Addition and Subtraction of polynomials
PLEASE SOLVE THIS I NEED THIS ASAP

The area of the rectangle in terms of b is 11b - b², and the perimeter is always 22, regardless of the value of b.

A rectangle is a four-sided flat shape with opposite sides that are equal in length and parallel to each other. It has four right angles (90-degree angles) at each corner. The two sides that are parallel to each other are called the length, and the other two sides are called the width.

The area of a rectangle is found by multiplying its length and width, and its perimeter is the sum of the lengths of all four sides. Rectangles are common in everyday life and can be found in many different contexts, such as books, doors, windows, and electronic screens.

According to given information,

Let's assume that the length of the rectangle is 'l' and the width is 'b'.

The area of a rectangle is given by the formula A = lb, where A is the area, l is the length, and b is the width.

The perimeter of a rectangle is given by the formula P = 2(l + b), where P is the perimeter, l is the length, and b is the width.

So, the area of the rectangle is:

A = lb = 28

And the perimeter of the rectangle is:

P = 2(l + b) = 40

P = (l+b) = 20

l= 20 -b

Now, we can substitute l = 20 - b into these formulas:

A = (20 - b)b

P = 2(20 - b + b)

Simplifying, we get:

A = 40b - b²

P= 40

So, the area of the rectangle in terms of b is 11b - b², and the perimeter is always 22, regardless of the value of b.

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The length of the rectangle is 10 cm and breadth of the rectangle is 4 cm.

What is rectangle?

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

The longer parallel sides are called length(l) and two shorter sides are called breadth(b).

Perimeter of a rectangle is 2(l+b).

Area of rectangle is l*b.

2(l+b)=28

L+b=28/2=14

L=14-b .....eq(1)

L*b=40

(14-b)b=40

14b-b^2=40

b^2-14b+40=0

b^2-10b-4b+40=0

b(b-10)-4(b-10)=0

(b-10)(b-4)=0

Either b=10 or b=4

If b=10 then l =4 but length can't be shorter than the breadth so b=4cm and l=10 cm is the answer.

Radian measure of an angle is defined to be the ratio of arc length to the radius of the circle. The length of the arc if a 60 degree angle is 1.0476. Therefore, the radian of the 60 degrees angle is 1.0476.

Radian measure of an angle is defined to be the ratio of arc length to the radius of the circle.

Arc length of sector of circle = (θ/360°) × 2πr

Arc length of sector of circle = (60°/360°) × 2 × 22/7 × 1

Arc length of sector of circle = 1.0476

radian measure of angle 60° = 1.04756/1

radian measure of angle 60° = 1.04756

In conclusion, radian measure of an angle is defined to be the ratio of arc length to the radius of the circle. The length of the arc if a 60 degree angle is 1.0476. Therefore, the radian of the 60 degrees angle is 1.0476.

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The linear separable SVM is not always applicable in case of noise in the training data. When dealing with noisy training data, the performance of a linear separable SVM can be negatively affected, as it tries to find a perfect separation between the classes, which may not be possible in noisy data.

To deal with noisy training data, SVM can be modified by introducing a "soft margin" approach, which allows some flexibility in class separation. This is achieved by using a parameter called C (cost parameter), which controls the trade-off between achieving a wider margin and minimizing classification errors. A higher value of C results in a smaller margin but fewer classification errors, making the model more sensitive to noise. A lower value of C results in a larger margin, allowing more classification errors but providing better generalization to handle noise.

Choosing the appropriate value for C is crucial for the SVM model's performance. Additionally, nonlinear kernel functions, such as the radial basis function (RBF) kernel, can be used instead of a linear kernel to map the data into a higher-dimensional space. This allows the SVM to find more complex decision boundaries, which can better handle noisy data.

In summary, to deal with noisy training data in SVM, one can use the soft margin approach by adjusting the cost parameter (C) and opt for nonlinear kernel functions like RBF, enabling the model to generalize better and handle noise effectively.

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Answer: Q.a Arun thinks that -29/36 is exactly halfway between -8/9 and -13/18. We can check if this is true by finding the midpoint between -8/9 and -13/18 and seeing if it equals -29/36.

To find the midpoint between two numbers, we take the average of the two numbers. So the midpoint between -8/9 and -13/18 is:

((-8/9) + (-13/18))/2 = (-16/18 + (-13/18))/2 = -29/36

Since -29/36 is the same as the midpoint, Arun is correct.

