10. Johnny is looking at a map and measures the distance between Chattanooga and Nashville to be 3.5 inches. He wants to know the actual distance between the two cities. According to the scale on the map, 1 inch = 38 miles. How many miles is there between Chattanooga and Nashville?​

The area that is enclosed by the figure which is being observed by Val would be = 3,364m²

To calculate the area of the enclosed figure, the area of 2 circles and a square should be calculated and added together.

The area of a circle = πr²

r = 58/2 = 49

area = 3.14×49×49

= 7539.14×2

= 15078.28m

Area of the enclosed region = 58×58 = 3,364m²

Therefore, Val is wrong with the area of he calculated.

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For the region above x + 3y = 9 and below x + 9 = y², we have:

a = 18, b = -9, f(x) = (y² - 9)/3, and g(x) = (9 - x)/3.

For single integration: α = -6, β = 3 and h(y) = [(9 - y²)/3 - (y² - 9)].

To solve this problem, we first need to find the intersection points of the two curves x + 3y = 9 and x + 9 = y². We can do this by solving the system of equations:

x + 3y = 9

x + 9 = y²

Rearranging the first equation, we get:

x = 9 - 3y

Substituting this expression for x into the second equation, we get:

9 - 3y + 9 = y²

Simplifying, we get:

y² - 3y - 18 = 0

Factorizing, we get:

(y - 6)(y + 3) = 0

So the solutions are:

y = 6 or y = -3

Substituting these values of y into the equation x + 3y = 9, we get:

When y = 6, x = -9

When y = -3, x = 18

So the intersection points of the two curves are (-9, 6) and (18, -3).

Now we can find the area between the two curves by splitting it into two regions: the region above the curve x + 3y = 9 and below the curve x + 9 = y², and the region below the curve x + 3y = 9 and above the curve x + 9 = y².

For the region above x + 3y = 9 and below x + 9 = y², we have:

a = 18

b = -9

f(x) = (y² - 9)/3

g(x) = (9 - x)/3

Alternatively, to compute the area between the two curves x + 3y = 9 and x + 9 = y² using a single integral, we need to express the area as a function of y instead of x.

We can rearrange the equations x + 3y = 9 and x + 9 = y² to get:

x = 9 - 3y

x = y² - 9

Setting these two expressions equal to each other, we get:

9 - 3y = y² - 9

Simplifying, we get:

y² + 3y - 18 = 0

Factorizing, we get:

(y + 6)(y - 3) = 0

So the solutions are:

y = -6 or y = 3

Substituting these values of y into the equation x + 3y = 9, we get:

When y = -6, x = 27

When y = 3, x = 0

So the intersection points of the two curves are (27, -6) and (0, 3).

The area between the curves can be expressed as the difference between the integrals of the curves' respective functions with respect to y, since the curves are better expressed in terms of y.

The function representing the curve x + 3y = 9 in terms of y is:

x = 9 - 3y

We can rearrange this equation to get:

y = (9 - x)/3

Substituting x = y² - 9, we get:

y = (9 - y² + 9)/3

Simplifying, we get:

y² + 3y - 18 = 0

This is the same equation we obtained before, so we know that the bounds of integration are -6 and 3.

The function representing the curve x + 9 = y² in terms of y is:

x = y² - 9

Substituting this expression into the formula for the area of a region between two curves, we get:

Area = ∫(y=α)^(y=β) [(9 - y²)/3 - (y² - 9)] dy

Where;

α = -6 and β = 3 are the bounds of integration, and

the integrand [(9 - y²)/3 - (y² - 9)] represents the difference between the y-values of the two curves at a given x-value.

Simplifying the integrand, we get:

Area = ∫(y=-6)^(y=3) (18 - 2y²)/3 dy

Integrating, we get:

Area = [(6y - (2/3)y³)/3] |(y=-6)^(y=3)

Plugging in the limits of integration, we get:

Area = [(18 - 216)/3] - [(-36 + 216)/3]

Simplifying, we get:

Area = 66

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As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

The slope of a line in mathematics serves as a gauge for how steep it is. Between any two locations on the line, it is the proportion of the shift in the vertical motion (y) to the shift in the horizontal position (x). If we take into account two points on a line, (x1, y1) and (x2, y2), we can use the following formula to get the slope of the line: slope equals (y2 - y1)/. (x2 - x1) . Depending on the line's direction, the inclination can be zero, positive, or negative. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.

given

Finding the derivative of the given function with respect to x can be our first step. By applying the quotient rule, we get:

F(x) = 8x 3 sin (y)

[tex][(sin(y))(-24x2)] = f'(x) - (-8x^3) (cos(y))(y')] / (sin(y))^2[/tex]

where the derivative of y with respect to x is denoted by y'.

