The following are body mass index (BMI) scores measured in 9 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.
25 27 31 33 26 28 38 41 24
What is the standard deviation of BMI?

Even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.

No, 2 is not a zero of the polynomial p(x)=3x^(4)-14x^(3)-9x^(2)+64x-28. To determine p(k), we simply need to plug in the value of k into the polynomial and simplify.

So, p(k) = p(2) = 3(2)^(4) - 14(2)^(3) - 9(2)^(2) + 64(2) - 28

= 3(16) - 14(8) - 9(4) + 128 - 28

= 48 - 112 - 36 + 128 - 28

= 0

Therefore, p(k) = p(2) = 0.

So, even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.

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Taking the given functions, we will obtain the following inverse functions

To find the inverse of each function, we need to switch the x and y values and solve for y. This will give us the inverse function.

1) [tex]y = log5 (4x + 1)[/tex]
Switch x and y:
[tex]x = log5 (4y + 1)[/tex]
Solve for y:
[tex]5^x = 4y + 1\\4y = 5^x - 1\\y = (5^x - 1)/4[/tex]
Inverse function:

2) [tex]y = log3 (2^x + 8)[/tex]
Switch x and y:
[tex]x = log3 (2^y + 8)[/tex]
Solve for y:
[tex]3^x = 2^y + 8\\2^y = 3^x - 8\\y = log2 (3^x - 8)[/tex]
Inverse function: [tex]f^-1(x) = log2 (3^x - 8)[/tex]

3) [tex]y = log4 (-2x + 9)[/tex]
Switch x and y:
[tex]x = log4 (-2y + 9)[/tex]
Solve for y:
[tex]4^x = -2y + 9\\-2y = 4^x - 9\\y = (9 - 4^x)/2[/tex]
Inverse function: [tex]f^-1(x) = (9 - 4^x)/2[/tex]

4) [tex]y = 5^x + 9/2[/tex]
Switch x and y:
[tex]x = 5^y + 9/2[/tex]
Solve for y:
[tex]5^y = x - 9/2\\y = log5 (x - 9/2)[/tex]
Inverse function: [tex]f^-1(x) = log5 (x - 9/2)[/tex]

5) [tex]y = 10^x + 3/ -3[/tex]
Switch x and y:
[tex]x = 10^y + 3/ -3[/tex]
Solve for y:
[tex]10^y = x - 3/ -3\\y = log10 (x - 3/ -3)[/tex]
Inverse function: [tex]f^-1(x) = log10 (x - 3/ -3)[/tex]

6) [tex]y = log5 (-4x + 10)[/tex]
Switch x and y:
[tex]x = log5 (-4y + 10)[/tex]
Solve for y:
[tex]5^x = -4y + 10-4y = 5^x - 10y = (10 - 5^x)/4[/tex]
Inverse function: [tex]f^-1(x) = (10 - 5^x)/4[/tex]

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Answer:

4 number x value is 10 in

5 number x value is 12mi

use formula of h2=p2+b2

The coordinate of P is ( 14/5, 23/5, 28/5)

For the line AB, the direction vectors are

l= 2-1= 1, m=3-1= 2 and n= 4-2= 2

so, the equation of the line AB can be given by

[tex]  \text{$\frac{x-1}{1}$ = $\frac{y-1}{2}$ = $\frac{z-2}{2}$ } [/tex]

let a point be P (x,y,z). lying on the line AB.

coordinate of the general point in AB can be given by

[tex]  \text{$\frac{x-1}{1}$ = $\frac{y-1}{2}$ = $\frac{z-2}{2}$ = t } [/tex]

so, x= t+1, y= 2t+1, z= 2t+2

so, P (x,y,z) can be P (t+1, 2t+1, 2t+2). Another point is C ( 4, 2, 2 ).

the direction ratios of the line CP is

l1= t+1-4 = t-3

m1= 2t+1-2 = 2t-1

n1 = 2t+2-2 = 2t

Dot product of the direction ratios of two orthogonal lines are 0.

so, 1(t-3)+2(2t-1)+2(2t)=0

or, t=9/5

so, x= (9/5)+1 = 14/5

     y= (9/5)*2 + 1= 23/5

     z= (9/5)*2 + 2 = 28/5

so, the coordinate of P is ( 14/5, 23/5, 28/5).

