There are 28 students whose last names begin with the letters G, H, J, or K. Information about the probability of randomly selecting one of these students is listed below • probability of selecting a student whose last name begins with G: 7 • probability of selecting a student whose last name begins with G or H: 5 14 O How many of these students have a last name that begins with H?
A4
B5
C6
D7​

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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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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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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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.--

Answer:

$128.37

Step-by-step explanation:

Find 33% of 389:

389(0.33) = 128.37

The amount of the discount is $128.37

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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Answer:

If 25 is 40% of a value, what is that value?

A. 85

B. 12.5

D. 60

Step-by-step explanation:

You're welcome.

Answer:

C) 62.5

Step-by-step explanation:

Write the expression:

40% of x = 25

Then calculate:

4x/10 = 25

4x = 250

x = 62.5

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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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

Answer:

you must pls pls post full question

Answer:

a) 60 villagers

b) 5%

Step-by-step explanation:

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.

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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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?

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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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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Answer:

5,5 m and 12 m

Step-by-step explanation:

Let's assume, the length of the rectangle is x and the width is y meters

Let's write 2 equations and put them in a system:

{x × y = 66,

{x = 2y + 1;

Let's replace x in the 1st equation with its value from the 2nd equation:

(2y + 1) × y = 66

[tex]2 {y}^{2} + y = 66[/tex]

[tex]2 {y}^{2} + y - 66 = 0[/tex]

a = 2, b = 1, c = -66

Let's solve this quadratic equation:

[tex]d = {b}^{2} - 4ac = {1}^{2} - 4 \times 2 \times ( - 66) = 1 + 528 = 529 > 0[/tex]

[tex]y1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 1 - 23}{2 \times 2} = \frac{ - 24}{4} = - 6[/tex]

Since y has to be a natural number (side lengths cannot have negative units), we cannot take this as an answer

[tex]y2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 1 + 23}{2 \times 2} = \frac{22}{4} = 5.5[/tex]

y = 5,5

x = 2 × 5,5 + 1 = 12

the dimensions of the rectangle are 5.5 meters by 12 meters.

The question states that the area of a rectangle is 66 m², and the length of the rectangle is 1 meter more than twice the width. We need to find the dimensions of the rectangle.

Let’s assume the width of the rectangle as “x”.

Then, according to the given information, the length will be (2x + 1).

Area of the rectangle = Length × Width

66 = (2x + 1) × x ⇒ 2x² + x - 66 = 0

Now we have to solve this quadratic equation. We can solve it by factoring or using the quadratic formula. Let’s use the quadratic formula:

x = [ -b ± √(b² - 4ac) ] / 2aHere, a = 2, b = 1, and c = -66

Therefore,x = [ -1 ± √(1² - 4(2)(-66)) ] / 2(2)x = [ -1 ± √(1 + 528)) ] / 4x = [ -1 ± √529 ] / 4

When we solve this, we get two possible solutions:

x = (-1 + 23) / 4 or x = (-1 - 23) / 4x = 22/4 or x = -24/4x = 5.5 or x = -6

The width of the rectangle cannot be negative. Therefore, the width of the rectangle is 5.5 meters.Length of the rectangle = 2 × 5.5 + 1= 11 + 1= 12 meters

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the 3D shape created by rotating the given rectangle around the X-axis will be a cylinder with its base centered at (-4,1.5), a radius of 1, and a height of 3.

What are 3D shapes?

The given coordinates (-3,0),(-5,0),(-5,3), and (-3,3) form a 2D rectangle lying in the XY-plane. When this rectangle is rotated around the X-axis, it will sweep out a 3D shape known as a cylinder.

A cylinder is a three-dimensional shape with a circular base and straight parallel sides. The base of the cylinder is formed by the 2D rectangle in the XY-plane, while the height of the cylinder is determined by the distance between the parallel sides of the rectangle. When the rectangle is rotated around the X-axis, it generates a circular cross-section at each height, resulting in a cylinder.

The center of the base of the cylinder will be located at (-4,1.5) on the XY-plane, which is the midpoint of the line joining the points (-3,0) and (-5,3). The radius of the base will be half of the width of the rectangle, which is (5-3)/2 = 1. The height of the cylinder will be the distance between the parallel sides of the rectangle, which is 3.

Therefore, the 3D shape created by rotating the given rectangle around the X-axis will be a cylinder with its base centered at (-4,1.5), a radius of 1, and a height of 3.

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Answer:

0.66667

Step-by-step explanation:

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:

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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The amount of time it takes to produce 2700 watts of power depends on the rate at which the power is produced. If we know the rate at which the power is produced, we can use the formula:

time = energy / power

where energy is the amount of energy produced (in watt-hours), power is the rate of power production (in watts), and time is the amount of time it takes (in hours).

If the rate at which the power is produced is constant at 2700 watts, then the amount of time it takes to produce 2700 watts of power is:

time = energy / power

time = 1 watt-hour / 2700 watts

time = 0.00037 hours

So, it would take approximately 0.00037 hours, or about 2.2 seconds, to produce 2700 watts of power at a constant rate of 2700 watts.

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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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 (-∞, ∞).

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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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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Hence, the distance between Hawkes Meadow and Brunswick Street is roughly 11.1 kilometres (km).

Distance is a unit used to express the distances between two objects or positions. This is a scalar value that is typically stated in length units like feet, metres, kilometres, or miles. Distance between two things is a physical concept that specifies their separation; it is frequently used to estimate how much space there is between them. The shortest distance, also referred to as "as the crow flies," can be calculated either along a horizontal path or a curved path. Displacement, or the shift in an object's position from its original location to its end position, is a notion in physics that is closely connected to distance.

given

Using the data from the timetable and the calculation, we can determine how many kilometres the bus travels between Hawkes Meadow and Brunswick Street:

Distance is determined by multiplying time and speed.

According to the timetable, the bus travels from Hawkes Meadow to Othello Avenue in 15 minutes (from 14:25 to 14:32), and from Othello Avenue to Brunswick Street in 8 more minutes (i.e., from 14:32 to 14:40). Hence, it takes 15 + 8 = 23 minutes to get from Hawkes Meadow to Brunswick Street.

Also, we are informed that the bus travels at an average speed of 29 km/h between Hawkes Meadow and Brunswick Street.

To utilise the calculation, we must first divide the time in minutes by 60 to convert it to hours:

23, divided by 60 hours, or 0.3833 hours (rounded to 4 decimal places)

Hence, we can compute the distance using the following formula:

11.12 kilometres is equal to 29 km/h times 0.3833 hours (rounded to 2 decimal places)

Hence, the distance between Hawkes Meadow and Brunswick Street is roughly 11.1 kilometres (km).

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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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Answer:

F = 0

Step-by-step explanation:

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).