13.) Springfield Elementary is putting on a school play
to raise money for their field trip. They are selling
adult's tickets for $6 and children's tickets for $3.50.
They made a total of $550 for selling 125 tickets. Write
and solve a system to determine how many of each
type they sold.

Answer:

[tex]\frac{12q^{\frac{7}{3}}}{p^{3}}[/tex]

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. [tex](a^{x})^{n} = a^{xn}[/tex]

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). [tex]a^{-x} = \frac{1}{a^{x}}[/tex], and to help with this question: [tex]\frac{a^{-x}b}{1} = \frac{b}{a^{x}}[/tex].

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. [tex](a^{x})(a^{y}) = a^{x+y}[/tex]

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. [tex]\frac{a^{x}}{a^{y}} = a^{x-y}[/tex]

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). [tex]a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}[/tex]

[tex]\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}[/tex]        Distribute exponent

[tex]=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}[/tex]        Simplify each exponent by multiplying

[tex]=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}[/tex]        Negative exponent rule

[tex]=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}[/tex]        Combine the like terms in the numerator with the base "q"

[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}[/tex]        Rearranged for you to see the like terms

[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}[/tex]        Multiplying exponents with same base

[tex]=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}[/tex]        2 + 1/3 = 7/3

[tex]=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}[/tex]        Fractional exponents as radical form

[tex]=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}[/tex]        Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.

[tex]=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}[/tex]        Multiply 4 and 3

[tex]=\frac{12pq^{\frac{7}{3}}}{p^{4}}[/tex]        Dividing exponents with same base

[tex]=12p^{(1-4)}q^{\frac{7}{3}}[/tex]        Subtract the exponent of 'p'

[tex]=12p^{(-3)}q^{\frac{7}{3}}[/tex]        Negative exponent rule

[tex]=\frac{12q^{\frac{7}{3}}}{p^{3}}[/tex]        Final answer

Here is a version in pen if the steps are hard to see.

Answer:

(A) [tex]4.9\times 10^{-7}\ m[/tex]

Step-by-step explanation:

Given:

Frequency of the wave (f) = [tex]6.1\times 10^{14}\ Hz[/tex]

Speed of the wave (v) = [tex]3.00\times 10^8\ m/s[/tex]

The wavelength equation of the wave is given as:

[tex]\lambda=\dfrac{v}{f}[/tex]

Here, [tex]\lambda \to wave\ wavelength[/tex]

Now, plug in the given values and simplify.

[tex]\lambda=\frac{3\times 10^8}{6.1\times 10^{14}}\\\\\lambda=4.9\times 10^{-7}\ m[/tex]

Therefore, the wavelength of the wave is option (A) [tex]4.9\times 10^{-7}\ m[/tex]

The value of the equation A = -6x + 7 ( 2x + 1 ) - 12 is A = 8x - 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -6x + 7 ( 2x + 1 ) - 12  be equation (1)

Now , let the equation B = 8x - 5

On simplifying the equation (1) , we get

A = -6x + 7 ( 2x ) + 7 ( 1 ) - 12

A = -6x + 14x + 7 - 12

On further simplification , we get

A = 8x - 5

So , the value of A = B

Therefore , the value of A is 8x - 5

Hence , the equation is A = 8x - 5

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Answer:

The Answer is A = -6x + 7 ( 2x + 1 ) - 12 is A = 8x - 5

Step-by-step explanation:

I got it right

Answer:

Step-by-step explanation:

Brown rice

16oz = 0.79

Since 16oz is half of 32oz, we can multiply this equation by 2:

32oz = $1.58

Comparing the two, the 16oz package of brown rice is a better deal because it costs less.

Answer:

  (4.5, 6)

Step-by-step explanation:

The distance covered is proportional to the rate, so the distance from A to C compared to the distance from B to C will have the same proportion as Phillip's and Bruce's rates.

__

  (C -A)/(B -C) = 7/5 . . . . . distance is proportional to rates

  5(C -A) = 7(B -C) . . . . multiply by 5(B -C)

  12C = 7B +5A . . . . . add 7C+5A

  C = (7B +5A)/12 = (7(7, 6) +5(1, 6))/12 = (49+5, 42+30)/12 = (4.5, 6)

Phillip and Bruce will meet at C(4.5, 6).

Answer:

he is right but the answer is (4,6) not (4.5,6)

Step-by-step explanation:

Answer

Step-by-step explanation:All you do is multiply $234 by 5.2% or .052 as a decimal

$234×.052×1

Answer:

It's 4500

Step-by-step explanation:

The polygon consists of a rectangle with dimensions 15 ft by 18 ft and a right triangle with a base of 8 ft and a hypotenuse of 17 ft. The perimeter is 76 ft, and the area is 330 sq ft. The correct option is A).