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Rewriting the quadratic function [tex]\[ f(x)=(x-8)^{2}+7 \][/tex], we obtain as a result, vertex: [tex](8,7)[/tex].

To rewrite the quadratic function in standard form, we need to complete the square. The standard form of a quadratic function is [tex]\[ f(x)=a(x-h)^{2}+k \][/tex] where [tex](h,k)[/tex] is the vertex of the parabola.

Step 1: Separate the constant term from the rest of the equation.
[tex]\[ f(x)=x^{2}-16 x+71 \\\[ f(x)=(x^{2}-16 x)+71 \][/tex]

Step 2: Complete the square by adding and subtracting the square of half the coefficient of the x term inside the parenthesis.
[tex]\[ f(x)=(x^{2}-16 x+64)+71-64 \\\[ f(x)=(x-8)^{2}+7 \][/tex]

Now the equation is in standard form. The vertex of the parabola is (8,7).

Answer: [tex]\[ f(x)=(x-8)^{2}+7 \][/tex], vertex: [tex](8,7)[/tex].

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Using two-point form, the equation of the line passing through the points A and B is x = 5.

The two-point form of a line is given by:
y - y₁ = [(y₂ - y₁)/(x₂ - x₁)] (x - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.

Given points A(5, 5) and B(5, -5), we can plug in the values into the equation:
y - 5 = [(-5 - 5)/(5 - 5)] (x - 5)

Simplifying the equation gives us:
y - 5 = (-10/0) (x - 5)

Notice that the slope (y₂ - y₁)/(x₂ - x₁) is equal to -10/0(indeterminate). This means that the line is a vertical line passing through x = 5.

The standard form of a line is Ax + By = C. So, the standard form of the equation of the line passing through points A and B is: x = 5.

Therefore, the equation of the line passing through the two points is x = 5.

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Answer:

12.15 m

Step-by-step explanation:

90 × 13.5 cm × (1 m)/(100 cm) = 12.15 m

Answer: 12.15 m (rounded 12.2)

Step-by-step explanation:

100 cm = 1 m

13.5(90) = 1,215

1215 divided by 100 = 12.15

The point (2, –2) with x-coordinate value 2 and y-coordinate value -2, is not satisfied the equation y = x.

We have an equation, y = x --(1) and point (2,-2). We have to check that point (2, –2) satisfy the equation y = x or not. To check that, we need to put the values of the point in the equation. If the equation satisfies them, the point belong to the line. Substituting the coordinates of the given point, i.e., x = 2 and y = -2, into the defining equation(1), we get, y = x

L.H.S, y = -2

R.H.S, x = 2

but -2 ≠ 2 so, L.H.S ≠ R.H.S

We now see from the above substitution and the resultant calculation that the coordinates (x, y) of the point (2, -2) does not make the equation y = x

Hence, the point ( 2,-2) does not satisfied equation y= x .

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The point of maximum growth rate is approximately (1.76, f'(1.76)) or (5.54, f'(5.54)) so the answer is (C) (5.54, 9).

What is the rate?

In mathematics, the rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

To find the point of maximum growth rate, we need to find the maximum value of the derivative of the function f(x).

First, we need to find the derivative of f(x):

[tex]f'(x) = (20 * 27e^{(-3x)}) / (1 + 9e^{(-3x)})^2[/tex]

To find the maximum value of f'(x), we set f''(x) = 0, where f''(x) is the second derivative of f(x):

[tex]f''(x) = (20 * 81e^{(-6x)} * (81e^{(-6x)} - 18e^{(-3x)} + 1)) / (1 + 9e^{(-3x)})^3[/tex]

Solving f''(x) = 0, we get:

[tex]81e^{(-6x)} - 18e^{(-3x)} + 1 = 0[/tex]

Letting [tex]y = e^{(-3x)}[/tex], we can rewrite the equation as:

81y² - 18y + 1 = 0

Using the quadratic formula, we get:

y = (18 ± √(18² - 4 * 81)) / (2 * 81) = 0.069 or 0.012

So,  [tex]y = e^{(-3x)}[/tex] = 0.069 or 0.012

Solving for x, we get:

x = ln(0.069) / (-3) ≈ 1.76 or x = ln(0.012) / (-3) ≈ 5.54

Therefore, the point of maximum growth rate is approximately (1.76, f'(1.76)) or (5.54, f'(5.54)).

