A point is dilated by a scale factor of 1/3 centered about the origin resulting in the new coordinates (-6,3). what are the coordinates of the point prior to the dilation

As per the given values, the height of the vase is approximately 7.3 cm.

The radius of the vase = 4.3cm

The volume of vase = 1330. 2 cm³

Two parallel circular bases are connected by a curving surface to form the three-dimensional object known as a cylinder. There are two round flat sides, two curved edges, and one curved surface.

Using the formula for the volume of a cylinder -

V = πr²h,

where r is the radius and h is the height.

Substituting the values -

1330.2 = π(4.3)²h

1330.2 = 58.09πh

Dividing both sides by 58.09π

1330.2/58.09π = 58.09πh/58.09π

h = 7.27

= 7.3 ( After rounding)

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Answer:

Step-by-step explanation:

Take the natural logarithm of both sides of the equation to remove the variable from the exponent. ln(e−6w)=ln(952) ln ( e - 6 w ) = ln ( 95 2 ).

Step-by-step explanation:

Three weeks would be the 21st and would be Sunday too,  then

22 Mon

23 Tues

24 Wed

25 Thur

The scale factor from A to B is 5 / 4.

The value of t in the diagram is 5.6 cm.

Scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Therefore, let's find the scale factor from the shape A to the shape B as follows:

5 / 4 = 15 / 12

Therefore, the scale factor is 5 / 4.

Hence, let's find the value of t in the diagram as follows:

Therefore, using the proportionality,

7 / t = 5 / 4

cross multiply

28 = 5t

divide both sides by 5

t = 28 / 5

t = 5.6 cm

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Answer:

x=2

Step-by-step explanation:

2x+y=10

3x=y

2x+3x=10

5x=10

x=2

The solution of the given problem of quadratic equation comes out to be K thus has a value of 63/4.

Regression modelling uses the polynomial solutions x = ax² + b + c=0 for one-variable equations. The First Principle of Algebra states that there can only be one solution because it has an extra order. There are both simple and complex solutions available. As the name suggests, a "non-linear formula" has four variables. This implies that there may only be one squared word. In the equation "ax² + bx + c = 0.

Here,

We know that if and are the zeros of the quadratic equation x²-x+k then:

=> α + β = 1

=> αβ = k

Additionally, we are told that 3 + 2 = 20.

We may find as = 1 - by using the equation + = 1.

By replacing this expression for in terms of in the formula k = a, we obtain:

=> (1 - β)β = k

=> β² - β + k = 0

=> 3α + 2(1 - α) = 20

=> α = 6 - 2β/3

=> (6 - 2β/3)²- (6 - 2β/3) + k = 0

=> 4β² - 36β + 72 + 3k = 0

=> 3(6 - 2β/3) + 2β = 20

=> 4β/3 = 2

=> β = 3/2

=> 4(3/2)² - 36(3/2) + 72 + 3k = 0

When we simplify and find k, we obtain:

=>k = 63/4

K thus has a value of 63/4.

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Answer:

21.8014 degrees (to 4 decimal places)

Step-by-step explanation:

The equation y=2/5x+9 forms a certain angle with the x-axis.  Note that all lines parallel to y=2/5x+9 also form the same angle with the x-axis, due to Corresponding Angles (the fact that the original line has a y-intercept of 9 is irrelevant).  Therefore, we could simplify this problem slightly by considering the angle that y=2/5x (a y-intercept of 0) forms with the x-axis.

To find the angle that this line makes with the x-axis, we'll need the vertex (the origin -- let's call this point "B"), and one point on each of two rays from the vertex (Let Ray #1 be the ray from the origin directly to the right; and let Ray #2 be the ray from the origin extending into Quadrant I -- up and to the right, along the equation y=2/5x).

One point on Ray #1 is (5,0) -- it is on the positive x-axis.  Call this point "A"

One point on Ray #2 is (5,2) -- inputting "5" for x, the result for y is "2"  Call this point "C"

To find the angle (Angle ABC), observe that the three points form a right triangle (the angle CAB is a right angle because the two lines are perpendicular).

To solve for [tex]\angle ABC[/tex], recall the definition of the tangent function:

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

The Opposite side, side AC, is just the height (or the y-value) of point C.  So, opposite = 2.

The Adjacent side, side BA, is just the x-coordinate of point A (and also point C).  So adjacent = 5.