To Find the area of each individual shape.

a. Area of the rectangle:

The area (A) of a rectangle is given by the formula: A = Length × Width.

Area of the rectangle = 18 ft × 15 ft = 270 sq ft

b. Area of the right triangle:

The area (A) of a right triangle is given by the formula: A = 0.5 × Base × Height.

Area of the right triangle = 0.5 × 8 ft × 15 ft = 60 sq ft

To Find the total area of the polygon.

Total area of the polygon = Area of the rectangle + Area of the right triangle = 270 sq ft + 60 sq ft = 330 sq ft

So, the perimeter of the polygon is 106 feet, and the area of the polygon is 330 square feet.

The perimeter of the polygon is the sum of the lengths of all its sides:

Perimeter = 15 ft (rectangle side) + 18 ft (rectangle side) + 18 ft (rectangle side) + 8 ft (triangle base) + 17 ft (triangle hypotenuse) = 76 ft

So, the correct perimeter of the polygon is 76 feet.

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The polygon is made up of a rectangle 15 feet by 18 feet in size and a right triangle with an 8-foot base and a 17-foot hypotenuse. The circumference is 76 feet long, and the size is 330 square feet. The correct answer is A).

Calculate the area of each individual form.

a. Rectangle surface area:

A rectangle's area (A) is provided by the formula: A = Length Width.

The rectangle's area is 18 ft 15 ft = 270 sq ft.

b. The right triangle's area:

The formula for calculating the area (A) of a right triangle is A = 0.5 Base Height.

Right triangle area = 0.5 8 ft 15 ft = 60 sq ft

To determine the polygon's overall area.

Total polygon area equals rectangle area + right triangle area = 270 sq ft + 60 sq ft = 330 sq ft

As a result, the polygon's perimeter is 106 feet, and its size is 330 square feet.

The polygon's perimeter is the sum of the lengths of all its sides:

Perimeter = 15 feet (rectangle side) + 18 feet (rectangle side) + 8 feet (triangle base) + 17 feet (triangle hypotenuse) = 76 feet

As a result, the polygon's correct perimeter is 76 feet.

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Answer:

24 + x = 60

Owen earns $36 in the Saturday afternoon.

Step-by-step explanation:

On Saturday morning, Owen earned $ 24. By the end of the afternoon, he had earned a total of $ 60.

Now, if Owen earned $x on Saturday afternoon, then the equation of x that models the situation will be  

24 + x = 60 (Answer)

Solving the above equation we get

x = $36

Therefore, Owen earns $36 on Saturday afternoon. (Answer)

The square root of 25/35, which simplifies down to the square root of 5/7 is an irrational number because the decimal form of the square root doesn't terminate or repeat.

The question is asking about the nature of the square root of the fraction 25/35. To solve it, we first simplify the fraction to its lowest terms, which is 5/7. The square root of 5/7 is a decimal that doesn't terminate or repeat, which means that it is an irrational number. In contrast, 25/35 rational refers to numbers that can be expressed as a ratio of two integers, which the square root of 5/7 cannot be.

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Answer:

Step-by-step explanation:

23.02 plus an additional 0.19 for each text.....x = # of texts

$ 0.19x + 23.02 = 27.77 is ur equation

Answer: B

Step-by-step explanation: i got it wrong trust me

There are approximately 745 pages in main story

Solution:

Let "x" be the number of pages in main story

Let "y" be the number of pages in prologue

Given that there are 750 pages in all

Therefore,

number of pages in main story + number of pages in prologue = 750

x + y = 750 ---------- eqn 1

The main story has 150 times as many pages as the prologue

Therefore, a equation is framed as:

number of pages in main story = 150(number of pages in prologue)

x = 150y ----------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

150y + y = 750

151y = 750

y = 4.967

Substitute y = 4.967 in eqn 2

x = 150(4.967)

x = 745.05

Thus there are approximately 745 pages in main story

Answer:

14

Step-by-step explanation:

23 - 9 = 14

Answer:

14

Step-by-step explanation:

23-9=14

Answer:

80 is the height of the platform

the rocket didnt launch from the ground so u need to add it in

Answer:

The rocket was launched from a platform 80 feet above the ground.

Step-by-step explanation:

The + 80 is where it starts

Answer:

[tex]m=55h[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

m ----> the distance in miles (y-coordinate)

h ----> the time in hours (x-coordinate)

In this problem the constant of proportionality k is given and is equal to

[tex]k=55\ \frac{miles}{hour}[/tex] ----> the speed

substitute

[tex]m=55h[/tex]

Answer:

Thymine 23

Guanine 27

Step-by-step explanation:

A DNA molecule consists of two long chains of DNA connected to each other through the bonds nitrogenous bases make one with another. However, this bonding is strictly regulated through Chargaff's rule. It basically says that adenine from one DNA chain can only bond with thymine from another chain and vice versa. Additionally, cytosine from one chain only bonds with guanine from another and vice versa:

[A] = [T]

[G] = [C]

That means that there should be an equal number of corresponding bases.

If there were 23% of adenine, there will also be 23% of thymine.

Similarly, if there were 27% of cytosine, there will also be 27% of guanine.

Also note that the sum of non-bonding bases is always 50%, in this case, adenine + cytosine was 23% + 27% = 50%.

The Answer is: Thymine 23

Then Guanine 27

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The solution is x = 8 and y = 2

Solution:

Given are the system of equations

2x + 3y = 22 -------- eqn 1

-2x + 5y = -6 ----- eqn 2

We can solve the system of equations by elimination method

Add eqn 1 and eqn 2

Eqn 1 + Eqn 2

2x + 3y -2x + 5y = 22 - 6

0x + 3y + 5y = 16

8y = 16

Divide both sides of equation by 8

Substitute y = 2 in eqn 1

2x + 3(2) = 22

2x = 22 - 6

2x = 16

Thus the solution is x = 8 and y = 2

Answer:

x = -4/5 = -0.800

Step-by-step explanation:

Pull out like factors :

-12 - 15x  =   -3 • (5x + 4)

Solve :  

-3   =  0

Solve  :

5x+4 = 0

5x = -4

x = -4/5 = -0.800

Answer:

378

Step-by-step explanation:

First: Start with the parentheses

Meaning to add 27 + 36 then divide by 3.

Second: You should have 21 afterwards,

when you have this number you can use the number

outside of the parentheses a.k.a (21 x 18)

Third: You should get the answer "378" unless you do something wrong.

To calculate the expression 18•(27+26/3), follow the order of operations: division, addition, and then multiplication. The result is approximately 642.006.

To calculate the expression 18•(27+26/3), we need to follow the order of operations. First, we perform the division 26/3 which gives us 8.66666... (rounded to the nearest thousandth, this is 8.667). Next, we add 27 and 8.667 which equals 35.667. Finally, we multiply 18 by 35.667 to get the final result of 642.006 (rounded to the nearest thousandth, this is 642.006).

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Answer:

A, (5x + 3)(5x – 3)

B, (7x + 4)(7x + 4)

E, (x – 9)(x – 9)

F, (–3x – 6)(–3x + 6)

Step-by-step explanation:

Answer:

A, B, E, F

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

2x-5y=13.........(1) × 3

-3x+2y=13.......(2) × 2

6x - 15y = 39

-6x + 4y = 26

Adding

6x - 6x - 15y + 4y = 13 + 13

Answer:

Step-by-step explanation:

2x - 5y = 13

-3x + 2y = 13

multiply the top equation by 3 and the bottom one by 2, then add <==

watch...

2x - 5y = 13.....multiply by 3

-3x + 2y = 13....multiply by 2

-----------------

6x - 15y = 39 (result of multiplying by 3)

-6x + 4y = 26 (result of multiplying by 2)

-----------------add

- 11y = 65.....notice how out x terms were eliminated :)

Answer:

A. x^2 – 2x – 8

Step-by-step explanation:

Answer:

The interest rate should be 11.6%.

Step-by-step explanation:

Let us assume that at r% rate of interest compounded annually is required to triple an investment of $P in 10 years.

So, using the formula of compound interest, we can write

[tex]3P = P(1 + \frac{r}{100})^{10}[/tex]

⇒ [tex]3 = (1 + \frac{r}{100})^{10}[/tex]

⇒ [tex](1 + \frac{r}{100}) = 1.116[/tex]

⇒ [tex]\frac{r}{100} = 0.116[/tex]

⇒ r = 11.6 %

Therefore, the interest rate should be 11.6%. (Answer)

Answer:

3.229 revolutions per minute

Step-by-step explanation:

The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.

To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.

The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.

To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.

In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.

Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.

Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.

Angular velocity = linear velocity / distance traveled in one revolution

Angular velocity = 17 centimeters per second / (20π centimeters per revolution)

Simplifying the expression, we get:

Angular velocity = 17 / (20π) revolutions per second

To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).

Angular velocity in revolutions per minute = (17 / (20π)) * 60

Calculating the value, we get:

Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute

Therefore, the wheel will s

AI-generated answer

The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.

To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.

The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.

To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.

In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.

Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.

Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.

Angular velocity = linear velocity / distance traveled in one revolution

Angular velocity = 17 centimeters per second / (20π centimeters per revolution)

Simplifying the expression, we get:

Angular velocity = 17 / (20π) revolutions per second

To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).

Angular velocity in revolutions per minute = (17 / (20π)) * 60

Calculating the value, we get:

Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute

Therefore, the wheel will spin at a rate of approximately 3.229 revolutions per minute.

