Randy is planning to drive from New Jersey to Florida. Every time Randy stops


for gas, he records the distance he traveled in miles and the total number of gallons


Lised. Assume that the number of miles driven is proportional to the number of


Dallons consumed in order to complete the table.

To find the local rate of change on a curve at a specific point, we need to find the slope of the tangent line at that point. The tangent line represents the instantaneous rate of change or the rate of change at that particular point.

To find the slope of the tangent line at (-6,8) on the parabola, we need to take the derivative of the function at that point.

Assuming that the parabola is defined by the equation [tex]y = ax^2 + bx + c,[/tex]

where a, b, and c are constants, we can find the derivative of the function as follows:

[tex]dy/dx = 2ax + b[/tex]

Substituting [tex]x = -6,[/tex] we get:

[tex]dy/dx = 2a(-6) + b[/tex]

To find the values of a and b, we need more information about the parabola.

If we have the equation of the parabola or another point on the curve, we can use it to find the values of a and b.

Once we have the values of a and b, we can substitute them into the derivative equation and evaluate it at [tex]x = -6[/tex] to find the slope of the tangent line at (-[tex]6,8[/tex]), which is the local rate of change at that point.

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The loss price of the product is Rs 11. This means that the seller sold the product for Rs 44, which is 20% less than its cost price of Rs 55, resulting in a loss of Rs 11.

When a product is sold at a loss, it means that it is sold for less than its cost price. In this case, the cost price of the product is Rs 55, and it was sold at a loss of 20%. This means that the selling price of the product is 80% of its cost price. To find out the selling price, we can multiply the cost price by 80% or 0.8.

Selling price = Cost price x (100% - Loss%)

Selling price = Rs 55 x (100% - 20%)

Selling price = Rs 55 x 80%

Selling price = Rs 44

So, the selling price of the product is Rs 44. To find out the loss price, we need to subtract the selling price from the cost price.

Loss price = Cost price - Selling price

Loss price = Rs 55 - Rs 44

Loss price = Rs 11

Therefore, the loss price of the product is Rs 11.

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Answer: 5 1/4

Step-by-step explanation: 3/4 times 7/1 equals 5.25

Turn the decimal to a fraction and get 5 1/4

Answer: x=4/3

Step-by-step explanation:

3x-2=2

3x=2+2

3x=4

x=4/3

In triangle ABC with angle B as a right angle, if the measure of angle A is greater than 75 degrees (e.g., 80 degrees), side BC can be approximately 9.848 units, and the hypotenuse AC can be 10 units.

In triangle ABC with angle B as a right angle, to find measures of side BC and hypotenuse AC such that the measure of angle A is greater than 75 degrees, we can use the sine function.

Determine the sine of angle A. Since angle A needs to be greater than 75 degrees, let's choose 80 degrees as an example.
sin(80°) = opposite side (BC) / hypotenuse (AC)

Choose a convenient value for the hypotenuse (AC). Let's choose AC = 10 units.

Solve for the opposite side (BC).
sin(80°) = BC / 10
BC = 10 * sin(80°)
BC ≈ 9.848

If the measure of angle A is more than 75 degrees (for example, 80 degrees), side BC and the hypotenuse AC in the triangle ABC with a right angle can both be 10 units.

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The surface area and volume of the triangular prism are:

S = [tex]204 in^2[/tex]

V = [tex]144 in^3[/tex]

The area= 12 inches

The volume = 144 cubic inches

The area of each triangular face is already calculated (A = 12 square inches). The three rectangular faces have dimensions 5 x 12, 6 x 12, and 4 x 12.

Calculate the area of each rectangular face:

5 * 12 = 60 square inches

6 * 12 = 72 square inches

4 * 12 = 48 square inches

Now, sum the areas of all faces to get the surface area (S):

S = (2 * 12) + 60 + 72 + 48 = 204 square inches.

So, the surface area and volume of the triangular prism are:

S = [tex]204 in^2[/tex]

V = [tex]144 in^3[/tex]

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The radius of the circle is 2mm

It is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.

The equation is written as;

C = 2πr

Such that the parameters are;

From the information given, we have thatt;

The radius of the circle = r

The circumference = 12.56mm

Substitute the values, we have;

12. 56 = 2×3.14r

Multiply the values

r = 12. 56/6. 28

divide the values

r = 2mm

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Using the combine clues method:

[tex]R_1=7\\\\R_2=9\\\\R_3=8\\\\S_1=2\\\\S_2=4\\\\S_3=5\\\\T_1=10\\\\T_2=14[/tex]

Certain items that must be worn, used, or accessed in order to access particular clues. The maximum skill level needed to solve each master clue is shown.