Q.b To find the fraction exactly halfway between -1 3/4 and -11/6, we can start by converting the mixed number to an improper fraction:

-1 3/4 = -7/4

-11/6

To find the midpoint between -7/4 and -11/6, we take the average:

((-7/4) + (-11/6))/2 = (-21/12 + (-22/12))/2 = -43/24

Therefore, -43/24 is the fraction exactly halfway between -1 3/4 and -11/6 on the number line.

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Hello there! Let's work this through:

Firstly, we might want to simply 2 1/2 into 5/2, for simplification.

So, we now have 4 * 7 * 5/2

Simplifying we have [tex]\frac{4*7*5}{2}[/tex]

We see that we can easily simplify 4/2 into 2 * 7 * 5

Further simplifying we get 10*7

Last bit and we get our answer of 70

From here we get 2

The length of the leg of the triangle (hypotenuse, opposite side, adjacent side) are 10, 17, and 5 respectively.

To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If this digit is less than 5 (1, 2, 3, 4) we don't have to do anything, but if the digit is 5 or greater (5, 6, 7, 8, 9) we must round up.

To find the length of each leg we need to consider the angle BAC.

[tex]sin60 = \frac{opposite side}{hypotenuse} =\frac{BC}{10}[/tex]

[tex]\frac{\sqrt{3} }{2} = \frac{BC}{10}\\ BC = \frac{\sqrt{3} }{2} * 10\\ BC = \sqrt{3} * 10\\ BC = 17.32 = 17[/tex]

[tex]cos60 = \frac{adjacent side}{hypotenuse} \\\frac{1}{2} = \frac{AB}{10} \\AB = \frac{1}{2} *10\\AB = 5[/tex]

Therefore the length of the leg of triangle are 17 and 5.

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Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.

To estimate the difference in earnings between Tamekia and Marsha, we can find the average hourly rates for each and use them to calculate an approximate earnings difference.

For Tamekia:

The hourly rate is between $6.00 and $6.25.

The average hourly rate is approximately $(6.00 + 6.25) / 2 = $6.125.

For Marsha:

The hourly rate is between $7.50 and $8.00.

The average hourly rate is approximately $(7.50 + 8.00) / 2 = $7.75.

If they each work 22 hours, Tamekia would earn approximately $6.125 x 22 = $134.75, and Marsha would earn approximately $7.75 x 22 = $170.50.

The difference in earnings between Marsha and Tamekia would be approximately $170.50 - $134.75 = $35.75.

Therefore, Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.

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Answer:

If the book was 25% off and the discounted price was $18, then 75% of the original price was $18.

In other words, 0.75 * Original Price = $18

Solving for Original Price, we get:

Original Price = $18 / 0.75

Original Price = $24

Therefore, the original price of the book was $24.

Step-by-step explanation:

The value of the expression  |1-|2-|3-|4-|5 is 1.

We can solve this expression by working from the inside out. Starting from the innermost absolute value, we have:

|5| = 5

Next, we move outward to the next absolute value:

|4-5| = |-1| = 1

Continuing outward:

|3-1| = |2| = 2

|2-2| = |0| = 0

Finally, we have:

|1-0| = |1| = 1

Therefore, the value of the expression is 1.

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Answer: x=14.75

2(2x+2)=3(21)

   4x+4 = 63

       4x = 63-4

          x = 59÷4

          x = 14.75

Check:  2(2*14.75+2)=3(21)

                             63 = 63

Answer: 63

Step-by-step explanation: It's stated that it equals 3(21) and that's 63.

Ms. Switer will need approximately 2981.388 square feet of sod for her front lawn.

Area is the measure of the amount of space inside a two-dimensional (2D) flat surface or shape, such as a rectangle, circle, or triangle. It is typically measured in square units, such as square meters or square feet. The formula for finding the area of a shape varies depending on the shape itself.

To find out how many square feet of sod Ms. Switer will need, we need to find the area of the lawn. The formula for the area of a rectangle is length x width. Therefore, the area of Ms. Switer's lawn is:

Area = Length x Width

Area = (36 2/3 ft) x (45 1/6 ft)

Area = (110/3 ft) x (271/6 ft)

Area = 2981.388... square feet (rounded to three decimal places)

Therefore, Ms. Switer will need approximately 2981.388 square feet of sod for her front lawn.

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Answer:

slope is 2

y-intercept is (0,4)

yk i got u

Answer: x=

2

y−4

​−2x+y=4

Subtract y from both sides.

−2x=4−y

Divide both sides by −2.