We can change x=1 and y=pi/2 in the equation above since we are interested in the slope at the position [1, pi/2].

Due to the fact that cos(pi/2) = 0 and sin(pi/2) = 1, we can write:

[tex]f'(1) = [(1)(-24) (-24) - (-8)(1)(0)(y')] / (1)^2[/tex]

f'(1) = -24 + 0

f'(1) = -24

As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

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A. Here's a sketch of a horizontal pipe at a maximum slope (1/2 inch per foot) and a minimum slope (1/4 inch per foot):   / / / / / / / / / / / / / / / / / / /

 / / / / / / / / / / / / / / / / / / /

/ / / / / / / / / / / / / / / / / / /

/ / / / / / / / / / / / / / / / / / /

The pipe on the left has a slope of 1/4 inch per foot, while the pipe on the right has a slope of 1/2 inch per foot.B. To determine the minimum and maximum angles, we need to use trigonometry. If we let the angle that the pipe makes with the horizontal be θ, then we have:Minimum angle: tan(θ) = 1/48 (since 1/4 inch per foot is equivalent to 1 inch of drop over 48 inches of horizontal distance) θ ≈ 1.2 degreesMaximum angle: tan(θ) = 1/24 (since 1/2 inch per foot is equivalent to 1 inch of drop over 24 inches of horizontal distance) θ ≈ 2.4 degreesSo the minimum angle is approximately 1.2 degrees and the maximum angle is approximately 2.4 degrees.C. To determine if the slope of Enrico's pipe is acceptable, we need to calculate the slope of the pipe in inches per foot. Enrico's pipe runs a horizontal distance of 172 inches and drops 6 inches. The slope is:Slope = Drop / Horizontal distance = 6 / 172Slope = 0.0349 inches per inchTo convert this to slope in inches per foot, we multiply by 12:Slope = 0.4188 inches per footSince this slope is between the acceptable range of 1/4 inch per foot and 1/2 inch per foot, Enrico's pipe slope is acceptable.


Correct me if I am wrong

A. Sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below. B. the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively. C. Yes, pipe slope is acceptable according to the given criteria.

B. Determine the minimum and maximum angles:

To find the angle, use the tangent function. The tangent of an angle is equal to the ratio of the height to the horizontal distance travelled.

Minimum angle:

Tangent of the angle= 1/4 inch per foot

Tangent of the angle = 0.25 inches per foot

Minimum angle (in degrees) = arctan(0.25)

Minimum angle ≈ 14.0 degrees

Maximum angle:

Tangent of the angle = 1/2 inch per foot

Tangent of the angle = 0.5 inches per foot

Maximum angle (in degrees) = arctan(0.5)

Maximum angle ≈ 26.6 degrees

C. Enrico's drain pipe:

Horizontal distance travelled  = 172 inches

Drop from the horizontal = 6 inches

Slope of the pipe = Drop / Run

Slope of the pipe = 6 / 172

Slope of the pipe ≈ 0.0349 inches per inch

To convert the slope to inches per foot:

Slope = 0.0349 × 12

Slope ≈ 0.4188 inches per foot

Hence, sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below, the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively, and yes, pipe slope is acceptable according to the given criteria.

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The area of the shaded region is 192 m².

We have,

(g)

The shaded region.

= Area of the rectangle - Area of the triangle

So,

Length = 16 m

Width = 18 m

Area of the rectangle.

= 16 x 18

= 288 m²

And,

Base² + 16² = 20²

Base² = 400 - 256

Base = √144 = 12

So,

Area of the triangle.

= 1/2 x base x height

= 1/2 x 12 x 16

= 96

Now,

The shaded region.

= Area of the rectangle - Area of the triangle

= 288 - 96

= 192 m²

Thus,

The area of the shaded region is 192 m².

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The smallest integer value of x that would be a solution in the inequality would be x = 2.