Substituting these known values into the tangent function, we get the following:

[tex]tan(m\angle ABC)=\dfrac{2}{5}[/tex]

To solve for the measure of angle ABC, we need to apply the inverse tangent function (also known as arctangent).

[tex]arctan(tan(m\angle ABC)=arctan(\dfrac{2}{5})[/tex]

The left side simplifies because they are inverse functions:[tex]m\angle ABC=arctan(\dfrac{2}{5})[/tex]

Calculating the right side of the equation (rounding to 4 decimal places):

[tex]m\angle ABC \approx 21.8014^{o}[/tex]

The maximum height of Marsha's math book is 36 feet.

To find the maximum height of Marsha's math book, we need to find the vertex of the parabolic equation h = [tex]-16x^2 + 24x + 30[/tex]. The vertex of a parabola is the highest or lowest point on the curve, depending on whether the parabola opens upward or downward.

To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c[/tex]. In this case, a = -16 and b = 24, so we have:

x = -b/2a = -24/(2*(-16)) = 0.75

To find the y-coordinate of the vertex, we can substitute x = 0.75 into the equation h = [tex]-16x^2 + 24x + 30[/tex], which gives us:

h = [tex]-16(0.75)^2 + 24(0.75) + 30 = 36[/tex]

Therefore, the maximum height of Marsha's math book is 36 feet.

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The area of the surface is [tex]\sqrt{\frac{15}{4}}\times \pi[/tex]  unit square.

To find the area of the surface, we need to first find the intersection curve between the plane and the cylinder.
From the equation of the cylinder, we know that [tex]x^2 + y^2[/tex] = 9200.

We can substitute [tex]x^2 + y^2[/tex] for [tex]r^2[/tex] and rewrite the equation as [tex]r^2[/tex] = 9200.
Next, we can rewrite the equation of the plane as

z = 12 - 4x - 3y.
Now, we can substitute 12 - 4x - 3y for z in the equation [tex]r^2[/tex] = 9200, giving us:
[tex]x^2 + y^2[/tex] = 9200 - [tex](12 - 4x - 3y)^2[/tex]
Expanding and simplifying, we get:
[tex]x^2 + y^2[/tex] = [tex]16x^2 + 24xy + 9y^2 - 24x - 36y + 884[/tex]
Simplifying further, we get:
[tex]15x^2 + 24xy + 8y^2 - 24x - 36y + 884 = 0[/tex]
We can recognize this as the equation of an ellipse:

To find the area of the surface, we need to find the area of this ellipse that lies within the cylinder.
To do this, we can first find the major and minor axes of the ellipse.

We can rewrite the equation as:
[tex]15(x - \frac{4}{5})^2[/tex] + 8([tex]y[/tex] - [tex]\frac{9}{10}[/tex][tex])^{2}[/tex] = 1

So the major axis has length [tex]2/\sqrt{15}[/tex] unit and the minor axis has length [tex]\frac{2}{\sqrt{8} }[/tex] unit.
The area of the ellipse is then given by:
A = π x ([tex]\frac{1}{2}[/tex] x [tex]\frac{2}{\sqrt{15} }[/tex] x ([tex]\frac{1}{2}[/tex] x [tex]\frac{8}{\sqrt{8} }[/tex])
Simplifying we get:
A = π x ([tex]\sqrt{\frac{2}{15} }[/tex]) x ([tex]\sqrt{\frac{2}{8} }[/tex])
A = π x ([tex]\sqrt{\frac{1}{60} }[/tex])
A = [tex]\sqrt{\frac{15}{4}} \times \pi[/tex] unit square

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Answer:

2

Step-by-step explanation:

0.50/0.25 = 50/25

= 2

Dividing 0.50/0.25 no. is same as 50/25 when we multultiply by 100/ 100 so it is 2

ans. = 2

0.50 / 0.25

5/10  x  100/5

=2

Answer:

if the two angles are equal

we use sss therom to solve it

2ft/6ft=24ft/xft

x=(6*24)/2

=72

The total bill was 520 pesos when the 4 people share the total bill and pay 130 pesos each.

Given data:

Bill paid by each = 130pesos,

Number of people = 4

We have to translate the problem into an equation. Let's assume that the total bill is x. There are a total of 4 people dividing the restaurant bill, Mike and his three friends. Since each of them paid 130 pesos, we need to multiply 130 by the total number of persons involved, we can write the equation as:

x/4 = 130

x = 4 × 130

x = 520

Therefore, the total bill was 520 pesos.