Now we need to calculate f'(1.76) and f'(5.54) to find the answer.

[tex]f'(1.76) = (20 * 27e^{(-5.28)}) / (1 + 9e^{(-5.28)})^2 = 9.62[/tex]

[tex]f'(5.54) = (20 * 27e^{(-16.62)}) / (1 + 9e^{(-16.62)})^2 = 1.01[/tex]

Rounding these values to the nearest hundredth, we get:

(1.76, 9.62) and (5.54, 1.01)

Therefore, the point of maximum growth rate is approximately (1.76, f'(1.76)) or (5.54, f'(5.54)) so the answer is (C) (5.54, 9).

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Chase's likely error is that he added instead of subtracting when finding his location on the number line.

What is the fractions?

A fraction is a way of representing a part of a whole or a ratio between two numbers. It consists of a numerator (top number) and a denominator (bottom number), separated by a line.

If Ellie's house is at 1 1/2 on the number line, and Chase lives 1 1/5 blocks west of Ellie, then the coordinate of Chase's house would be:

1 1/2 - 1 1/5 = 3/2 - 6/5

To subtract these fractions, we need a common denominator, which is 10:

(3/2) * (5/5) - (6/5) * (2/2) = 15/10 - 12/10 = 3/10

So Chase's house is located 3/10 blocks west of Ellie's house on the number line. Therefore, the correct coordinate for Chase's house is:

1 1/2 - 3/10 = 1 2/5

Chase's likely error is that he added instead of subtracting when finding his location on the number line.

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In the following question, Starting time: 9:55 A. M. Elapsed time: 27 minutes provide a snapshot of a specific moment in time and the amount of time that has passed since a particular event or task began.

You have provided two pieces of information: the starting time and the elapsed time.

The starting time is 9:55 A.M., which means that an event or task began at that time. The time is given in the 12-hour clock format, where A.M. stands for "ante meridiem" and refers to the period between midnight and noon.

The elapsed time is 27 minutes, which means that 27 minutes have passed since the event or task started. "Elapsed time" refers to the amount of time that has passed since the start of an event or task.

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Option A is correct, Clearly, r needs to be recalculated.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables.

The value of r always falls between -1 and 1, where a negative value indicates a negative correlation (i.e., as one variable increases, the other tends to decrease), and a positive value indicates a positive correlation (i.e., as one variable increases, the other tends to increase).

However, the value of r cannot be less than -1 or greater than 1.

Therefore, a correlation coefficient of -1.91 is not a valid value.

Hence, Option A is correct, Clearly, r needs to be recalculated.

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Answer:

12

Step-by-step explanation:

12 × 3= 36

36 + 4= 40

so the answer is 12

Answer:

Not true with all numbers!

Step-by-step explanation:

see.Ex.3x3=9+4=13 not 40

Instead of regular six-sided dice, some games use dodecahedronal - or 12-sided - dice. If you rolled a pair of dodecahedronal dice (each label 1 through 12) 100 times, you would expect the values on the two dice to add up to 4about 3 times. The correct answer is c) 3.


When rolling two dodecahedronal dice, there are a total of 12 x 12 = 144 possible outcomes. To find the probability of rolling a sum of 4, we need to look at the possible combinations that can result in a sum of 4:

1 + 3

2 + 2

3 + 1

There are a total of 3 possible combinations that can result in a sum of 4. Therefore, the probability of rolling a sum of 4 is 3/144 = 1/48.


If we roll the dice 100 times, we would expect to get a sum of 4 about (1/48) x 100 = 2.08333 times. Since we can't roll a fraction of a time, we can round this to the nearest whole number, which is 3. So, we would expect to roll a sum of 4 about 3 times out of 100 rolls.The correct answer is c) 3.

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Answer:

The angles are adjacent and the value of x is 63

Step-by-step explanation:

The required graph represents that the solution to the given inequality x - 8 ≥ -3 is x ≥ 5.

A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To solve for x:

x - 8 ≥ -3

x ≥ -3 + 8

x ≥ 5

So, the solution is x ≥ 5.

For the graph of the solution, draw a number line and mark a closed circle at 5 since the inequality includes 5. Then, shade to the right of 5 to represent all values of x that satisfy the inequality.

