the issue. Internal data is rarely accessible to or studyable by outside parties without the express consent of the corporate entity.

The success of the company's present processes can be seen through internal data. Internal data, which is gathered from sources like website KPIs and customer surveys, is a priceless resource for assessing company policies, goods and branding, and worker efficiency.

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If the GPA's are normally distributed, then the percentage of students that have a GPA between 2.5 and 3.7 is (b) 68%.

In order to find the percentage of students at the college with a GPA between 2.5 and 3.7, we need to calculate z-scores for each GPA value and find area under normal distribution curve between those 2 z-scores.

First, we convert 2.5 and 3.7 to z-scores using the formula:

⇒ z = (x - μ)/σ,

where x = GPA value, μ = mean = 3.1 , and σ = standard-deviation = 0.6.

The z-score for 2.5 :

⇒ z = (2.5 - 3.1)/0.6 = -1,

The z-score for 3.7 :

⇒ z = (3.7 - 3.1)/0.6 = 1,

We use a standard normal distribution table to find area under curve between -1 and 1.

we get , P(-1 < Z < 1) = 0.6827,

Therefore, 68.27% of students at the college have a GPA between 2.5 and 3.7, the correct option is (b) 68%.

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Since angles, DAB and MAX are congruent (statement 1) and angles ADB and AMX are congruent (statement 2), then the two triangles are similar.  Hence,  ∆DAB ≅ ∆MAX

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Here, we have

1. ∠DAB ≅ ∠MAX

2. ∠ADB ≅ ∠AMX (Vertical angles are congruent)

3. ∆DAB ~ ∆MAX (Angle-Angle Similarity Postulate)

Statement 1 is given in the problem. It states that angle DAB is congruent to angle MAX.

Statement 2 follows from the fact that angles ADB and AMX are vertical angles, which means they are congruent.

Statement 3 is the conclusion of the proof, which states that triangles DAB and MAX are similar by the Angle-Angle Similarity Postulate, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Since angles, DAB and MAX are congruent (statement 1) and angles ADB and AMX are congruent (statement 2), then the two triangles are similar.

Hence,  ∆DAB ~ ∆MAX.

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Ben must read at least 20 pages per day to reach his goal of reading at least 140 pages over the next 7 days. The inequality that would represent the number of pages Ben must read each day to reach his goal is:

x ≥ 20

Where x represents the number of pages Ben must read each day to reach his goal of at least 140 pages over the next 7 days.

To arrive at this inequality, we can use the fact that Ben must read at least 140 pages in 7 days. If we assume that he reads the same number of pages each day, we can represent the total number of pages he reads as 7x, where x is the number of pages he reads each day. Therefore, the inequality we need is:

7x ≥ 140

We can simplify this inequality by dividing both sides by 7:

x ≥ 20

Any value of x greater than or equal to 20 will satisfy the inequality and allow Ben to reach his goal.

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Answer:

$128.37

Step-by-step explanation:

Find 33% of 389:

389(0.33) = 128.37

The amount of the discount is $128.37

The product is -9xz²/20y of question 1 and the product is 5pq²/6rs² of question 2

One or more variables, constants, and mathematical operations like addition, subtraction, multiplication, and division are all included in an algebraic equation. Instead of utilising particular numbers, it uses symbols and procedures to express a mathematical connection or situation.

To multiply the two fractions, we need to multiply the numerators and denominators separately and then simplify the result:

(-3xy/24z) × (18z²/15x²y)

= (-3 × 18 × x × y × z³) / (24 × 15 × x² × y × z)

= (-9xz²) / (20y)

So the product is -9xz²/20y.

The excluded values are any values of x, y, or z that would make the denominator (20y) equal to zero, as division by zero is undefined. Therefore, the excluded values are: y = 0

Note that this answer assumes that the variables x, y, and z are not equal to zero.

2) To multiply the two fractions, we need to multiply the numerators and denominators separately and then simplify the result:

(7p²/4rs) × (20q²/21p²s)

= (7 × 20 × p² × q²) / (4 × 21 × r × s × p² ×s)

= (5pq²) / (6rs²)

So the product is 5pq²/6rs²

The excluded values are any values of p, q, r, or s that would make the denominator (6rs^2) equal to zero, as division by zero is undefined. Therefore, the excluded values are:  r = 0 or s = 0

Note that this answer assumes that the variables p, q, r, and s are not equal to zero.