Clue 1: [tex]R_1 + R_2 + R_3 = 24[/tex]

Clue 2: [tex]R_1 + R_2 =16[/tex]

Since, [tex]R_1 + R_2 + R_3 = 24[/tex] (from clue 1)

[tex]R_1 + R_2 + R_3 = 24\\\\16 + R_3 = 24[/tex]

Subtract both the sides by 16,

[tex]R_3=8[/tex]

Clue 3:

We need to find the blank [tex]R_1 +[/tex] __ [tex]+S_2=20[/tex] and [tex]S_2=4[/tex]

Since, [tex]R_1 + R_2 = 16[/tex] (from clue 2)

So,

[tex]R_1 + R_2 + S_2 = 20\\\\16 + S_2 = 20[/tex]

Subtract 16 from both sides.

[tex]16 + S_2 - 16 = 20 -16\\\\S_2 = 4[/tex]

So,

[tex]R_1 + R_2 + S_2 = 20[/tex]

Clue 4:

We need to find the blank [tex]R_2[/tex] = __

[tex]S_2 + R_2 = 13[/tex]

Since, [tex]S_2 = 4[/tex]

[tex]S_2 + R_2 = 13\\\\4 + R_2 = 13[/tex]

Subtract 4 from both sides.

[tex]R_2 = 9[/tex]

So, [tex]R_2 = 9[/tex]

Clue 5:

We need to find the blank ___ [tex]+ T_2 = 22[/tex] and [tex]T_2=[/tex] ___

[tex]R_3 + T_2 = 22[/tex]

Since, [tex]R_3 =8[/tex] (from the Clue 2)

[tex]R_3 + T_2 = 22[/tex]

[tex]8 + T_2 = 22[/tex]

Subtract both the sides by 8,

[tex]T_2 = 14[/tex]

So, [tex]R_3 + T_2 = 22[/tex]

Clue 6:

We need to find the blank [tex]T_1 +[/tex] ___ = 24 and ___ = 10

Since, [tex]T_1 + T_2 = 24[/tex] (from the Clue 5)

[tex]T_1 + 14 = 24[/tex]

Subtract both the sides by 14,

[tex]T_1 = 10[/tex]

Clue 7:

We need to find the value of [tex]S_1[/tex],

Given [tex]T_1 + R_3 + S_1 =20[/tex]

Since, [tex]T_1=10[/tex] and [tex]R_3=8[/tex]

[tex]10+ 8 + S_1 = 20\\\\18 + S_1 = 20[/tex]

Subtract both the sides by 18,

so, [tex]S_1=2[/tex]

Combining this with what we learned from Clue 2 and Clue 6, we know

[tex]S_1=2[/tex]

Now, we need to find the blank, [tex]S_1 + S_2 +[/tex] ___ = 11

Combining this with what we learned from Clue 3 and Clue 7, we know:

___ = 5

[tex]S_1 + S_2 + S_3 = 11\\\\2 + 4 + S_3 = 11\\\\6 + S_3 = 11[/tex]

Subtract both the sides by 6,

[tex]S_3 = 5[/tex]

For [tex]R_1[/tex]

Since,

[tex]R_1 + R_2 + R_3 = 24\\\\R_1 + 9 + 8 = 24\\\\R_1 + 17 = 24[/tex]

Subtract both the sides by 17,

[tex]R_1 = 17[/tex]

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To create a dot plot that represents the given data, we need to place each data point on a number line and then represent it with a dot above its corresponding value. The number line should range from 0 to the maximum number of pets owned by any student, which in this case is 4.

First, we place a dot above the value 0, which occurs twice in the data set. Then, we place three dots above the value 1, which occurs five times in the data set. Next, we place two dots above the value 2, which occurs twice in the data set. Finally, we place one dot above the value 3 and one dot above the value 4.

In summary, the dot plot will have one dot above 3 and one dot above 4 for the number of pets axis, and for the number of students axis, we will have two dots above 0, five dots above 1, two dots above 2, and no dots above 3 or 4. This represents the distribution of the data in a visual way.