Thus, the required graph represents that the solution to the given inequality is x ≥ 5.

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Answer:

Step-by-step explanation:

If x represents one day of sales and x=12, then we can substitute that value into the equation to find the total number of pencils sold:

y = 160x

y = 160(12)

y = 1920

So the supply store sold a total of 1920 pencils on the day when x=12.

Answer:

Your answer is Point T

Step-by-step explanation:

Answer:

s

Step-by-step explanation:

The correct way to name the figure shown is PQ. This figure consists of two perpendicular lines, P and Q, which intersect at a point. The lines are labeled P and Q, so the correct name for the figure is PQ.

Perpendicular lines are those two lines that intersect each other at a 90 degree angle. These lines are also known as orthogonal lines. When two lines intersect at a 90 degree angle, they are said to be perpendicular.

The figure is a basic geometric shape and is used to illustrate the concept of perpendicular lines. In the figure shown, the angle formed by the intersection of the two lines is a right angle, so the lines are perpendicular.

The figure can also be used to illustrate the concept of a transversal. A transversal is a line that intersects two other lines at different points. In the figure, the line PQ is a transversal intersecting the two lines P and Q.

In conclusion, the correct way to name the figure shown is PQ. This figure is used to illustrate the concepts of perpendicular lines, line segments, and transversals.

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As a result, the balance in the account at the end of seven years is, to the closest cent, $116177.20.

The term "amount" in mathematics typically denotes a sum, total, or quantity. It could be a numerical value or some other kind of measurement. Depending on the context, the word "amount" may also be used to refer to quantity, total, sum, volume, or magnitude. \

The term "amount" is used in algebra and calculus to describe the outcome of an operation, such as the amount of change in a function or the quantity of a variable needed to satisfy an equation. In many disciplines, including finance, science, and engineering, the word "amount" is frequently used to refer to quantities or measurements.

given

The amount of money in the account after 7 years can be calculated using the formula V = Pe(rt), where V is the value of a account in t years, P is the principal implementation, e is the base of a natural log, and r is the rate of interest:

V = P*e(rt) = 67700*e(0.077*7)

[tex]V = 67700 * e^{(0.539) (0.539)[/tex]

V = 67700 * 1.716

V = 116177.20

As a result, the balance in the account at the end of seven years is, to the closest cent, $116177.20.

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Mmaximum number of apples produced per year is 98000 when 70 apple trees are planted in the farm.

To find the maximum number of apples per year, we need to find the vertex of the quadratic equation y=-20x^(2)+2800x. The x-coordinate of the vertex can be found using the formula x=-b/(2a), where a=-20 and b=2800.

Plugging in the values for a and b, we get:
x=-2800/(2*-20)
x=-2800/(-40)
x=70

So, the maximum number of apples per year will be produced when 70 apple trees are planted in the farm. We can find the y-coordinate of the vertex by plugging x=70 back into the equation:

y=-20(70)^(2)+2800(70)
y=-20(4900)+196000
y=-98000+196000
y=98000

Therefore, the maximum number of apples produced per year is 98000 when 70 apple trees are planted in the farm.

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Answer:

There are 500 total people. 215 gave blood and 159 helped set up, giving a total of 374. However, since 89 people did both, we counted those 89 people twice. So we subtract 89 to get 285 total volunteers.

500-285=215 did not volunteer

There were 220 people that neither donated nor helped.

To find out how many people neither donated nor helped, we can use the formula for the union of two sets:

  A∪B = A + B - A∩B.

In this case, A is the number of people who donated, B is the number of people who helped, and A∩B is the number of people who both donated and helped.