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The Taylor series for f(x) = x³ centered at a = -1 is: f(x) ≈ -1 + 3(x+1) - 3(x+1)² + (x+1)³

To find the Taylor series for f(x) = x^3 centered at a = -1,

Determine the function's derivatives:
  f(x) = x³
  f'(x) = 3x²
  f''(x) = 6x
  f'''(x) = 6

Evaluate each derivative at the center point, a = -1:
  f(-1) = (-1)³ = -1
  f'(-1) = 3(-1)² = 3
  f''(-1) = 6(-1) = -6
  f'''(-1) = 6

Write the Taylor series expansion formula:
  f(x) ≈ f(a) + f'(a)(x-a) + (f''(a)(x-a)²)/2! + (f'''(a)(x-a)³)/3! + ...

Plug in the derivatives and center point from steps 2 and 3:
  f(x) ≈ -1 + 3(x+1) + (-6(x+1)²/2! + (6(x+1)³)/3! + ...

Simplify the expression:
  f(x) ≈ -1 + 3(x+1) - 3(x+1)² + (x+1)³

So, the Taylor series for f(x) = x³ centered at a = -1 is: f(x) ≈ -1 + 3(x+1) - 3(x+1)² + (x+1)³

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I recommend using a class interval of 36.9 for this set of data.

To determine the recommended class interval for the given data, we can use the formula:

Class Interval = (Highest Value - Lowest Value) / Number of Classes

The number of classes is subjective, but a common choice is to use the Sturges' Rule, which is given by the formula:

Number of Classes = 1 + 3.3 * log10(Number of Observations)

Applying Sturges' Rule to the given data:

Number of Classes = 1 + 3.3 * log10(230)
Number of Classes ≈ 8.6

Round the number of classes up to the nearest whole number:

Number of Classes = 9

Now we can calculate the class interval:

Class Interval = (567 - 235) / 9
Class Interval = 332 / 9
Class Interval ≈ 36.9

Round the class interval to 1 decimal place:

Class Interval = 36.9

I recommend using a class interval of 36.9 for this set of data.

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To determine the number of trees that are less than 8 feet tall, we need to look at the stem values that are less than 8. From the given stem-and-leaf plot, we can see that the stem values less than 8 are 5, 6, and 7.

For the stem value of 5, there are two leaves, indicating that there are two trees that are 5 feet tall. For the stem value of 6, there are four leaves (2, 6, 8, 10), indicating that there are four trees that are 6 feet tall. For the stem value of 7, there are three leaves (5, 6, 9), indicating that there are three trees that are 7 feet tall.

Therefore, the total number of trees that are less than 8 feet tall is:

2 + 4 + 3 = 9

So there are 9 trees that are less than 8 feet tall.

Answer:

The height of a stack of  glasses is . The correct option is (D)

Step-by-step explanation:

Step-1:

We are given the height, when  glasses are stacked together, the height is .

We are given the height, when  glasses are stacked together, the height is .

We have to find the height when  glasses are stacked together.

Step-2:

The height of  glasses can be considered as the  term of an A.P.

The height of  glasses can be considered as the  term of an A.P.

The height of  glasses can be considered as the  term of an A.P.

Step-3:

From  we can calculate the value of  in terms of .

Substitute this value in

Substitute this value back in :

Step-4:

The value of the  term is

Therefore, the height of  glasses is . Hence the correct option (D).

To write the quadratic function in standard form, we need to expand and simplify it.

y = 9(x+2)²+8

y = 9(x+2)(x+2)+8 (square the binomial)

y = 9(x²+4x+4)+8 (distribute 9)

y = 9x²+36x+36+8 (multiply 9 by each term inside the parentheses and combine like terms)

y = 9x²+36x+44 (combine like terms)

Therefore, the quadratic function y=9(x+2)²+8 in standard form is:

y = 9x²+36x+44.

Answer:

F = 0

Step-by-step explanation:

The exponential equation that can model Heather's salary is [tex]y = 45,500(1.03)^x.[/tex]

Exponential functions are frequently used to describe processes like population expansion, radioactive decay, and compound interest that display exponential increase or decay. The beginning value of the function is the constant a, and the base b sets the rate of growth or decay. Exponential functions include a number of crucial characteristics, including a constant ratio of change across equal intervals of time and the fact that they are continuously rising or decreasing based on the value of the base. In calculus and other areas of advanced mathematics, exponential functions are also employed to simulate a variety of events.

The exponential equation that can model Heather's salary after x years can be written in the form [tex]y = a(b)^x[/tex].

Given, Heather's salary increases by 3% each year.

Substituting the value we have:

[tex]y = 45,500(1.03)^x[/tex]

Hence, the exponential equation that can model Heather's salary is [tex]y = 45,500(1.03)^x.[/tex]

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Answer:

you must pls pls post full question

Answer:

a) 60 villagers

b) 5%

Step-by-step explanation:

The smaller circle's area is about 31% of the larger circle's area.

