The number of ways that he can reach the bottom step in 5 jumps will be 792.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
Running down the stairway is someone. He could hop over some steps since he is in a hurry. When a staircase has 12 steps (including the top one, where he begins, and the last one, where he ends).
The number of ways will be given as,
¹²C₅ = (12!) / [(12 - 5)! x 5!]
¹²C₅ = (12 x 11 x 10 x 9 x 8 x 7!) / [7! x 5 x 4 x 3 x 2 x 1]
¹²C₅ = 11 x 9 x 8
¹²C₅ = 792
The number of ways that he can reach the bottom step in 5 jumps will be 792.
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What is the length of BC in the right triangle below?
The length of BC in the right triangle is the correct option is B which is 15.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides. The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together. This is written as a2 + b2 = c2 in the usual algebraic notation.The measure of angle A is 90°. It means triangle ABC is a right angle triangle.
Using Pythagoras in triangle A B C,
[tex]& B C^2=A C^2+A B^2 \\[/tex]
[tex]& B C^2=(12)^2+(9)^2 \\[/tex]
[tex]& B C^2=144+81 \\[/tex]
[tex]& B C^2=225[/tex]
Take square root both side.
[tex]& B C=225 \\[/tex]
[tex]& B C=15[/tex]
The complete question is,
What is the length of BC in the right triangle below
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How long does it take to get from London to Birmingham on Saturday if you take the 9:34am train?
Answer:
3 hours ......... ........
Find sin L, cos L, tan L, sin M, cos M, and tan M. Express each ratio as a fraction and as L
mal to the nearest hundredth.
L =12, m=12 square root 4, n=24
The values of the trigonometric function are sin L = 1 / 2, cos L = √3 / 2, tan L = 1 / √3, sin M = √3 / 2, cos M = 1 / 2, and tan M = √3.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine, cosine, and tangents are their names and acronyms (tan).
Given:
l = 12, m = 12√3, n = 24
Calculate the value of sin L, cos L, tan L, sin M, cos M, and tan M as shown below,
sin L = l / n
sin L = 12 / 24
sin L = 1 / 2
cos L = m / n
cos L = 12√3 / 24
cos L = √3 / 2
tan L = l / m
tan L = 12 / 12√3
tan L = 1 / √3
sin M = m / n
sin M = 12√3 / 24
sin M = √3 / 2
cos M = l / n
cos M = 12 / 24
cos M = 1 / 2
tan M = m / l
tan M = 12√3 / 12
tan M = √3
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Find the value of each variable.
x= and y=
(Simplify your answers. Type exact answers, using radicals as needed.)
The values of x and y using trigonometry ratio is 3.5
What are trigonometry ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin (tetha) = opposite/ hypotenuse
cos (tetha) = adjascent/ hypotenuse
tan ( tetha) = opposite/ adjascent
In the triangle, tetha is 45°
therefore sin 45 = x/5
1/√2 = x/5
√2x = 5
x = 5/√2
rationalizing
x = (5√2)/2
x = 2.5 × 1.41
x = 3.5
since the triangle is an isosceles right-angled triangle , then x = y = 3.5
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Evaluate the expression when a = 1/4 and b = 6 16a^2 - 4b
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{16a^2 - 4b}[/tex]
[tex]\mathsf{= 16(\dfrac{1}{4})^2 - 4(6)}[/tex]
[tex]\mathsf{= 16(\dfrac{1}{4} \times \dfrac{1}{4}) - 4(6)}[/tex]
[tex]\mathsf{= 16\times \dfrac{1(1)}{4(4)} - 4(6)}[/tex]
[tex]\mathsf{= 16(\dfrac{1}{16}) - 4(6)}[/tex]
[tex]\mathsf{= \dfrac{16}{1}(\dfrac{1}{16}) - 4(6)}[/tex]
[tex]\mathsf{= \dfrac{16(1)}{1(16)} - 4(6)}[/tex]
[tex]\mathsf{= \dfrac{16}{1} - \dfrac{4(6)}{1}}[/tex]
[tex]\mathsf{= 1 - 4(6)}[/tex]
[tex]\mathsf{= 1 - 24}[/tex]
[tex]\mathsf{= -23}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{-23}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
y = -2/3x + 4 (table graph)
1.
Which correctly gives the slope and y-intercept of the line represented by the equation below?
x - y = 2
slope = 1; y-intercept = -2
slope = -1; y-intercept = 2
slope = -2; y-intercept = 1
slope = 2; y-intercept = -1
The option that correctly gives the slope and y - intercept of the line is A. slope = 1; y-intercept = -2.
How to find the slope and y - intercept ?The form that the equation of a line takes is :
y = mx + b
Where :
m = slope
b = y - intercept
The equation given of, x - y = 2 can be rewritten to be in slope - intercept form as :
x - y = 2
x = 2 + y
y = x - 2
In this instance, the y - intercept can be seen to be - 2. The slope would then be 1 as there is no number next to x.
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Please help me with this page.
nswer: The perimeter is approximately equal to 43.7 ft.
Step-by-step explanation:
since we are working with a square, we know all the sides tend to have equal measurements including the side which acts as a hypotenuse to the triangle. Therefore, if we somehow find the measurement of the hypotenuse we'll be able to get the measurement of all sides of the square which we could add in to the two other sides of the triangle to get the perimeter.
Joshua calculated the hypotenuse wrong. The correct calculation is:
hypotenuse² = 7² + 7²
hypotenuse = √( 7² + 7²)
hypotenuse = √( 49 + 49)
hypotenuse = √( 98)
hypotenuse = 7√2
now it's going to be easy doing further calculation. We will three sides of square add them to two other sides of the triangle and get the perimeter.
Perimeter of Pentagon :
perimeter = 7√2 + 7√2 + 7√2 + 7 + 7
perimeter = 43.6984848098
perimeter ≈ 43.7 ft ANSWER
hope that helps...
What inequality is represented here?
Answer:
y ≥ x + 1
Step-by-step explanation:
The slope is 1. Rise over run 1/1 = 1
The y-intercept is 1. Where the line crosses the y axis. The shaded part is above the line so that would be greater than or equal to.
Answer:
y >= x+1
Step-by-step explanation:
The Slope is x + 1 and the shaded area plus the solid line is the inequality. The shaded area represents y so y >= x+1.
Hope this helps!
HOW TO DO THIS. HELP ME.
The naming method for naming a plane by making use of the names of three non colinear points on the plane, indicates that the possible name of the plane is PRL
What are non colinear points?Three or more points are non colinear points if they are not located on the same straight line.
A plane in geometric is the concept of a surface which flat, extends continuously in its dimensions, and it is without thickness or edges. A plane is therefore, a two dimensional flat surface, with no thickness and infinite extension in two dimensions.
A flat surface such as a wall, a table surface, a flat screen, a flat piece of paper, or a door are a part of a plane.
In geometry, surfaces which are flat are known as plane figures.
A plane can be formed by three non colinear points, or a line and a point which is not located on the line, and a plane can also be formed by two intersecting lines.
Therefore, a plane can be named by making use of the letters indicating three non colinear points.
Three non colinear points in the plane in the question are P, R, and L, therefore, the plane highlighted in the diagram can be named as the plane PRL
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Amanda’s family is taking a road trip. Their car can travel no more than 352 miles without needing to refill the gas tank. They have traveled 108 miles since they last filled the gas tank. Amanda knows that the inequality representing this situation is 108 + x< 352. Select from drop-down menu to correctly interpret the solution of this inequality.
The correct interpretation of the inequality 108 + x < 352 is given as follows:
Amanda's family has already traveled 108 miles, and needs to fill the tank after traveling more 244 miles.
What is the meaning of the inequality?
The inequality for this problem is defined as follows:
108 + x < 352.
The variable x represents the number of miles that the car can still travel until needing to refill the gas tank.
The solution is obtained similarly to an equality, isolating the variable x and obtaining a range of values, as follows:
x < 352 - 108
x < 244.
(the difference is that the solution of the inequality obtains a range of a values, while for the equality it is a single value).
Hence the family can travel at most 244 miles until needing to refill the tank again to continue the trip.