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Answer:

9th term is

[tex]a_9 = \dfrac{1280}{2187}\\[/tex]

Step-by-step explanation:

This sequence is clearly a geometric progression where the ratio of any term to the previous term is constant and known as common ratio

The 3 terms given are:
15, 10 and 20/3

10 ÷ 15 = 2/3

20/3 ÷ 10 = 2/3

So the common ratio is 2/3

For a geometric sequence with common ratio r and first term a₁, the nth term is given by the equation

aₙ = a₁ · rⁿ⁻¹

Here a₁  = first term = 15

r = 2/3

So the general equation for the nth term of this equation is
aₙ = 15 · (2/3)ⁿ⁻¹

The 9th term would be

[tex]a_9 = 15 \cdot \left(\dfrac{2}{3}\right)^{9-1}\\\\a_9 = 15 \cdot \left(\dfrac{2}{3}\right)^{8}\\\\a_9 = 15 \cdot \left(\dfrac{256}{6561}\right)\\\\a_9 = 15 \cdot \left(\dfrac{256}{6561}\right)\\[/tex]
15 is divisible by 3 giving 5
6561 is divisible by 3 giving 2187

So the above expression simplifies to
[tex]a_9 = 5 \cdot \dfrac{256}{2187}\\\\a_9 = \dfrac{1280}{2187}\\[/tex]

Answer:

It the distance from mid line to top of wave.

Step-by-step explanation:

Answer:

Height of a wave (from mid line to max.

Step-by-step explanation:

The required values on the graph, the solution is approximate x = -0.33.

We can begin by combining like terms on the left-hand side:

3x² - 6x - 4 - 2/x + 3 + 1 = 0

3x² - 6x - 2/x = -3

Next, we can factor out the x term:

x(3x - 2) - 2(3x - 2) = -3

(x - 2)(3x - 2) = -3

Since the equation is equal to -3, we can add 3 to both sides to get:

(x - 2)(3x - 2) + 3 = 0

We can then factor the left-hand side to get:

(x - 2)(3x - 2 + 3) = 0

(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0

This equation has two solutions: x = 2 and x = -1/3.

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

The range of the data set is 19 hours. None of the options are correct.

The given data set represents the number of hours Raymond spent practicing the piano each week for several weeks: 24, 8, 6, and 5 hours. To calculate the range, follow these steps:

1. Identify the highest and lowest values in the data set.
  - The highest value is 24 hours.
  - The lowest value is 5 hours.

2. Subtract the lowest value from the highest value to find the range.
  - Range = Highest value - Lowest value
  - Range = 24 hours - 5 hours
  - Range = 19 hours

This means that there is a 19-hour difference between the maximum and minimum number of hours Raymond spent practicing the piano each week. None of the options (a. 8 hours, b. 2 hours, c. 5 hours, and 6 hours) provided matches the correct answer, which is 19 hours.

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To multiply -1(x^2-4x+8), we need to distribute the -1 to each term inside the parentheses:

-1(x^2-4x+8) = -x^2 + 4x - 8

So, the product of -1 and the expression (x^2-4x+8) is -x^2 + 4x - 8.

A restaurant meal cost $90 and there was a 6% meals tax on the price of the meal. The meal tax was $5.40 and the total price of the meal with the meal tax was $95.40.

Find the meal tax, you need to calculate 6% of the $90 meal cost.
Convert the percentage to a decimal by dividing by 100, so 6% = 0.06.
Multiply the meal cost by the decimal. In this case, $90 × 0.06 = $5.40.
So, the meal tax was $5.40.
Find the total price of the meal with the meal tax, you need to add the meal tax to the original cost of the meal.
Add the meal tax to the original cost, so $90 + $5.40 = $95.40.
The total price of the meal with the meal tax was $95.40.

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Stem plots (also known as stem-and-leaf plots) have several advantages over frequency distributions, including:

1. Stem plots show individual data points: Unlike frequency distributions, which group data into intervals, stem plots show each individual data point. This makes it easier to see the distribution of the data, including the shape, the range, and any outliers or gaps. Stem plots can also reveal patterns and trends in the data that may not be apparent from a frequency distribution.

2. Stem plots are easy to construct: Constructing a stem plot requires minimal computation and is relatively simple to create by hand. It involves only sorting the data and then splitting each data point into a stem (the leading digits) and a leaf (the trailing digit). This makes stem plots a convenient tool for quick exploratory data analysis, especially when dealing with small to moderate-sized datasets. In contrast, constructing a frequency distribution can be more time-consuming, as it requires choosing appropriate intervals and counting the number of data points in each interval.