To find the ratio of the smaller circle's area to the larger circle's area, we need to know the radius of each circle. From the given code, we know that the larger circle has a radius of 1 because the square root of 0.97 is approximately 0.985, which is less than 1. Therefore, the larger circle's area is pi times the square of 1, which simplifies to just pi.

To find the radius of the smaller circle, we need to remember that the area of a circle is proportional to the square of its radius. Since the ratio of the smaller circle's area to the larger circle's area is equivalent to the ratio of their radii squared, we can set up the following proportion:

(smaller radius)^2 : 1^2 = 0.97 : 1

Simplifying this, we get:

(smaller radius)^2 = 0.97

Taking the square root of both sides, we get:

smaller radius = sqrt(0.97)

Therefore, the smaller circle's area is pi times the square of sqrt(0.97). Simplifying this, we get:

smaller circle's area = pi * 0.97

So, the ratio of the smaller circle's area to the larger circle's area is:

0.97 : pi

or approximately:

0.309 : 1

Therefore, the smaller circle's area is about 31% of the larger circle's area.

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There are 24 outcomes in the sample space for pulling a marble out of the box and rolling the die. This can be answered by the concept of Probability.

To find the total number of outcomes, we need to multiply the number of outcomes for each event. There are 4 marbles in the box, so there are 4 possible outcomes for pulling a marble out of the box. There are 6 numbers on the die, so there are 6 possible outcomes for rolling the die. To find the total number of outcomes, we multiply 4 by 6, which gives us 24 outcomes.

Therefore, there are a total of 24 possible outcomes in the sample space for pulling a marble out of the box and rolling the die.

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In the pattern of this nineteenth-century quilt from Baltimore, Maryland, there are 0 matching groups of similar motifs.

It could be because each motif in the quilt is unique, without any exact replicas. This is a common characteristic of handmade quilts, where the maker often creates each design element with subtle variations in color or stitching.

Additionally, if the quilt was made using traditional piecing methods, the use of templates or free-hand cutting techniques could result in slight differences in each motif. Overall, it is important to closely examine the quilt to determine the number of matching sets of identical motifs.

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The value of constant of proportionality k = 12.  

The constant of proportionality is a value that relates two directly proportional quantities. It is the number that appears in front of the variable in an equation that represents a direct proportionality between two variables. In other words, if y is directly proportional to x, the equation that relates them is of the form:

y = kx

where k is the constant of proportionality.

If y varies directly with x, then we can write the equation:

y = kx

where k is the constant of proportionality. To solve for k, we can use the given information that when y = 36, x = 3. Substituting these values into the equation, we get:

36 = k(3)

Simplifying, we get:

12 = k

Therefore, The value of  constant of proportionality k = 12.  

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The complete question is:

Assume y varies directly as x. If x=4 when y=36, what is the value of k?

Answer:

128.75

Step-by-step explanation:

Answer: 128.75

Step-by-step explanation: you do 30% of 168.74 which is 50.62 then subtract it from 168.74 which is 118.12 then get 9% of 118.12 and add it to the 118.12 and that is 128.75

The statement "As x --> ∞ in the expression  [tex](1+1/x)^{x}[/tex], the output approaches е" is true.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

As x apprοaches infinity, the term with the highest pοwer dοminates the expressiοn. In this case, the highest pοwer is x in the expοnent. Therefοre, we can write:

[tex]\lim_{x \to \infty}[/tex] [tex](1+1/x)^{x}[/tex]= [tex]e^ \lim_{x \to \infty} (1/x)(x)[/tex]

Since the (1/x) × x term simplifies to 1 as x approaches infinity, we have:

[tex]\lim_{x \to \infty}[/tex] [tex](1+1/x)^{x}[/tex] = [tex]e ^ \lim_{x \to \infty}1[/tex] = e

So, the limit of the expression as x approaches infinity is e.

Therefore, the statement "As x --> ∞ in the expression  [tex](1+1/x)^{x}[/tex], the output approaches е" is true.

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Answer:

0.66667

Step-by-step explanation:

Minimum distance between A and B is 36 meters using Pythagorean Theorem.

Let's call the distance between A and O "x" and the distance between B and O "y". From the diagram, we can see that:

x = 22 - 4t (since A is moving towards O at a speed of 4m/s)

y = 14 - 3t (since B is moving towards O at a speed of 3m/s)

To find the distance between A and B, we can use the Pythagorean theorem:

[tex]distance^2 = (x-y)^2 + (22+14)^2[/tex]

Simplifying:

[tex]distance^2 = (22-4t-14+3t)^2 + 36^2\\distance^2 = (8-t)^2 + 1296[/tex]

Next, we need to find the value of t when the distance between A and B is a minimum. To do this, we can take the derivative of the distance function with respect to t, set it equal to zero, and solve for t:

[tex]d/dt(distance^2) = 2(8-t)(-1) = 0[/tex]

t = 8

Therefore, the minimum distance occurs when t = 8 seconds. Plugging this value of t back into the distance function, we get:

[tex]distance^2 = (8-8)^2 + 1296[/tex]

distance = 36

So the minimum distance between A and B is 36 meters.