Answer:

Step-by-step explanation:

2x = 10.....there are 2 ways to solve this....u can either divide by 2 on both sides, or multiply by 1/2 on both sides. However, the inverse operation would be the dividing by 2 because it is the inverse of multiplying.

so ur answer is : divide by 2 on both sides

Divide by 2 on both sides to get the inverse operation to solve the equation 2x=10.

Two or more expressions with an equal sign is called as Equation.

2x = 10.....there are 2 ways to solve this

Either divide by 2 on both sides, or multiply by 1/2 on both sides. However, the inverse operation would be the dividing by 2 because it is the inverse of multiplying.

Hence divide by 2 on both sides is the operation used to solve the equation 2X=10.

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Answer: y = -2x + 10

Step-by-step explanation:

Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if the two lines are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1

The equation of the line given :

y = 1/2x - 1

comparing with the equation of line in slope intercept form

y = mx + c , where m is the slope and c is the y - intercept , it implies that

[tex]m_{1}[/tex] = 1/2

Therefore :

[tex]m_{2}[/tex] = -2

To find the equation of the line with slope -2  and passes through the point ( 3 , 4 ) we will use the formula

[tex]y-y_{1}[/tex] = m ([tex]x-x_{1}[/tex] )

y - 4 = -2 ( x - 3 )

y - 4 = -2x + 6

y = -2x + 6 + 4

y = -2x + 10

Answer:x > -3

Step-by-step explanation:

The inequality can be written as follows:

x > -3

Given is number line with an open circle at -3 and goes infinitely in right [positive] direction, we need to find the inequality that is represented by the number line​.

If there is an open circle at -3 on the number line, it means that -3 is not included in the solution set. The number line continues infinitely in the positive direction.

To represent the inequality using the number line, we use the open circle to indicate that -3 is not included and an arrow pointing to the right to show that the numbers continue infinitely in the positive direction.

The inequality can be written as follows:

x > -3

This inequality indicates that x is greater than -3 and includes all numbers to the right of -3 (but not -3 itself) on the number line.

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The equivalent expressions are:

[tex](x+y)^2 = x^2+2xy+y^2[/tex]

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

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

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

Solution:

We have to find the equivalent expression for the given expression

Given expression is:

[tex](x+y)^2[/tex]

Let us first use the algebraic identity

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Therefore,

[tex](x+y)^2 = x^2+2xy+y^2[/tex]

From above we get,

[tex](x+y)^2 = x^2+2xy+y^2[/tex]

2xy can be rewritten as xy + xy

Thus we get,

[tex]x^2+2xy + y^2 = x^2+xy+xy+y^2[/tex]

Group the terms we get,

[tex]x^2+2xy + y^2 = (x^2+xy)+(xy+y^2)[/tex]

Factor out "x" from first bracket and "y" from second bracket

[tex]x^2+2xy+y^2 = x(x+y)+y(x+y)[/tex]

Thus the equivalent expression is:

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

[tex]\text{We know that } a^2 = a \times a[/tex]

Therefore,

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

By commutative property we know that,

[tex]a + b = b + a[/tex]

Therefore,

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

Thus the equivalent expressions are found

Final answer:

The missing fraction in the equation 9/10 + ?/? = 99/100 is 9/100 because 9/10 is equivalent to 90/100 and 99/100 - 90/100 equals 9/100.

Explanation:

To find the missing fraction in the equation 9/10 + ?/? = 99/100, we need to find a common denominator and then solve for the numerator of the missing fraction. The common denominator for 10 and 100 is 100, so we must convert 9/10 into an equivalent fraction with a denominator of 100, which is 90/100. Now, to find the missing numerator, we subtract 90/100 from 99/100 which gives us 9/100. Therefore, the missing fraction is 9/100.

Answer:

D. He recorded his paycheck amount for April 23rd incorrectly. Yes, this was Adam's mistake. The correct amount should be 341.60 and not 338.45.

Step-by-step explanation:

1. Let's review the information given to us to help Adam to determine where his error is.

A. He completely forgot to include the clothes he bought from Bargains RUS. No, he didn't. It was recorded properly,  including the sales tax amount.

B. He made an arithmetic error in the balance column. No he didn't, the balance was calculated correctly after each transaction.

C. He recorded one of his withdrawals in the deposit column. No, he didn't. All of the withdrawals are in the right column.

D. He recorded his paycheck amount for April 23rd incorrectly. Yes, this was Adam's mistake. The correct amount should be 341.60 and not 338.45.

Adam's error in the register lies in the paycheck amount recorded for the April 23rd deposit. His hourly wage is $9.76 and he worked for 35 hours, which should result in a pay of $341.60, but he recorded it as $338.45.

The error in Adam's register appears to be in the paycheck amount recorded for the April 23rd deposit. Here's how we can figure it out

So, Adam recorded his paycheck amount for April 23rd incorrectly.

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