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A general formula that gives all the times when the voltage will be 0 is t = ±√((pπ)/10)

To find the general formula for the times when the voltage will be 0, we need to analyze the given equation: V(t) = 12sin(5t²). Since V(t) represents the voltage at time t, we want to find the values of t for which V(t) = 0. This will occur when the sine function equals 0.

The sine function, sin(x), is equal to 0 when its argument x is a multiple of π. Mathematically, this can be expressed as:

sin(x) = 0 ⟺ x = nπ, where n is an integer (0, ±1, ±2, ...)

In our case, the argument of the sine function is 5t². Thus, we want to find values of t for which:

5t² = nπ, where n is an integer.

Now, let's solve this equation for t:

t² = (nπ)/5

t = ±√((nπ)/5)

Since the question asks for a formula in terms of p, let's define p as an integer such that p = 2n (n can be any integer). Thus, the formula becomes:

t = ±√((pπ)/10)

This formula represents the general sequence of times t (in milliseconds) when the voltage V(t) will be equal to 0. Here, p is an even integer (0, ±2, ±4, ...) representing different instances when the voltage is zero.

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The maximum volume of a cone that can be carved from the foam cylinder is approximately 9.42 cubic inches.

Given data:

diameter = 3 inches

radius = r = 3 ÷ 2 = 1.5 inches

height = 4 inches

We need to find the maximum volume of a cone that can be carved from the foam cylinder. The volume of a cone is given by the formula:

V = [tex]\frac{1}{3}\pi r^2h[/tex]

where:

V = volume

r = radius of the base

h = height

π = 3.14.

Substituting the r, h, and  π values in the formula, we get:

V = [tex]\frac{1}{3}[/tex]π[tex]r^2[/tex]h

V = [tex]\frac{1}{3}[/tex] × π × (1.5)² ×(4)

V =  [tex]\frac{1}{3}[/tex] × π × 2.25 ×(4)

V = 3 π

V = 9.42 cubic inches

Therefore, the maximum volume of a cone is 9.42 cubic inches.

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The value of b in the exponential function fx =1000bx is 1.02.

The problem states that interest is compounded annually, which means that the interest earned in a year is added to the principal amount at the end of the year. Using the given information, we can set up the following equations:

f₁ = 1000(1+b) = 1020

f₂ = 1000(1+b)² = 1040.40

We can solve for b by dividing the second equation by the first equation and taking the square root:

(1+b)² / (1+b) = 1040.40 / 1020

1+b = √1.02

b = 1.02 - 1 = 0.02

Therefore, the value of b is 0.02 or 2%. The exponential function is fx = 1000(1+0.02)ᵗ, where t is the time in years.

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Answer:

(x-2.75)^2=4.25

Step-by-step explanation:

2x^2-11x+14=0

divide through by two

x^2-5.5x+7=0

x^2-5.5x=-7

x^2-5.5x+(-5.5/2)^2=-7+(-5.5/2)

(x-2.75)^2=4.25

To find the work done by the force, we need to integrate the product of the force and the distance over the range of x.

Given that the force is F(x) = x^2 * 9.24 N and the distance is x, we have:

Work = ∫ F(x) * dx
     = ∫ (x^2 * 9.24) * dx
     = 9.24 ∫ x^2 dx
     = 9.24 * [x^3 / 3]

Evaluating the integral between the limits of 0 and 6 (since the distance is given as x), we get:

Work = 9.24 * [(6^3 / 3) - (0^3 / 3)]
    = 9.24 * (72)
    = 665.28 Joules

Therefore, the work done by the force is 665.28 Joules.

To find the work done by the force, we need to calculate the integral of the force function with respect to distance. Given the force function F(x) = 6x, and the distance x ∈ [0, 2.9], we can set up the integral as follows:

Work = ∫(6x dx) from 0 to 2.9

To find the integral, we'll apply the power rule for integration:

∫(6x dx) = 3x^2 + C

Now, we need to evaluate the definite integral from 0 to 2.9:

Work = (3 * (2.9)^2) - (3 * (0)^2) = 3 * (8.41) = 25.23 N·m

So, the work done by the force is approximately 25.23 N·m.

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Your answer: a. $525

The "12 months is the same as cash" plan means that if you pay off the laptop within 12 months, you won't be charged any interest.

Since you plan to pay off the laptop in 11 months, which is within the 12-month period, you will not be assessed the 15.5 percent APR.

Therefore, you only need to pay the original cost of the laptop, which is $525.
To summarize, as long as you pay the full amount within the specified 12-month period, you avoid the additional interest charges. In this case, you will pay the laptop off in 11 months, so your total payment will be $525.