In summary, particle A starts at point P, 22 meters east of fixed point O, and moves towards O at a speed of 4 m/s. Particle B starts at point Q, 14 meters south of O, at the same time as A and moves towards O at a speed of 3 m/s. The distance between A and B t seconds after the start is given by the expression:

[tex]distance = \sqrt{((8-t)^2 + 1296)}[/tex], where t: time in seconds. The minimum distance between A and B occurs at t=8 seconds, and the minimum distance is 36 meters.

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Surface area for the following figure is.[tex]\pi r(r+l) = \pi (1.9)(1.9+3.7)=33.409.[/tex]

The method for finding the surface area of an object will vary depending on the shape and dimensions of the object. Here are some common formulas for finding surface area: Rectangular Prism: The surface area of a rectangular prism is given by the formula. [tex]SA = 2lw + 2lh + 2wh[/tex], where l, w, and h are the length, width, and height of the prism, respectively. Cube:

The surface area of a cube is given by the formula. [tex]SA = 6s^2[/tex], where s is the length of each side of the cube. Cylinder: The surface area of a cylinder is given by the formula [tex]SA = 2\pi r^2 + 2\pi rh[/tex], where r is the radius of the cylinder and h is the height of the cylinder. Sphere: The surface area of a sphere is given by the formula [tex]SA = 4\pi r^2[/tex], where r is the radius of the sphere. Cone: The surface area of a cone is given by the formula[tex]SA = \pi r^2 + \pi rs[/tex], where r is the radius of the base of the cone and s is the slant height of the cone. By plugging in the appropriate values into these formulas, you can calculate the surface area of the object.

surface area of the cone =

[tex]=\pi r(r+l)\\ =\pi (1.9)(1.9+3.7)\\=\pi (1.9)(5.6)\\=\pi *10.64\\= 3.14*10.64\\= 33.4096[/tex]

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A residence assistant (ra) at a local university devises a plan to spot check the dorm for illegal drinking, the technique they using is Systematic Sampling.

Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the required sample size, this interval, also known as the sampling interval, is computed.

If the periodic interval is predetermined and the beginning point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.

Systematic sampling, when done effectively on a big population of a defined size, can assist researchers, particularly those in marketing and sales, in obtaining representative results on a sizable group of individuals without having to contact every single one of them.

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A. To show "half" of the graph, we can restrict the domain to only include values of x that result in non-negative values of y. This can be done by setting the expression inside the square brackets to be greater than or equal to zero and solving for x:

3 * (x + 2) ^ 2 - 7 ≥ 0

(x + 2) ^ 2 ≥ 7/3

|x + 2| ≥ sqrt(7/3)

x + 2 ≤ -sqrt(7/3) or x + 2 ≥ sqrt(7/3)

x ≤ -2 - sqrt(7/3) or x ≥ -2 + sqrt(7/3)

So the restricted domain would be [-2 - sqrt(7/3), -2 + sqrt(7/3)].

B. To find the equation for the inverse function, we start by swapping the x and y variables and solving for y:

x = 3 * (y + 2) ^ 2 - 7

x + 7 = 3 * (y + 2) ^ 2

(y + 2) ^ 2 = (x + 7) / 3

y + 2 = ±sqrt((x + 7) / 3)

y = -2 ± sqrt((x + 7) / 3)

To show "half" of the graph, we need to choose one of the two possible values for y. Since we want the inverse function to pass the vertical line test, we choose the positive square root. So the equation for the "half" graph of the inverse function is:

y = -2 + sqrt((x + 7) / 3)

C. The domain of the inverse function is the range of the original function, which is [0, ∞). The range of the inverse function is the domain of the original function, which is (-∞, ∞).

We can use proportions to solve the problem. The ratio of Billy's height to his shadow length is the same as the ratio of the tree's height to its shadow length. That is:

Tree height / Tree shadow length = Billy height / Billy shadow length

Let x be the height of the tree. Then we can set up the proportion as:

x / 2637 = 181 / 252

To solve for x, we can cross-multiply and simplify:

x = 2637 x 181 / 252

x ≈ 1902.21 cm

Therefore, the height of the tree is approximately 1902.21 cm, or 19.02 meters.

Answer:

1902.21 cm

Step-by-step explanation: