Answer:
10 years old
Step-by-step explanation:
let his age be x , then in 20 years
x + 20 = 3x ( subtract x from both sides )
20 = 2x ( divide both sides by 2 )
10 = x
Charlie is 10 years old
A piece of land is shaped like a right triangle. Two people start at the right angle of the triangle at the same time and walk at the same speed along different legs of the triangle. If the area formed by the positions of the two people and their starting point (the right angle) is changing at 2 sq. meter per seconds, then how fast are the people moving when they are 5 meters from the right angle? (Round your answer to two decimal places.)
definetly not a
Step-by-step explanation:
because it is an incompetent answer
Mr. avanzado has an underground in his house. what unit of measure will he use to find its value
Answer: Volume
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
m∠5 + m∠6 =180°m∠2 + m∠3 = m∠6m∠2 + m∠3 + m∠5 = 180°Step-by-step explanation:
m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.
m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.
m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.
The three right options are:
m∠5 ₊ m∠6 = 180° which represents a linear pair.
∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.
m∠2 m∠3 m∠5 = 180° as the sum-triangle
sum-triangleproperty.
Given,
the interior angles of the triangle are 2,3,5
the exterior angle at ∠2 is ∠1.
the exterior angle at ∠3 is ∠4.
the exterior angle at ∠5 is ∠6.
Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.
Apply the exterior angle property of a triangle.
The sum of the opposing internal angles determines the outer angle of a triangle.
For exterior ∠1 we get
∠1 = ∠5 ₊ ∠3
Similarly, for exterior ∠4 we get
∠4 = ∠5 ₊ ∠2
Then for exterior ∠6 we get
∠6 = ∠2 ₊ ∠3
∴ through the exterior angle property we get the correct option as
m∠6 = m∠2 ₊ m∠3
Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°
∴ m∠2 ₊ m∠3 ₊ m∠5 = 180°
We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,
∴ m∠5 ₊ m∠6 = 180°
Hence we get the statements which match the diagram are:
m∠5 ₊ m∠6 = 180°
m∠2 ₊ m∠3 ₊ m∠5 = 180°
m∠6 = m∠2 ₊ m∠3
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A gas tank consists of a cylinder with a hemisphere on top. It is made of metal that is 1 cm
thick. It has an overall height of 90 cm and an external diameter of 20 cm. Calculate:
a the surface area of the tank
b the internal volume of the tank.
(Give answers correct to two significant figures)
The surface area of the cylinder is 5969.03 cm²
The internal volume is 23156.68 cm³
Given:
A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm
To Find
a) the surface area of the tank
We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.
So, the surface area of the cylinder is
[tex]\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2[/tex]
= π×(100+1600+200)
= π×(1900)
= 5969.03 cm²
b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm
= [tex]\frac{4}{3}\times \pi \times 9^3[/tex]+[tex]\pi\times 9^2\times 79[/tex]
= 23156.68 cm³
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PLEASE HELP!!!
Part A: Solve the equation 4(x + 5) = 9x + 4x − 34, and show your work. (5 points)
Part B: Use this list of properties to justify each step of your math work. Justifications may be used more than once if needed. (5 points)
Distributive Property
Subtraction Property of Equality
Combine Like Terms
Multiplication Property of Equality
Division Property of Equality
Given
Addition Property of Equality
Answer:
See below
Step-by-step explanation:
4(x + 5) = 9x + 4x − 34
4x + 20 = 9x + 4x − 34 [Distributive]
4x + 20 = 13x − 34 {Combine Like Terms]
4x - 13x + 20 = 13x - 13x − 34 [Subtractive: -13x both sides]
-5x + 20 = - 34 [Combine Like Terms]
-5x + 20 - 20 = -34 - 20 [Subtractive: - 20 both sides]
-5x = -54 [Combine Like Terms]
x = -54/-5 [Division Property: divide both sides by -5]
x = - 10 4/5
What is the range of the relation in the table below?
Range is the set of all values which the given function can output. The correct option is A.
What is domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.Since y is the output for the given function, and the only outputs that can be seen for the function are 0, 2, and 4. Therefore, the range of the function is {0,2,4}.
Hence, the correct option is A.