To find the smallest integer value of x that satisfies the inequality 5x + 3 ≥ 10, first solve the inequality for x:

Subtract 3 from both sides:

5x ≥ 7

Divide by 5:

x ≥ 7/5

The inequality states that x must be greater than or equal to 7/5, which is equal to 1.4. Since we are looking for the smallest integer value, we should round up to the next integer, which is 2. Therefore, the smallest integer value of x that satisfies the inequality is x = 2.

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The velocity and direction of the jet and the velocity and direction of the wind, expressed as vectors are;

(a) (0. 45)

(b) (450, 0)

(c) (450, 45)

(d) 452

84.3 °E

A vector quantity is one that has both magnitude and direction.

The direction of the pilot is heading = Due east

The speed of the jet relative to the air = 450 mi/h

The direction of the wind = Due north

Speed of the wind = 45 mi/h

(a) The velocity of the wind expressed as a vector is therefore;

[tex]\vec{v}_w[/tex] = 0·i + 45·j

Which indicates that the vector component form of the velocity of the wind is (0, 45)

(b) The velocity of the jet relative to the wind expressed as a vector therefore is; [tex]\vec{v}_j[/tex] = 450·i + 0·j

Which indicates that the vector form of the velocity of the jet relative to the wind is; (450, 0)

(c) The true velocity of the jet expressed as a vector is the sum of the two vectors, which indicates;

The true velocity of the jet = 0·i + 45·j + 450·i + 0·j = 450·i + 45·j

The vector form of the true velocity of the jet is (450, 45)

(d) The true speed of the jet is the magnitude of the vector of the true velocity of the jet, which is;

Speed = √((450 mi/h)² + (45 mi/h)²) ≈ 452 mi/h

The direction of the jet is the arctangent of the ratio of the components of the vector of the true velocity of the jet

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The expected value of winning a dollar when the coin comes down heads is:

Earnings from heads = 1 * 0.5 = 0.5

The expected value of losing fifty cents when the coin comes down tails is:

Earnings from tails = -0.5 * 0.5 = -0.25

The expected value of earnings for one toss is:

Earnings per toss = Earnings from heads + Earnings from tails = 0.5 - 0.25 = 0.25

Therefore, the expected earnings for 20 tosses is:

Expected earnings for 20 tosses = 20 * Earnings per toss = 20 * 0.25 = 5

So, you would expect to earn $5 after 20 tosses.

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After converting [tex]4.5 * 10^4[/tex] to decimal format, one gets 45,000 as an answer. Thus, option (A) is the correct answer.

To convert numbers multiplied by 10 with having an exponent number to decimal format, one first needs to check the sign on the exponent.

If the sign is positive, we must shift the decimal to the right with each power of 10. The exponent indicates the number of zeros added after the number in case no decimal is used.

And if the sign is negative, we have to shift the decimal to the left with each power of 10. One has to divide the number by the number one gets after multiplying 10 by itself as many times as the exponent.

Therefore, to convert [tex]4.5 * 10^4[/tex] to decimal format, we shift the decimal by 4 places and we get 45,000 as the answer.

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We got x = 84.50 by using Pythagorean theorem.

angle of semicircle is always be 90°.

[tex]115^2 = 78^2 + x^2[/tex]

[tex]13225 = 6084 + x^2[/tex]

[tex]x^2 = 13225- 6084[/tex]

[tex]= 7141[/tex]

[tex]x = \sqrt{7141}[/tex]

[tex]x = 84.50[/tex]

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A blocked design compares different independent variable levels by using homogeneous groups of experimental units.

In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.

By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.

In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.

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Answer:

A. x<-5

Step-by-step explanation:

-0.4x - 1.2 > 0.8

-0.4x > 2

x < -5

So, the answer is A. x<-5

Korey expect to make in profits in his fifth year of operation is $15,149.72. So, the correct answer is option A) $15,149.72.

To calculate Korey's expected profits in his fifth year of operation, we need to consider the expected growth rate of profits over the next four years.

Korey expects profits to increase by 6% each year for the next four years. To calculate his expected profits for each of the next four years, we can use the following formula:

Profit = Previous year's profit + (Previous year's profit x growth rate)

Using this formula, we can calculate Korey's expected profits for each of the next four years:

Year 1: $12,000 (average monthly profit of $1,000)

Year 2: $12,720 ($12,000 + ($12,000 x 0.06))

Year 3: $13,478.40 ($12,720 + ($12,720 x 0.06))

Year 4: $14,278.30 ($13,478.40 + ($13,478.40 x 0.06))

To calculate his expected profits in the fifth year, we can use the same formula:

Year 5: $15,149.72 ($14,278.30 + ($14,278.30 x 0.06))

Therefore, the correct answer is option A) $15,149.72.