−2

−2x

​

=

−2

4−y

​

Dividing by −2 undoes the multiplication by −2.

x=

−2

4−y

​

Divide 4−y by −2.

x=

2

y

​

−2

Step-by-step explanation:

PLEASE GIVE ME BRAINLIEST

When collecting data for research, it is important to determine the error range of the data set. In the given question, Jacob was researching the number of hours the average adult sleeps each night. He collected data from five individuals.

The data collected by Jacob is as follows:Subject 1: 6 hours of sleepSubject 2: 6.5 hours of sleepSubject 3: 6 hours of sleep Subject 4: 7.5 hours of sleepSubject 5: 5 hours of sleepWe have to find the standard error of the sample mean. The formula for the standard error of the sample mean is:Standard Error = s / sqrt (n)Where,s = the sample standard deviation,n = the sample size.

For the given data set, the sample size is 5. The sample mean can be calculated as:(6 + 6.5 + 6 + 7.5 + 5) / 5 = 6.2The sample standard deviation can be calculated as:√[((6 - 6.2)² + (6.5 - 6.2)² + (6 - 6.2)² + (7.5 - 6.2)² + (5 - 6.2)²) / 4]≈ 1.306The standard error of the sample mean can be calculated as:Standard Error = 1.306 / sqrt (5)≈ 0.58Therefore, the standard error of the sample mean is 0.58. None of the options given in the question is closest to the calculated value. Hence, none of the options is the correct answer.

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The coordinates of the endpoints of the image A''B'', following the rotation and reflection transformation are are;

A''(-5, 2), and B''(1, -1)

A reflection transformation is a type of transformation that takes each point on a figure and flips or reflects it across a line known as the line of reflection to create a mirror image.

What is a rotation transformation?

A rotation transformation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees about a specified point.

The transformations in the question are a reflection and a rotation

The coordinates of the point (x, y) on the coordinate plane, following a reflection across the y-axis is; (-x, y)

The coordinate of the point (x, y) following a rotation of 90° counterclockwise about the origin is; (-y, x)

Therefore, the coordinates of the image of points A and B following a reflection across the y-axis are;

A(-2, 5) → A'(2, 5)

B(1, -1) → B'(-1, -1)

The coordinates of the image of points A' and B' following a rotation of 90° counterclockwise about the origin are;

A'(2, 5) → A''(-5, 2)

B'(-1, -1) →  B''(1, -1)

The coordinates of the endpoints of the image, A''B'' are therefore;

A''(-5, 2) and B''(1, -1)

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Answer:To find Angel's monthly net pay, we can use the following steps:

Calculate Angel's annual net pay:

Her net pay is 68% of her gross pay, so we can find her net pay by multiplying her gross pay by 0.68:

Net pay = Gross pay x 0.68

Net pay = $59,600 x 0.68

Net pay = $40,648

Divide Angel's annual net pay by 12 to find her monthly net pay:

Monthly net pay = Annual net pay / 12

Monthly net pay = $40,648 / 12

Monthly net pay = $3,387.33 (rounded to two decimal places)

Therefore, Angel's monthly net pay is $3,387.33.

Step-by-step explanation:

Answer:

Let's start by finding out how long it takes Jim to fold the washing in minutes. Since there are 60 minutes in an hour, Jim takes 60 minutes to fold the washing. Sara can do the same job in half the time, so she takes 30 minutes to fold the washing. To find out how long it would take them to fold the washing together, we can use the formula: Time = (Work) / (Rate) In this case, the "work" is folding the washing, and the "rate" is how long it takes each person to do the work. We can add their rates together to get the combined rate: Combined rate = Jim's rate + Sara's rate Combined rate = 1/60 + 1/30 To add these fractions, we need to find a common denominator, which is 60:

Answer: you will have 20 percent chance of finding a red jelly bean

4 jelly beans out of 20 are going to be red.

20-4=16

16/20=80%

1-0.8=.2

20%

Step-by-step explanation:

The value of x is 14.

What is the triangle?

A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.

The sum of the angles in a triangle is 180°, so we can set up an equation:

(4x+3) + 76 + (4x-11) = 180

Simplifying and solving for x:

8x + 68 = 180

8x = 112

x = 14

Therefore, the value of x is 14.

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Answer:

The area of the trapezoid is 165.06mi.

Step-by-step explanation:

We can find the area of a trapezoid by the following formula:

[tex]\boxed{A_T = \frac{(B + b) \cdot h}{2} }[/tex]

Note: Base are the parallel sides of the trapezium.