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Factor 18cd − 45c2d.
3cd(6 − 15c)
6cd(3 − 45c2d)
9c2d(2 − 5)
9cd(2 − 45c2d)
Answer:
9c2d(2 − 5)
Step-by-step explanation:
I need help on this one 5 1/2 + 4 1/3
Answer:
9 5/6
Step-by-step explanation:
Add the whole numbers and the fractions separately
(5 + 4) + (1/2 + 1/3)
Add
9 + 5/6
Write as a mixed number
9 5/6
Answer:
9 and 5/6
Step-by-step explanation:
We can start by adding 5 + 4 which equals 9
Then we add 1/2 to 1/3
Both these numbers can be changed to one with the same denominator
So, 1/2 = 3/6 and 1/3 = 2/6
= 3/6 + 2/6
= 5/6
Add 5/6 back to the 9 we got earlier, we get 9 5/6
Try It
58°
3
4
●
2
106°
Is the measure of angle 1 equal to the measure of angle 2?
Why?
O yes, because they intercept the same arc
Ono, because the sides of 22 are longer
Ono, because they intercept the circle at different
points
The solution is Option A.
Yes , The measure of angle 1 and angle 2 are same because they intercept the same arc of the circle
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
From the circle , the four angles are 1 , 2 , 3 , and 4
And , from the circle theorem
In a circle, the measures of the angles subtended by the same arc on the circumference of the circle are equal
So , from the circle , we can see that
∠1 and ∠2 are subtended by the same arc AB at points C and D respectively
And , the points C and D lies on the circumference of the circle
So , the measures of the angle must be equal
Hence , The angles ∠1 and ∠2 have equal measures because they intercept the same arc of the circle
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18 adults and 165 students going on a field trip. Each bus holds 50 people. How many buses are needed to take everyone?
Answer: 4
Step-by-step explanation:
Lincoln is driving on a long road trip. He currently has 9 gallons of gas in his car. Each hour that he drives, his car uses up 1.25 gallons of gas. How much gas would be in the tank after driving for 2 hours? How much gas would be left after tt hours?
Answer:
The car will use up 1.25 gallons of gas per hour of driving, so after 2 hours of driving, the car will have used 2 * 1.25 = 2.5 gallons of gas.
If Lincoln started the trip with 9 gallons of gas in the car, after 2 hours of driving, he will have 9 - 2.5 = 6.5 gallons of gas left in the tank.
We can generalize this to any number of hours by using the formula:
Gas left = 9 - (1.25 * number of hours driven)
So if he drives for t hours, the amount of gas he will have left in the tank is:
Gas left = 9 - (1.25 * t)
Step-by-step explanation:
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
The area of the triangle is 38 cm^2.
Find the area of the triangle below?To find the area of the triangle given, we need to know the length of the third side.The third side, ac, can be found using the Pythagorean theorem.The Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.In this case, the hypotenuse is ac, so we can create the equation a^2+b^2=c^2, where a and b are the lengths of the two sides of the triangle.Since a is 18 cm and b is 13 cm, we can solve the equation to get c^2=18^2+13^2=361. Therefore, ac=√361=19 cm.Now that we have the length of the third side, ac, we can use the formula for the area of a triangle, Area=1/2(base)(height).In this case, the base of the triangle is 19 cm and the height is 4 cm. Therefore, the area is 1/2(19)(4)=38 cm^2. Therefore, the area of the triangle is 38 cm^2.ac=√(18^2+13^2)=21.93 cmarea=1/2(ab)(height)=1/2(18)(4)=36 cm^2.To learn more about The formula for the area of a triangle refer to:
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On a coordinate grid that is labeled in miles, two cities are located at (−25,−84)
-
25
,
-
84
and (−73,−84)
-
73
,
-
84
. How far apart are these two cities?
By using a formula for the distance between two points, we will see that the distance between the two cities is 48 miles.
How far apart are the two cities located?Remember that if we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points can be calculated as:
distance = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
In this case we want to find the distance between (−25,−84) and (−73,−84), we will get:
distance = √( (-25 + 73)^2 + (-84 + 84)^2)
distance = √( (48)^2 ) = 48
And the grid is on miles, then we conclude that the distance is 48 miles.