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Answer:

A. ) 15,149.72

Answer:

It can be deduced that the set of fractions that is an example of reciprocal fractions include, 1/2, 3/1, and 1/6.

Step-by-step explanation:

If 14 inches represents the length of a square, then the approximate area of that square would be 196 square inches.

If the 14 inches represents the length of a square, we can calculate the area of the square by multiplying its length by its width. However, since a square has four sides of equal length, we know that its width is also 14 inches. Therefore, the area of the square can be calculated as:

Area = length x width = 14 inches x 14 inches = 196 square inches.

In general, the formula for the area of a rectangle is length x width, while the formula for the area of a circle is πr^2, where r is the radius of the circle.

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Complete question is:

If the 14 inches represents the length of a square. what is the approximate area in square inches.

The average rate of change in revenue as the number of bluetooth speakers sold increases from 20 to 40 units is $34.50 per unit.

To find the average rate of change in revenue, we need to calculate the change in revenue over the change in units sold.

First, let's calculate the revenue for 20 and 40 units sold:

R(20) = 35(20) - 0.01(20)^2 = $670

R(40) = 35(40) - 0.01(40)^2 = $1360

Now we can calculate the change in revenue:

ΔR = R(40) - R(20) = $1360 - $670 = $690

And the change in units sold:

Δx = 40 - 20 = 20

Finally, we can calculate the average rate of change in revenue:

ΔR/Δx = $690/20 = $34.50

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Answer:

$2,611.9.

Step-by-step explanation:

To find the operating cost for the lowest 2% of the airplanes, we need to find the corresponding z-score from the standard normal distribution using a z-table.

Using the formula:

z = (x - μ) / σ

where x is the cost we are interested in, μ is the mean cost, and σ is the standard deviation.

For the lowest 2% of airplanes, the z-score can be found by looking up the area to the left of z in the z-table. This area is 0.02.

Looking up 0.02 in the z-table gives a z-score of approximately -2.05.

So we have:

-2.05 = (x - 3403) / 398

Solving for x, we get:

x = -2.05 * 398 + 3403 = $2,611.9

Therefore, the operating cost for the lowest 2% of the airplanes is approximately $2,611.9.

Inequality for this scenario

x ≤ 4.75

So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.

Let x be the weight of each package (in pounds).

The inequality for the scenario can be written as:

21 + 4x ≤ 40

This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.

To solve for x, we can subtract 21 from both sides of the inequality:

4x ≤ 40 - 21

4x ≤ 19

Finally, we divide both sides by 4 to isolate x:

x ≤ 19 / 4

Let x be the weight of each package (in pounds).

The inequality for the scenario can be written as:

21 + 4x ≤ 40

This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.

To solve for x, we can subtract 21 from both sides of the inequality:

4x ≤ 40 - 21

4x ≤ 19

Finally, we divide both sides by 4 to isolate x:

x ≤ 19 / 4

x ≤ 4.75

So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.

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Answer:

Step-by-step explanation:

The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.

The turn the minute hand made is about 180 degrees when Mark finished his lunch.

To calculate time with angle, you need to know the angle between the hour hand and the minute hand. With that, you can use the formula

θ = 30H - 11/2M

where H is the current hour and M is the current minute.

Once you calculate the angle, you can use the formula

t = θ/30 to find the elapsed time in hours and decimal fractions of an hour.

The minute hand of a clock makes a full revolution (360 degrees) in 60 minutes (1 hour). Therefore, in 30 minutes, the minute hand will turn half the way around the clock face, which is 180 degrees.

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The complete question is: "Mark took 30minutes to finish lunch describe the turn the minute hand made when he finished his lunch".

The value of v is 13 degrees.

Supplementary angles are a set of given measure of angles which add up to 180 degrees. Thus producing a measure of the sum of angles on a straight line.

To determine the value of v in the given diagram, we have;

60 + (9v + 3) = 180       (sum of angles on a straight line)

So that;

9v + 3 = 1890 - 60

9v + 3 = 120

9v = 120 - 3

    = 117

v = 117/ 9

  = 13

v = 13^o

The value of v in the question is 13 degrees.