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x y 1 -1 2 -3 3 -5 4 -7
A. y = 1 − 2x B. y = -x − 1 C. y = x − 2 D. y = 2x − 1
Answer:
A) y = 1 - 2x
Step-by-step explanation:
Substitute the points given into all of the equations
Let's take point (1, -1)
A) y = 1 - 2x
-1 = 1 - 2(1)
-1 = 1 - 2
-1 = -1 ✓
B) y = -x - 1
-1 = -1 - 1
-1 = -2 ✘
C) y = x - 2
-1 = 1 - 2
-1 = -1 ✓
D) y = 2x - 1
-1 = 2(1) - 1
-1 = 2 - 1
-1 = 1 ✘
So far, lines A and C can be possible solutions. Let's try point (2, -3)
A) y = 1 - 2x
-3 = 1 - 2(2)
-3 = 1 - 4
-3 = -3 ✓
C) y = x - 2
-3 = 2 - 2
-3 = 0 ✘
Thus, line A is the correct answer
Given the function h of x equals negative 5 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (–∞, 0).
The function is decreasing on the interval (0, ∞).
The function is increasing on the interval (0, ∞).
Answer:
The function is decreasing on the interval ( 0,∞)The function h(x) = -5√x is decreasing on the interval (–∞, 0) is true, Option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function h of x equals negative 5 times the square root of x.
h(x) = -5√x
The value of h(x) decreases as the value of x increases.
The function h(x) is a decreasing function over the interval (–∞, 0) because it is a negative function over the interval.
Hence, the function is decreasing on the interval (–∞, 0) is true.
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Write the sentence as an equation.
253 equals the product of 232 and k
Type a slash ( / ) if you want to use a division sign.
Answer:
253=232×k
Step-by-step explanation:
please mark me as brainlest
The graphs below have the same shape. The equation of the blue graph is f(x)
=|x|. Which of these is the equation of the red graph, g(x)?
y f(x) = |x|
A. g(x)=|x-5|
B. g(x)=|xl-5
C. g(x)=|x + 5|
D. g(x)=|x|+5
The required correct answer is C. g(x) = |x + 5|. This equation satisfies both conditions we identified above: it involves the term "x+5", and it shifts the graph of f(x) = |x| to the left by 5 units.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Since both graphs have the same shape, the red graph is a transformation of the blue graph.
When we compare the two graphs, we can see that the red graph is shifted horizontally to the left by 5 units. This means that the equation of the red graph must involve the term "x+5" or "x-5" in some way.
Also, we can see that the red graph intersects the y-axis at the point (0, 5). This means that the equation of the red graph must involve the term "+5" in some way.
The correct answer is C. g(x) = |x + 5|. This equation satisfies both conditions we identified above: it involves the term "x+5", and it shifts the graph of f(x) = |x| to the left by 5 units. When we plot this equation, we get a graph that has the same shape as f(x) = |x|, but is shifted to the left and intersects the y-axis at (0, 5).
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The time it takes me to wash the dishes is uniformly distributed between 7 minutes and 15 minutes.
What is the probability that washing dishes tonight will take me between 13 and 14 minutes?
Give your answer accurate to two decimal places.
How do you write an equation in function form?
Answer: Writing an equation in function form. You want to remove the x term from the side y is on and move it to the other side of the equal sign. To do this either add or subtract the x term from both sides. Next divide by the coefficient of the y term. Now your equation is in function form.
explanation: like 57 * Y =142500
what is the number for Y if u don't know u could divided 142500 by 57 and it equals? 2500;) hope I helped
i need this for sparx hwk
what is 1/5 plus 1/10
Step-by-step explanation:
hope it helps you and give me a brainliest
Step-by-step explanation:
[tex] = \frac{1}{5} + \frac{1}{10} \\ [/tex]
Now make the denominator same...
[tex] = \frac{1}{5} \times \frac{2}{2} + \frac{1}{10} \\ [/tex]
[tex] = \frac{2}{10} + \frac{1}{10} \\ [/tex]
[tex] = \frac{3}{10} \\ [/tex]
:)
..
Please help with this
Answer:
(a) Horizontal line test
Step-by-step explanation:
A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.
Inverse relationThe inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.
Inverse functionIf the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to pass.
A function will have an inverse function if it passes the Horizontal Line Test.
__
Additional comment
The attached graph shows a function (red curve) that does not pass the horizontal line test. Its inverse relation is the green curve, which you can see is not a function. It does not pass the vertical line test.
The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. find the missing term. the roots of x2 − ( ) 34 are 5 ± 3i.
The missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have the roots of a quadratic equation:
5 ± 3i
To find the quadratic equation:
(x - (5+3i))(x - (5-3i))
[tex]\rm =x^2+x\left(-\left(5-3i\right)\right)-\left(5+3i\right)x-\left(5+3i\right)\left(-\left(5-3i\right)\right)[/tex]
= x² -10x + 34
The missing value is 10x
The quadratic equation is:
= x² -10x + 34
Thus, the missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
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An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
Answer:
[c] The value of w cannot be a negative number.
[d] Substitution is used to replace the variable l with a value of 20.
[e] The subtraction property of equality is used to isolate the term with the variable w.
Step-by-step explanation:
To figure out which steps of the solution are true, let us solve.
2 l plus 2 w equals 62 -> 2l + 2w = 62
----
2l + 2w = 62
2(20) + 2w = 62 <- Substitution is used to replace the variable l with a value of 20.
40 + 2w = 62
2w = 22 <- The subtraction property of equality is used to isolate the term with the variable w.
w = 11
This means that the value of w is not 10 feet so the first option is incorrect. This shape is a rectangle, so the value of w cannot be 0. Since we cannot have a negative measurement, option three is incorrect. This leaves us with the last three options as our answer, shown by the work above.
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AB is a common external tangent to circles D and C. The points of tangency are at A and B. DC = 13, BC = 2 and AD = 7.
Find AB.
Based on the calculations, the length of side AB is equal to 13.93 units.
How to find the length of AB?Since the points of tangency are at A and B, we would determine the side length of the point lying between side A and D as follows:
AM = AD - BC
AM = 7 - 2
AM = 5 units.
Now, we can determine the length of side AB by applying Pythagorean's Theorem:
AB² = BM² + AM²
AB² = 13² + 5²
AB² = 169 + 25
AB = √194
AB = 13.93 units.
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I need help with a question
Solution :-
Here we have been given with two equations :
x + 5y = 0 (Equation No.1)3y + 2x = -21 (Equation No.2)¤ From Equation No.1 :
>> x = -5y
¤ In Equation No.2 :
Substituting the value of x which we got above as -5y here.
>> 3y + 2(-5y) = -21
>> 3y + 2 × (-5y) = -21
>> 3y - 10y = -21
>> -7y = -21
>> 7y = 21
>> y = 21 / 7
>> y = 3
¤ Finding out value of x :
>> x = -5y
>> x = -5(3)
>> x = -15
y = 7x (6/7,-1/4) ….
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = 7x (6/7, -1/4)
we can plug in the point (6/7, -1/4)
-1/4 = 7(6/7)
-1/4 = 6
-1/4 does not equal 6 so this point is not on the line
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Need help (pic included)
Answer:
r = 5
Step-by-step explanation:
The zeroes ( where the function intersects the x - axis) are equi-distant from the vertex line of symmetry
vertex 2,4 to get to -1 , 0 you have to go three units in the negative x direction ..... the other zero is on the OTHER side of the vertex 3 units which would be 5,0 so r = 5
Here is a graph to look at:
Find the constant of proportionality
(
r
)
(r)left parenthesis, r, right parenthesis in the equation
y
=
r
x
y=rxy, equals, r, x.
The constant of proportionality is 0.1
Complete questionFind the constant of proportionality (r)in the equation y=rx.
r =
x y
14 1.4
16 1.6
21 2.1
How to determine the constant of proportionality?The equation is given as:
y = rx
When x = 14 and y = 1.4, we have:
1.4 = r * 14
Divide both sides by 14
r = 0.1
Hence, the constant of proportionality is 0.1
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!!!! PLEASE HELP !!!!
The senior classes at High School A and High School B planned separate trips to
New York City. The senior class at High School A rented and filled 4 vans and 3
buses with 133 students. High School B rented and filled 9 vans and 1 bus with 167
students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry
A) Van: 23, Bus: 16
C) Van: 6, Bus: 34
B) Van: 25, Bus: 36
D) Van: 16, Bus: 23
What would be the cost for 5 of the gift cards?
Answer:
$100
Step-by-step explanation:
It appears that each gift card costs $20, so 5 of them would be $20 * 5 gift cards = $100
Answer:
$100
Step-by-step explanation:
From the graph we see that each card costs $20.
Find the area of the smaller sector.
Round to the nearest tenth.
50°
7.13 ft
Area = [?]ft²
Answer:
A ≈ 22.2 ft²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{50}{360}[/tex]
= π × 7.13² × [tex]\frac{5}{36}[/tex]
= 50.8369π × [tex]\frac{5}{36}[/tex]
≈ 22.2 ft² ( to the nearest tenth )
Determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g.
Answer:
Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit
Step-by-step explanation:
Parent function: [tex]f(x)=x[/tex]
The graph of the parent function is a straight line graph that intersects the axes at the origin (0, 0) and has a positive slope of 1 unit.