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There would be of 11.3 times rs. 1300 is the value including 13% vat on rs. 13000

To find out how many times Rs. 1300 is contained in the value including 13% VAT on Rs. 13000, we need to first calculate the total value including VAT.

VAT is a tax that is added to the net price of a product or service. In this case, the net price is Rs. 13000 and the VAT is 13% of the net price, which is:

VAT = 13% of Rs. 13000

= 0.13 x 13000

= Rs. 1690

So, the total value including VAT is:

Total value = Net price + VAT

= Rs. 13000 + Rs. 1690

= Rs. 14690

Now, to find out how many times Rs. 1300 is contained in this value, we divide the total value by Rs. 1300:

Number of times = Total value / Rs. 1300

= Rs. 14690 / Rs. 1300

= 11.3 (approx)

Therefore, the value including 13% VAT on Rs. 13000 is about 11.3 times the value of Rs. 1300.

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The ages of the​ teacher's three children whose product is 72 will be 3,3,8.

Let the age of three children be x, y, z

x × y × z = 72

x + y + z = No. of rooms

Now possible answers can be three numbers whose product is 72

There are two possible answers in which the product of the number is 72 and the sum of the number is also same

1) 2 × 6 × 6 = 72  and 2 + 6 + 6 = 14

2) 3 × 3 × 8 = 72  and 3 + 3 + 8 = 14

Now teacher gave a hint that his oldest child is good at math

Oldest means one of the three child is oldest so the only possible answer could be 3,3,8

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Answer: 141

Step-by-step explanation: 188 x 75% = 141

Answer:

141

Step-by-step explanation:

I looked it up.

The value of the function at that point is equal to the z-coordinate of the point on the plane.

A horizontal tangent plane is a plane that is parallel to the x-y plane and tangent to a surface at a point where the slope in the horizontal direction is zero.

To use the tangent plane equation to find a horizontal tangent plane, we need to find the partial derivatives of the function with respect to x and y, evaluate them at the point of interest, and check if they are both zero.

If they are both zero, then the tangent plane is horizontal and the equation simplifies to f(a,b) = z.

The tangent plane equation is given by:

f(a,b) + f(1)(x-a) + f(2)(y-b) = z

where (a,b) is the point where the tangent plane intersects the surface, and f(1) and f(2) are the partial derivatives of the function with respect to x and y, evaluated at (a,b).

To use this equation to find the horizontal tangent plane, we first find the partial derivatives f(1) and f(2), and evaluate them at the point where we want to find the tangent plane. If f(1) and f(2) are both zero at that point, then the tangent plane is horizontal and the equation simplifies to:

f(a,b) = z

This means that the value of the function at that point is equal to the z-coordinate of the point on the plane.

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System of equation Sam can use is 13b + 4t = 327.50 and 6b + 2t = 142.47 where "b" represents bushes and "t" represents trees.

Let the cost of bushes represented by b

cost of trees represented by t

First order is 13 buses and 4 trees and total is $327.50

By using the data equation form will be

13b + 4t = 327.50

Second order is 6 bushes and 2 trees and total is $142. 96

By using data the equation form will be

6b + 2t = 142.96

These set of equation will for and can be used.

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The value or n(C) based on the information will be 6.

In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. More formally, if a is a factor of b, then b can be expressed as a product of a and some other number or expression.

For example, in the expression 12 = 2 x 2 x 3, the numbers 2 and 3 are factors of 12. Similarly, in the expression x² - 4, (x - 2) and (x + 2) are factors because if we multiply them together we get x² - 4.

The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the set C contains six elements. Hence, n(C) = 6.

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The values based on the exponent will be:

0.024

5670

41952

0.005

73

0.34

900

6

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

1) 2.4 × 10^-2 = 0.024

2) 5.67 x 10^3 = 5670

3) 4.1952 x 10^4 = 41952

4) 5 × 10^-3 = 0.005

5) 7.3 × 10^1 = 73

6) 3.4 × 10-1 = 0.34

7) 9 × 10^2 = 900

8) 6 × 10*0 = 6

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The population growth rate for 2019 would be 800 people.

The population size at the start of 2020 would be 149, 800 people.

The formula is:

Growth rate = rmax × Population × ( 1 - ( Population / Carrying Capacity ) )

Growth rate = 0.8 × 149,000 × ( 1 - ( 149, 000 / 150, 000) )

Growth rate = 0.8 × 149, 000 × 0. 0067

Growth rate = 800 people

The population size at the start of 2020 would therefore be:

=  Initial Population + Growth Rate

= 149, 000 + 800

= 149, 800 people

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The equation of the perpendicular line to y = -3x + 4 and passing through (-6, 2) is y = (1/3)x + 4.