Now, let's change the values in the previous formula:

[tex]A_T = \frac{(B + b) \cdot h}{2}\\\\A_T = \frac{(6.7 + 18.5) \cdot 13.1}{2}\\\\A_T = \frac{25.2 \cdot 13.1}{2}\\\\A_T = \frac{330.12}{2}\\\\A_T = 165.06[/tex]

Therefore, the area of this trapezoid is 165.06 mi.

I hope I've helped.

Happy studying! =D

The probability that the average size of the fish you caught is more than 13 inches is approximately 0.0918

We can solve this problem by using the Central Limit Theorem, which states that the sample mean of a sufficiently large sample size will be normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, we are given that the population mean is 11 inches and the population standard deviation is 3 inches. We are also given that we have a sample size of 4.

First, we need to calculate the standard error of the mean (SE) using the formula

SE = σ / sqrt(n)

where σ is the population standard deviation and n is the sample size.

SE = 3 / sqrt(4) = 1.5

Next, we need to standardize the sample mean using the formula

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

z = (13 - 11) / 1.5 = 1.33

Finally, we can use a standard normal distribution table or calculator to find the probability that a standard normal variable is greater than 1.33. The probability is approximately 0.0918.

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Given two similar triangles

The corresponding sides are proportions

So,

[tex]\dfrac{x}{y} =\dfrac{20}{90} =\dfrac{2}{9}[/tex]

So, the relation between x and y will be:

[tex]x=\dfrac{2}{9} y[/tex]

The area of the smaller triangle = 45 cm²

So, area =

[tex]\dfrac{1}{2} x\times y=45[/tex]

Substitute with x into the equation of the area to find the value of y

         [tex]\dfrac{1}{2} \times\dfrac{2}{9} y\times y=45[/tex]

[tex]y^2=\dfrac{45\times1\times9}{2} =\dfrac{405}{2}=202.5[/tex]

                [tex]y=\sqrt{202.5}[/tex]

Substitute with y into x

[tex]x=\dfrac{2}{9} \times\sqrt{202.5} =\frac{2\sqrt{202.5} }{9}[/tex]

So, the answer will be:

[tex]x=\frac{2\sqrt{202.5} }{9}[/tex]

[tex]y=\sqrt{202.5}[/tex]

Jamie will therefore need five days to complete the book as a result, P – 90 pages equals 3/8 of the book.

A mathematical strategy for resolving proportionality issues is the unitary method. Finding the price of one unit is the first step, and utilizing that value to determine the value of yet another quantity with a different quantity is the second. Consider being told, for instance, that an automobile drives 300 kilometres in 5 hours. You are able to employ the unitary technique as shown below to determine how far the car drives in eight hours. For example, 1 hour is equal to 300/5, or 60 miles. To calculate the value of eight hours, use this value: Since 8 hours are equal to 8/1 units, 480 miles are covered in 8 hours.

given

Let P represent the book's total number of pages.

Jessica reads 30 pages per day, which translates to 330 pages after 3 days, or 90 pages total.

5/8 of the book is still to be read, which indicates that 3/8 of it has already been. As a result, P – 90 pages equals 3/8 of the book.

Divide both sides by 5, and you get:

P = 144

The book thus has 144 pages.

Regarding the second query:

She reads 45 pages per 225 pages, or 1/5 of the book.

We divide the total number of pages by the average number of pages Jamie reads each day to determine the number of days Jamie will need to finish the book.

Jamie will therefore need five days to complete the book as a result, P – 90 pages equals 3/8 of the book.

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The area of carpet the school need to order for the room, the school is designing the new classroom shown in the figure is 5 sq. cm

What is area?

Area is the region covered by the two dimensional shapes like square, rectangle, rhombus, triangle, circle etc. The area of square is given by side x side. The rectangle area is found by length times width.

Here the coordinates of the given quadrilateral are, A(2,2); B(1,4); C(3,5); D(4,3)

To identify the type of quadrilateral we need to find the distance between the points: Distance formula=[tex]\sqrt{(X-x)^{2}+(Y-y)^{2} }[/tex]

AB=[tex]\sqrt{(1-2)^{2}+(4-2)^{2} }[/tex]

   =[tex]\sqrt{5}[/tex]

BC=[tex]\sqrt{(3-1)^{2} +(5-4)^{2} }[/tex]

   =[tex]\sqrt{5}[/tex]

CD=[tex]\sqrt{(4-3)^{2} +(3-5)^{2} }[/tex]

   =[tex]\sqrt{5}[/tex]

DA=[tex]\sqrt{4-3)^{2} +(3-2)^{2} }[/tex]

    =[tex]\sqrt{5}[/tex]

As length of all sides are equal, it can be rhombus or a square.