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Simplify: √2+ √6
A.) √2+√3
B.) √2
C.)3√2
D.)None of the above
Answer: Option (D) None of the above
Step-by-step explanation:
To simplify the expression [tex]\sqrt{2} + \sqrt{6}[/tex], we need to try to express both [tex]\sqrt{2}[/tex] and [tex]\sqrt{6}[/tex] in a way that allows us to combine them.
One way to do this is to rewrite [tex]\sqrt{6}[/tex] as [tex]\sqrt{2 * 3}[/tex] = [tex]\sqrt{2} \sqrt{3}[/tex] .Substituting this into the original expression, we get:
[tex]\sqrt{2} + \sqrt{2} * \sqrt{3}[/tex]
We can simplify this by using the fact that
[tex]\sqrt{a}\sqrt{b} = \sqrt{a * b}[/tex].
[tex]\sqrt{2} \sqrt{3} = \sqrt{2 * 3}[/tex]=[tex]\sqrt{6}[/tex].
Substituting this back into the original expression, we get:
[tex]\sqrt{2} + \sqrt{6} = \sqrt{2} + \sqrt{6}[/tex]
Thus, Option (D) None of the above,
Please help I can’t figure it out
well, let's first off find out how many actually do favor it in the first place.
[tex]\stackrel{total}{4000}\cdot \cfrac{3}{8}\implies \stackrel{seniors}{\text{\LARGE 1500}}\hspace{12em}\stackrel{total}{4000}-1500=\stackrel{not~seniors}{\text{\LARGE 2500}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{seniors}{\text{\LARGE 1500}}\cdot \cfrac{1}{6}\implies \stackrel{in~favor}{\text{\LARGE 250}}\hspace{11em} \stackrel{not~seniors}{\text{\LARGE 2500}}\cdot \cfrac{3}{5}\implies \stackrel{in~favor}{\text{\LARGE 1500}} \\\\[-0.35em] ~\dotfill\\\\ 250+1500\implies \stackrel{in~favor}{\text{\LARGE 1750}}\hspace{15em}\boxed{\underset{\textit{do not favor it}}{\stackrel{4000~~ - ~~1750}{\text{\LARGE 2250}}}}[/tex]
Solution to this image attached below please
Answer:
I need to see the picture a little more please
1:What is the name of the shape to the left?
2:Draw a net of the figure to the left
On solving the provided question we can say that - Pythagorean Theorem triangle [tex]5^2+x^2=10^2 = > x²=100−25=75[/tex]x=√75=√3×25=5√3
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
On solving the provided question, we can say that the value of x = 5√3
values of x and y
Pythagorean theorem,
The trigonometric ratio: soh-cah-toa, and
According to the given question:
Using the table of trig values, we find that
sin30°=1/2
So, this gives us:
[tex]1/2 = sin 30° = 5/y\\1/2 = 5/y\\(1xy)/2 = 5\\y= 2×5 =10\\[/tex]
Pythagorean Theorem
[tex]5²+x²=10²\\x²=100−25=75\\[/tex]
x=√75=√3×25=5√3
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A sample of 100 items is taken from a process that has been adjusted after it was found that its mean had shifted. The sample mean is 65. The sample standard deviation is 10. Which of the following is a 90 percent confidence interval.
62 to 68
59 to 69
63 to 67
65 to 67
A 90 percent confidence interval estimate for the mean of the sample is 63 to 67.
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x (SD / √n)
where CI = confidence interval
μ = sample mean
z = found by using a z-score table
SD = sample standard deviation
n = sample size
At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.647
Plug in the values and solve for the confidence interval.
CI = μ ± z x (SD / √n)
CI = 65 ± 1.96 x (10 / √100)
CI = 65 ± 1.96
CI = [63.04, 66.96]
CI ≅ 63 to 67
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Question 1 Part A: (4 Points): A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, and n days.