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Answer:

A triangle with side lengths of 38, 38, and 104 is an isosceles triangle. This is because it has two sides of equal length (the two sides that are both 38 units long).

Step-by-step explanation:

Then the answer is C. not a real number

An exponent of 1/2 is equivalent to the square root, so we can write:

√-25

That is the square root of a negative number, so we will get the complex numbers ±i

Then the answer is C.

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Answer:

below

Step-by-step explanation:

Yes, there is another exponent.

When you are multiplying exponents, you add the exponents.

So from the equation 2^6 x 2^5, you can keep the 2 the same, as this is the base:

2^11

and add the exponents (6+5)

To check:

2^6=64

2^5=32

64x32=2048

2^11=2048

So, 2^11 is equivalent to your equation.  Hope this helps ;)

1. The equation of the line in graph 1 in slope-intercept form is

y = (2/3)x + 2/3.

2. The equation of the line in graph 2 is

y = (1/3)x + 4/3.

a. To find the equation of the line passing through (3, 4) and (0, 2) (points obtained from the graph) in slope-intercept form, we need to first find the slope of the line.

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

Substituting the given values, we get:

slope = (2 - 4) / (0 - 3) = -2 / (-3) = 2/3

The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is given by:

y - y1 = m(x - x1)

y - 4 = (2/3)(x - 3)

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

b. points obtained from the graph (-3, 1) and (-6, 0)

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

slope = (0 - 1) / (-6 - (-3)) = -1 / (-3) = 1/3

y - y1 = m(x - x1)

y - 1 = (1/3)(x - (-3))

y = (1/3)x + 4/3

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She will fertilize 69.76 square feet outside of the circular flowers.

In order to get the area that she will fertilize outside of the circular flowers, we will calculate area of the entire rectangular garden and the area of the circular flowers.

The area of the rectangular garden is:

[tex]= 10 ft * 12 ft\\= 120 sq ft[/tex]

The area of the circular flowers is:

[tex]= \pi r^2\\= 3.14 * 4^2\\= 50.24 sq ft[/tex]

To find area to be fertilize outside of the circular flowers, we will subtract these area which gives us:

[tex]= 120 sq ft - 50.24 sq ft\\= 69.76 sq ft[/tex]

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Answer: Vertical text sets are arranged in columns from top to bottom, while horizontal text sets are arranged in rows from left to right. The major differences between the two include:

Readability: Vertical text sets may be more difficult to read for individuals who are accustomed to reading horizontally, while horizontal text sets may be more natural for them to read.

Space utilization: Vertical text sets can utilize space more efficiently, especially in situations where vertical space is available, such as in tall and narrow posters or banners. Horizontal text sets, on the other hand, can utilize space more efficiently in situations where horizontal space is available, such as in wide-screen displays or landscape-oriented documents.

Cultural conventions: In some cultures, such as Japan and China, vertical text sets are traditionally used for writing, while in other cultures, such as the United States, horizontal text sets are the norm. Thus, the use of one or the other may depend on cultural context.

One situation where vertical text sets may be more beneficial is in designing a tall and narrow billboard. In this case, a horizontal text set may be difficult to read from afar, while a vertical text set can make use of the available space and be easily read from a distance. On the other hand, in designing a website, horizontal text sets may be more beneficial as they can utilize the full width of the screen and provide more space for additional content.

Step-by-step explanation:

To ensure that the replica will fit on an 8.5-by-11-inch paper, we need to choose a scale that will result in dimensions that are smaller than or equal to 8.5 inches by 11 inches.

Choosing an appropriate scale for a replica depends on the size of the original object and the desired size of the replica. To fit a replica on an 8.5-by-11-inch paper, we need to determine the maximum size that the replica can be while still fitting on the paper.

One common method for determining the appropriate scale is to measure the dimensions of the original object and then divide them by the desired size of the replica. For example, if the original object is 20 inches wide and we want to create a replica that is 8 inches wide, the scale would be 20/8, or 2.5.

In order to fit the replica on an 8.5-by-11-inch paper, we need to make sure that the dimensions of the replica are smaller than or equal to 8.5 inches by 11 inches.

We can use the scale factor to determine the maximum dimensions of the replica. For example, if the scale factor is 2.5 and we want the replica to be 8 inches wide, the maximum height of the replica would be 8/2.5, or 3.2 inches.

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