Now length of diagonals,

AC=[tex]\sqrt{(3-2)^{2} +(5-2)^{2} }[/tex]

    =[tex]\sqrt{10}[/tex]

BD=[tex]\sqrt{(4-1)^{2} +(3-4)^{2} }[/tex]

    =[tex]\sqrt{10}[/tex]

As the length of diagonals are equal, the given quadrilateral is a square.

Area of square= side x side

                        =[tex]\sqrt{5}[/tex] x  [tex]\sqrt{5}[/tex]

                        = 5 sq. units

∴The area of carpet to be ordered is 5 sq. units

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Step-by-step explanation:

Endplate  area  * depth = volume

Endplate area is a composite area:

  rectangle   2x 7 = 14  cm^2

  and trapezoid area = height x average of bases = 3 x (3+7)/2 = 15  cm^2

      total endplate area = 29  cm ^2

29cm^2 * depth = volume

29 * 8 = 232 cm^3

The probability of the center of a circle being contained within a randomly formed triangle using three points along its perimeter is 1/4 or 25%. This probability remains the same for any size of the circle.

The probability that the center of the circle is contained within the triangle formed by selecting three random points along its perimeter is 1/4 or 25%. This is because any triangle that contains the center of the circle must have all of its vertices on the circumference of a smaller circle with half the radius of the original circle. The probability of selecting three random points on the circumference of this smaller circle is 1/4 or 25%.

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The two streets that are the legs of the Triangle are Streets A and B.

The length of C street can be found to be 3. 61 miles.

If Dan can bike 4 miles in half an hour, then he can make the trip to Sarah's house in 30 minutes.

The length of C street can be found using the Pythagorean Theorem which is:

Length C ² = Leg A ² + Leg B²

This means the length of C street is:

Length C ² = 2 ² + 3 ²

Length C ² = 13

Length C = √ 13

= 3. 61 miles

This means that Dan can get to Sarah's house in 30 minutes if he is going at 4 miles per half hour.

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Solomon's study on circadian rhythms in a sample of 45 pregnant women admitted to a hospital in the first 6 months of 2021 due to severe preeclampsia is an example of consecutive sampling.

Consecutive sampling, also known as continuous or complete sampling, is a non-probability sampling method.

In this approach, researchers collect data from every subject that meets the eligibility criteria within a specific time frame.

In Solomon's study, the eligibility criteria were pregnant women admitted to the hospital with severe preeclampsia during the first 6 months of 2021.

By including all eligible subjects during this period, Solomon ensured that the sample was representative of the population under study.

The consecutive sampling method has several advantages, including ease of implementation and the potential for a relatively large sample size.

Additionally, it can provide a comprehensive view of the population during the specified time frame.

However, it may be susceptible to biases if there is a change in the population over time, or if the subjects who meet the eligibility criteria within the given period are not representative of the overall population.

In summary, Solomon's study on circadian rhythms in pregnant women with severe preeclampsia used consecutive sampling, a non-probability sampling method that involves collecting data from every subject meeting the eligibility criteria within a specific time frame.

This method is straightforward to implement and can yield a large sample size, but it may be susceptible to biases if the sample is not representative of the overall population.

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first off, something noteworthy is that we have two angles of 60°, that means that the angle atop is also 60°, so we really have an equilateral triangle, with an altitude or height as shown above, so

[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{15} \end{cases}\implies 4\sqrt{15}=\cfrac{s\sqrt{3}}{2}\implies 8\sqrt{15}=s\sqrt{3} \\\\\\ \cfrac{8\sqrt{15}}{\sqrt{3}}=s\implies \cfrac{8\sqrt{2\cdot 3}}{\sqrt{3}}=s\implies \cfrac{8\sqrt{2}\cdot \sqrt{3}}{\sqrt{3}}=s\implies 8\sqrt{2}=s \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \textit{\LARGE perimeter} }{8\sqrt{2}~~ + ~~8\sqrt{2}~~ + ~~8\sqrt{2}}\implies 24\sqrt{2}[/tex]

The value of b, given the graph, the vertical and horizontal asymptote, would be - 8 .

At the y-intercept, x = 0. We can plug this into the equation and solve for y:

-4 = (a(0) + b) / (0 + c)

-4 = b / c

The vertical asymptote occurs when the denominator is equal to 0:

x + c = 0

x = -2

Thus, c = 2.

The horizontal asymptote occurs when the limit of the function as x approaches infinity is equal to a constant value:

y = a/c

3 = a/2

a = 3 * 2

= 6

The value of b would therefore be:

-4 = b / 2

b = -8

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