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Option D is the correct answer as it groups the numbers into sets of five, assigns them as either a "make" or a "miss", and preserves the order of the original set.

The set of random numbers provided represents the binary outcome of a basketball player making or missing a free throw. To simulate the event of making five free throws in a row, we need to group the numbers into sets of five and assign each set as either a "make" or a "miss".

Option A simply groups the numbers into sets of five, but does not indicate whether they are a "make" or a "miss". Option B groups the numbers into sets of five and assigns them as either a "make" or a "miss", but the order of the numbers has been changed.

Option C groups the numbers into sets of five, assigns them as either a "make" or a "miss", and preserves the order of the original set.

This allows for an accurate simulation of the event of making five free throws in a row using the provided set of random numbers.

So, correct option is D.

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Complete question is:

Suppose the following set of random numbers is being used to simulate the event of a basketball player making five free throws in a row. How should the numbers be rearranged?

860583 785814 010122 337198 621549 034076 796495 978078 433330

333153

A. 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978

078 433 330 333 153

B. 8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597

8078 4333 3033 3153

C. 86058 37858 14010 12233 71986 21549 03407 67964 95978

07843 33303 33153

D. 860583 785814 010122 337198 621549 034076 796495 978078

433330 333153

5 bonds were traded during this session.

Based on the provided bond listing for Pacific Bell, the number of bonds traded during this session is 5. Here's the breakdown of the information in the 5-column table:

- Column 1 (Bonds): PacBell 6 5/8 34
- Column 2 (Current Yield): 6.55
- Column 3 (Volume): 5
- Column 4 (Close): 99 1/4
- Column 5 (Net Change): +1/8

The "Volume" column indicates the number of bonds traded during the session. In this case, the volume entry is 5. Therefore, 5 bonds were traded during this session.

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The perimeter of the rectangle with a length of 10 feet and breadth of 11 feet is 42 feet.

In a rectangle, opposite sides are equal in length. So, you have two pairs of sides that are equal. The length of the two equal sides is given by l, which is 10 feet, and the length of the other two equal sides is given by b, which is 11 feet.

Therefore, to find the perimeter of the rectangle, you need to add up the length of all four sides:

Perimeter = 2(l + b)

Substituting the given values of l = 10 feet and b = 11 feet, we get:

Perimeter = 2(10 + 11) feet

Simplifying the expression inside the parentheses, we get:

Perimeter = 2(21) feet

Multiplying 2 and 21, we get:

Perimeter = 42 feet

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Complete Question:

Directions: find the perimeter of each rectangle. be sure to include the correct unit.

Where l = 10 feet and b = 11 feet.

AB is dilated by a scale factor of 3 to form A'B'. Point O, which lies on AB, is the center of dilation.

The slope of AB is 3. The slope of A'B' is 3. A'B' passes through point O.

Dilation is a process of transformation used to resize an object.

The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though.

By multiplying the x and y coordinates of the original figure by the scale factor, you may locate locations on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation.

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Answer: x = 1, y = 5

Step-by-step explanation:

I assume you want to solve this system of linear equations:

from the first one:

2x + y = 7

.: y = 7 - 2x

substituting this for the y in the second equation:

3x - 2(7 - 2x) = -7

3x - 14 + 4x = -7

7x = 7

x = 1

From before we know that y = 7 - 2x

so now that we know x = 1, we can say y = 7 - 2(1) = 5

So x = 1, y = 5

The equation y=0.96x represents the cost in dollars and cents, y, for x bottles of apple juice at store A. This means that if Landon wants to buy x bottles of apple juice from store A, he would pay 0.96x dollars and cents. However, we do not know the value of x from the given information.

On the other hand, we know that Landon can buy 14 bottles of apple juice from store B for $34.16. This means that the cost of one bottle of apple juice at store B is $2.44 (34.16 ÷ 14). We do not know the cost of one bottle of apple juice at store A, but we can use the equation y=0.96x to find out.

Let's assume that Landon wants to buy 14 bottles of apple juice from store A as well. We can substitute x=14 in the equation to find the total cost:

y = 0.96(14) = 13.44

This means that Landon would pay $13.44 for 14 bottles of apple juice at store A. However, we can see that buying 14 bottles of apple juice from store B is cheaper than buying the same amount from store A, as Landon would pay $34.16 at store B and $13.44 at store A. Therefore, it is more cost-effective for Landon to buy apple juice from store B in this case.