Plugging in the given values, we get:

  A∪B = 217 + 156 - 93 = 280

This tells us that there were 280 people who either donated or helped. To find out how many people neither donated nor helped, we can subtract this number from the total number of people surveyed:

  500 - 280 = 220

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x1 = 0.75, x2 = 5, x3 = 0, x4 = 12

To transform the augmented coefficient matrix to echelon form using elementary row operations:

1. Subtract twice the first row from the second row.

2. Subtract the first row from the third row.

3. Subtract the first row from the fourth row.

4. Subtract the third row from the fourth row.

The resulting augmented coefficient matrix in echelon form is:

4x1 - 2x2 - 3x3 + x4 = 3

0x1 - 4x2 - 8x3 = -16

0x1 + x2 + 2x3 + x4 = 17

0x1 + 0x2 + x3 + x4 = 12

To solve the system by back substitution:

1. x4 = 12 (from the last equation)

2. x3 = 12 - x4 = 0 (substitute x4 from step 1 into the third equation)

3. x2 = (17 - x4) / (1) = 5 (substitute x4 from step 1 into the second equation)

4. x1 = (3 - 2*5 - 3*0) / (4) = 0.75 (substitute x2 and x3 from steps 2 and 3 into the first equation)

The solution is x1 = 0.75, x2 = 5, x3 = 0, x4 = 12.

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The each of two individuals will get 54 and 27 sweets according to provided ratio.

Let us assume the amount of sweets each get be 2x and x. Now we know the sum is 81, so representing the information in equation form.

2x + x = 81

Performing addition on Left Hand Side of the equation

3x = 81

Rewriting the equation

x = 81/3

Performing division on Right Hand Side of the equation

x = 27

So, first person will get amount of sweets = 2×27

First person = 54

Amount of sweets for second person = 27

Thus, each will get 54 and 27 sweets.

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The area of the shaded segment of the circle is 5.79 square metre.

The area of a segment is equal to the area of a sector less the triangle-shaped portion.

A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]

Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the centre. All lines that cross the circle join together to produce the line of reflection symmetry. Moreover, every angle has rotational symmetry around the centre.

r=8m

∅=60°

Applying the formula's values, we obtain

A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]

A=[tex]\frac{1}{2}[/tex]([tex]\frac{π}{3}[/tex]-Sin60°)×[tex]8^{2}[/tex]

A=5.79

Hence,  the area of the shaded segment of the circle is 5.79 square metre.

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1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,

Here, we have

Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any​ direction.

Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.

The area of a circle is given as:

Area = πr²

Radius = 24 feet

Area = 3.14(24)²

Area = 1808.64

Hence, 1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

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Answer:

1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

What is an area of a circle?

The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,

Here, we have

Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any​ direction.

Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.

The area of a circle is given as:

Area = πr²

Radius = 24 feet

Area = 3.14(24)²

Area = 1808.64

Hence, 1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

Both models assume that the tax expenditures are $5000 on January 1st, 2000.

The accountant is using two different models to estimate the tax expenditures for the small business. Both models assume that the tax expenditures are $5000 on January 1st, 2000. The accountant wants to estimate the tax expenditures, e, in thousands of dollars t years after January 1st, 2000.

Let's call the two models Model 1 and Model 2. Model 1 assumes that the tax expenditures increase by a fixed amount every year. Let's call this fixed amount a. Therefore, the tax expenditures, e, under Model 1 can be represented by the equation:

e = 5000 + at

Model 2 assumes that the tax expenditures increase at a constant percentage rate every year. Let's call this percentage rate r. Therefore, the tax expenditures, e, under Model 2 can be represented by the equation:

e = 5000(1 + r)ˣ

Now, let's substitute t = 0 into both equations to find the value of e on January 1st, 2000.

For Model 1:

e = 5000 + a(0) = 5000

For Model 2:

e = 5000(1 + r)⁰ = 5000

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Answer: If the ratio is 1:200,000 then the length of the road in centimeters is 800,000 centimeters meaning the conversion of this to kilometers would be 8 kilometers

Step-by-step explanation: every 100k (100,000) cm in kilometers would be 1 kilometer so take that and for the 200,000 times 4 is 800,000 which means the answer is 8 kilometers

________________________________________________________

The dealer bought the car, which he sold to a man and made a profit of 15 percent at $209,000.

To compute the dealer's purchase price, we use backward calculations and percentages.

First, the man's purchase price is determined as $240,350 since he incurred a loss of 50% amounting to $120,175.

By equating the proportional loss to the selling price, we can determine the purchase price paid by the man as $240,350.

Since the dealer generated a profit of 15% on $240,350, we determine his cost as $209,000 based on the profit percentage.

The dealer's profit percentage = 15%

The man's loss percentage = 50%

The selling price by the man to the woman = $120,175

The purchase price by the man = $240,350 ($120,175/50%)

The dealer's purchase price = $209,000 ($240,350/1.15)

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