Complete the inequality below by dragging and dropping the answers on the left into the given boxes
Answer:
0 ≤ n ≤ 5
Step-by-step explanation:
We have the function for growth as
[tex]g(n) = 10(1.02)^n[/tex]
We also know that after a specific n days, the flower has grown to 11.04 inches
Since g(n) represents the height of the flower, we can substitute 11.04 for g(n) and solve for n
∴We get
[tex]11.04 = 10(1.02)^n[/tex]
Switching sides we get
[tex]10(1.02)^n = 11.04[/tex]
Divide both sides by 10 to get
[tex]1.02^n = 1.104[/tex]
Take log on both sides
[tex]\log(1.02^n) = \log(1.104)[/tex]
[tex]\log(x^a) = a \log(x)[/tex]
So
[tex]\log(1.02^n) = n \log(1.02)[/tex]
Therefore
[tex]n \log(1.02) = \log(1.104)[/tex]
[tex]n = \dfrac{\log(1.104)}{\log(1.02)}[/tex]
Using a calculator this works out to
[tex]n = 4.9963[/tex]
Therefore it takes at least these many days for the flower to reach 11.04 inches
Rounding number of days to 5, we get the right side of the inequality as n ≤ 5
n cannot be negative so it starts of with a value of 0 so on the right side of the inequality we get n ≥ 0 which can be rewritten as 0 ≤ n
Together the domain of n can be represented as
0 ≤ n ≤ 5
Hope that helps
24. Consumer Price Index The consumer price index for food
and beverages in 2003 was 184.0 after a hefty 2.3% increase from
the previous year. What was the consumer price index for food
and beverages in 2002? (Source: U.S. Bureau of Labor Statistics)
d 57 miles per hour on a 182-mile
Answer: parisslasheaa_ on IG
(5/8 - 1/2) x 5/6 =
Final answer in the form a/b
Answer:
5/48
Step-by-step explanation:
(5/8 - 1/2) x 5/6
(5/8 - 4/8) x 5/6
1/8 x 5/6
5/48
Answer:
[tex]\dfrac{5}{48}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{5}{8} - \dfrac{1}{2}\right) \times \dfrac{5}{6}[/tex]
First, represent 1/2 as 4/8.
[tex]\dfrac{1}{2} \times \dfrac{4}{4} = \dfrac{4}{8}[/tex]
[tex]\left(\dfrac{5}{8} - \dfrac{4}{8}\right) \times \dfrac{5}{6}[/tex]
Then, simplify the subtraction.
[tex]\dfrac{1}{8} \times \dfrac{5}{6}[/tex]
Finally, multiply the numerators and denominators of the resulting fractions.
[tex]\dfrac{1 \times 5}{8 \times 6}[/tex]
[tex]\dfrac{5}{48}[/tex]
1.
(03.03 MC)
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answer:
sept one
Step-by-step explanation:
please help algebra homework help asap now
Step-by-step explanation:
(any GlRL WANT TO TALK???any gi_rl want to have f
Which quantitly is greater than 3 meters A 9ft B 120in C 3.2yd D 0.002km
The quantity that is greater than 3 meters is 120 inches. Option B
What is the conversion factor?
We know that the conversion factor has to do with the manner in which we can be able to convert one value to the other. In this case, we have the fact that the central length that we are considering has been given in the unit of meters.
Now;
We know that;
39.37 inches = 1 meter
120 inches would now be given as;
120 inches * 1 meter/ 39.37 inches
= 3.05 meters
Thus, 120 inches would have more value in meters than 3 meters.
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Please do both
You're supposed to decide if the information that's marked in addition to any other information you can determine from the picture is enough to prove the triangles congruent with the pattern listed in the problem. If yes, just write yes. If not, state the additional information that would need to be marked to make them congruent using the given pattern. (By a pattern I mean, SSS or ASA or SAS etc. listed in the problem)
Yes, the two problems are congruent by the given information
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
ΔIJH≅ΔKHJ
The three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Yes the two triangles are congruent because both triangles sides are congruent.
Now ΔTNS≅ΔUHS
the hypotenuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.
Yes the triangles congruent with the pattern listed in the problem
Hence, Yes the two problems are congruent by the given information
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