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A sequence of transformations that maps figure 1 onto figure 2 and then figure 2 onto figure 3 include the following: D. a translation followed by a rotation.

In Mathematics and Geometry, a translation can be defined as a type of rigid transformation which moves every point of the object in the same direction, as well as for the same distance.

This ultimately implies that, a translation is a type of rigid transformation  that does not change the orientation of the original geometric figure (pre-image).

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

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Complete Question:

Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?

a reflection followed by a translation

a rotation followed by a translation

a translation followed by a reflection

a translation followed by a rotation

The first four nonzero terms are 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8

To find the first 4 nonzero terms of the Taylor series for the function f(t) = e^(t)cos(t) about 0,

we can use the known Taylor series for e^(t) and cos(t).

The Taylor series for e^(t) is:

e^(t) = 1 + t + (t^2)/2! + (t^3)/3! + ...

And the Taylor series for cos(t) is:

cos(t) = 1 - (t^2)/2! + (t^4)/4! - (t^6)/6! + ...

To find the Taylor series for f(t) = e^(t)cos(t), we can multiply these two series together using the distributive property of multiplication. We get:

f(t) = (1 + t + (t^2)/2! + (t^3)/3! + ...) * (1 - (t^2)/2! + (t^4)/4! - (t^6)/6! + ...)

Expanding this out, we get:

f(t) = 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8 + (t^5)/15 - (t^6)/72 - ...

The first 4 nonzero terms of this series are:

f(t) = 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8 + ...

So, the first 4 nonzero terms of the Taylor series for f(t) = e^(t)cos(t) about 0 are:

1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8

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The new volume of the inflatable ball after the radius becomes half of the original one is 16π.

The original volume of the ball is given as 96π

The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.

The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³

With this the original volume of the ball is

(4/3)π X r³

and the new volume of the ball after it's halved is

V₂ = (4/3)π X (r/2)³

After simplification

V₂ = (4/3)π X (r³/8)

The new volume of the ball is:

V₂ = (1/6) X πr³

So the new volume is (1/6) of the original volume. We can calculate this as

V₂ = (1/6) X 96π

= 16π

Therefore, the new volume of the inflatable ball is 16π.

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Mr. Robins earns a commission of 15% on the airfares he books, as he earned $31.29 on $208.60 worth of airfare bookings.

Let x be the amount of commission earned by Mr. Robins on the airfares he booked. Then, we can write the equation:

x = 15% of $208.60

Simplifying this equation, we get:

x = 0.15 x $208.60

x = $31.29

Therefore, Mr. Robins earned a commission of $31.29 on $208.60 worth of airfare bookings. To verify this, we can calculate his commission rate as:

Commission rate = Commission earned / Airfare bookings

Commission rate = $31.29 / $208.60

Commission rate = 0.15 or 15%

Hence, Mr. Robins earns a commission of 15% on the airfares he books.

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For a snowboard cost that was reduced by 40% by the end of the season, the snowboard cost $450 when it was new.

To find the original cost of the snowboard, let the original price of the snowboard be x.

After a 40% reduction in price, the snowboard costs 60% of its original price, therefore the cost remaining percentage of the original prize times the reduction percentage = the price after reduction:

100% - 40% = 60%

60/100 = 0.6

0.6x = 270

Solving for x to get:

x = 270/0.6 = 450

Therefore, the original price of the snowboard was $450.

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The number of students in each bus is 15, and the number of students in each van is 28.

To find the number of students in each van and bus for the field trip to Yellowstone National Park, we can set up a system of equations using the given information. Let x represent the number of students in each van and y represent the number of students in each bus.

For high school A, we have:
2x + 8y = 254

For high school B, we have:
6x + 11y = 398

Now, we can solve this system of equations using the substitution or elimination method. We will use the elimination method:

Step 1: Multiply the first equation by 3 to make the coefficients of x the same in both equations:
6x + 24y = 762

Step 2: Subtract the second equation from the new first equation:
(6x + 24y) - (6x + 11y) = 762 - 398
13y = 364

Step 3: Divide both sides by 13 to find the value of y:
y = 364 / 13
y = 28

Now that we have the number of students in each bus, we can find the number of students in each van:

Step 4: Substitute y back into the first equation:
2x + 8(28) = 254
2x + 224 = 254

Step 5: Subtract 224 from both sides to find the value of x:
2x = 30

Step 6: Divide both sides by 2 to find x:
x = 15

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