To determine the sequence of transformations, find the equation of the transformed function in slope--intercept form.
Slope-intercept form of a linear function: [tex]f(x)=mx+b[/tex]
(where m is the slope and b is the y-intercept)
To calculate the slope of the transformed function, choose two points on the line and use the slope formula:
Let (x₁, y₁) = (0, -1)Let (x₂, y₂) = (1, -4)[tex]\implies \sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-(-1)}{1-0}=-3[/tex]
The y-intercept (where the line crosses the y-axis) of the transformed function is (0, -1).
Therefore the equation of the transformed function is:
[tex]g(x)=-3x-1[/tex]
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Comparing the transformed function's equation with the parent function:
[tex]\begin{cases}f(x)=x\\g(x)=-3x-1\end{cases}[/tex]
Transformations
1. Reflection in the y-axis:
[tex]f(-x)=-x[/tex]
2. Vertically stretched by a factor of 3:
[tex]3f(-x)=-3x[/tex]
3. Shifted 1 unit down:
[tex]3f(-x)-1=-3x-1[/tex]
Summary
Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit
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A music-streaming service charges $9 per month for a single user. Additional users within the same household can be added for $3 per month.
Write an equation that shows how the monthly cost, y, depends on the number of additional users in the household, x.
Do not include dollar signs in the equation.
y=
Answer:
y=9+3x
Step-by-step explanation:
It starts with y=.
Then you have to put the 9 for the streaming service.
Then you add.
You multiply by 3 for all the x in the household plan.
Answer:
y = 9 + 3x
Step-by-step explanation:
$9 per month for a single user
$3 per month for additional users
Find monthly cost, y, where additional cost is represented by x
The cost for a single user = fixed cost (It remains constant)
The cost of the additional user = variable (It increases with the number of users)
The monthly cost increases with the number of additional users
The monthly cost = cost of single user + the cost of additional users
y = 9 + 3x
Match each box plot to the data set it represents.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
{20,18,8,18,10,8,4}
{12,14,16,20,4,8,10}
{12,16,4,20,8,6,8}
An expression can either be an equation or an inequality.
The correct classification of the terms are:
Expression; 4x+20
Inequality: 4x+20>40
Equation: 4x+20=40
We have given that,
{20,18,8,18,10,8,4}
{12,14,16,20,4,8,10}
{12,16,4,20,8,6,8}
How to determine the correct classification?To determine the correct classification, we make use of the following highlights
When an expression has the =, then the expression is an equation.
When an expression has any of the following signs>, <, >=, <= or != , then the expression is an inequality.
When the expression is neither an equation nor an inequality, then it is just an expression.
Hence, the correct classifications are:
Expression; 4x+20
Inequality: 4x+20>40
Equation: 4x+20=40
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Kayla has just subscribed to a music streaming service. For a one-time fee of $12.99, she can download songs for $0.65 each, for an entire month. Kayla's budget will allow her to spend no more than a total of $27 on the streaming service this month. What is the maximum number of songs she can download while still remaining within her budget?
a) x <= 22
b) <= 41
c) x <= 21
d) X <= 42
The maximum number of songs she can download while still remaining within her budget is x <= 21
How to determine the maximum number of songs?The given parameters are:
One-time fee = $12.99
Rate = $0.65 per song
Budget = $27
The inequality is then represented as:
One-time fee + Rate * x <= Budget
So, we have:
12.99 + 0.65x <= 27
Subtract 12.99 from both sides
0.65x <= 14.01
Divide both sides by 0.65
x <= 21.55
Round down
x <= 21
Hence, the maximum number of songs she can download while still remaining within her budget is x <= 21
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A survey was given to ask a group of adults if they liked chocolate or vanilla ice cream more. The table shows the survey results of three age groups.
(see attachment for table)
A person is selected at random. Determine the probability of each described event. Round your answers to two decimal places.
P(20s | Chocolate) = ________
P(Chocolate | 30s) * P(Vanilla | 30s) = ________
The probability of P(20s | Chocolate) and P(chocolate | 30s) x P(vanilla | 30s) will be 0.26 and 0.25, respectively.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Adults were polled to determine whether they preferred vanilla or chocolate ice cream. The survey findings for three age groups are displayed in the table.
There are 127 people who enjoy chocolate, and 33 of them are in their 20s is given as,
P(20s | Chocolate) = 33 / 127 = 0.26
There are 122 persons in their 30s, and 53 of them prefer chocolate 69 others prefer vanilla is given as,
P(chocolate | 30s) x P(vanilla | 30s) = 53/122 x 69/122 = 0.25
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