There are a lot of perpendicular lines that we may see in reality. The corners of a chalkboard, a window, the sides of a set square, and the Red Cross symbol are a few examples.

Knowing that the slopes of perpendicular lines are the negative reciprocals of one another is necessary to determine the equation of a line perpendicular to a given line.

The given line has a slope of -3, so the slope of a line perpendicular to it would be the negative reciprocal of -3, which is 1/3.

We also know that the line passes through the point (-6, 2).

The equation of the line passing through (-6, 2) and perpendicular to y = -3x + 4 can be found using the point-slope form of a line:

y - 2 = (1/3)(x + 6)

Simplifying this equation, we get:

y = (1/3)x + 4

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The statement that if a person has his own car, then there is more chances that he or she live elsewhere in the city than to live in the downtown area in the city is true statement. So, the option(a) is right answer for problem.

We have, a sample of sample size, n

= 200

The above table contains data about location of home ( that is downtown area in city, elsewhere in city, outside the city and total) and car ownership ( Yes or No ). Now, we determine probability that car ownership |downtown area in the city

= 10/70

= 1/7

probability that car ownership | elsewhere in the city = 15/70

= 3/14

Probability that car ownership | outside in the city = 35/60 = 7/12

As we see, 1/7 < 3/14 < 7/12

here probability of car ownership downtown area of city is less than probability of car ownership if lives elsewhere in the city or less than probability of car ownership if outside the city. So, statement (a) is true in this case. Also consider,

Probability that no car ownership | downtown area in the city = 60/70 = 6/7

Probability that no car ownership | elsewhere in the city = 55/70 = 11/14

Probability that no car ownership|outside the city = 25/60 = 5/12

As we see probabilities, 5/12 < 11/14 < 6/7

Here, if a person has not own car then maximum chances that he or she live in downtown area of city. So, statement (b) is false.

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Complete question:

The above figure complete the question. A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table above. Which of the following statements about a randomly chosen person from these 200 employees is true? responses

a) if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.

b) if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere).

c) the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city.

d) the person is more likely to live in the downtown area in the city than elsewhere in the city.

e) the person is more likely to own a car than not to own a car.

The roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex]also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

To find the roots of equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3,[/tex] we can substitute [tex]y = 2^(^x^-^2^)[/tex]to get:

[tex]y + 2^(^5^-^x^)^/^y = 3[/tex]

Multiplying both sides by y, we get:

[tex]y^2 + 2^(^5^-^x^) = 3y[/tex]

Substituting y = 2^(x-2), we get:

[tex]2^(^2^x^-^8^) + 2^(^5^-^x^) = 3 * 2^(^x^-^2^)[/tex]

Multiplying both sides by 2^8, we get:

[tex]4(2^x) + 32 = 768(2^(^2^-^x^))[/tex]

Simplifying, we get:

[tex]4(2^x) - 768(2^-^x) + 32 = 0[/tex]

Dividing both sides by 4, we get:

[tex]2^x - 192(2^-^x) + 8 = 0[/tex]

Multiplying both sides by [tex]2^x[/tex], we get:

[tex]4^x - 192 + 2^x = 0[/tex]

Adding 192 to both sides, we get:

[tex]4^x + 2^x - 192 = 0[/tex]

This is the same as the given equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

Therefore, we have shown that the roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex] also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

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a. The actual area of the kitchen is 128 square feet.

b.  the couch measures 1.25 inches across in the scale drawing.

The scale is 1/4 inch = 2 feet,

meaning that in the drawing, each inch represents 8 feet (since 2 feet/0.25 inches = 8 feet/inch).

The kitchen in the drawing has an area of 2 square inches.

we apply  the scale factor to find the actual area in square feet,

1 inch in the drawing = 8 feet in real life

So, 2 square inches in the drawing = 2 x 8 x 8 = 128 square feet in real life.

Hence,  the actual area of the kitchen is 128 square feet.

we also apply  the scale factor to  find the couch measurement in the scale drawing,

1 inch in the drawing = 8 feet in real life

10 feet in real life = 10/8 = 1.25 inches in the drawing.

In conclusion,  the couch measures 1.25 inches across in the scale drawing.

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