We know that RS is parallel to PQ by comparing RS and PQ and both vector have the same value and hence prove to be parallel.
We know that R, S, Q and P are midpoints of OC, CB, BA and OA, and we are given that OR = a, CS = b and OP = c
we have to prove that RS is parallel to PQ,
therefore we need to find, PQ = PA + AQ,
= c - c + a + b = a + b,
since we get that PA = OP = c
therefore when we compare RS and PQ ,we get,
RS = PQ = a + b
now that it is clear that both the vectors are same and have the same value we can conclude that they are parallel.
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If area of a rectangle is 20m^10n^4 and the length is 5m^3n what is the width
The width of the rectangle is 4*m⁷*n³
How to find the width of the rectangle?Remember that for a rectangle of length L and width W the area is given by the formula:
A = W*L
Here we know that:
A = 20*m¹⁰*n⁴
L = 5*m³*n
Then we can write:
20*m¹⁰*n⁴ = (5*m³*n)*W
Now we can solve that for W.
(20/5)*(m¹⁰/m³)*(n⁴/n) = W
4*m¹⁰⁻³*n⁴⁻¹ = W
4*m⁷*n³ = W
That is the width.
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-2x + 8
what the
is this
Answer: linear function y=-2x+8, x-intercept at x=4, y-int at (0,8)
Step-by-step explanation:
if it is set equal to y, it is a linear function y=-2x+8, and if set equal to zero, it is an x-intercept to be solved. If an x-intercept is x=4 as you get x by itself by moving the eight over by subtracting and then dividing by negative 2.
(hope it helps as I am not sure what you are asking)
it is -2 multiplied by a number of x, plus 8
Answer:
This is an algebraic expression.
Step-by-step explanation:
This is an algebraic expression. It represents a linear function in which the variable "x" is multiplied by -2 and then 8 is added to the result. In mathematical terms, it represents a straight line with a slope of -2 and a y-intercept of 8. If we were to plot this expression on a graph, the line would have a negative slope and would cross the y-axis at the point (0, 8). The expression can be used to model a relationship between two variables, such as the relationship between time and distance, or between temperature and pressure, for example.
if 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that
The probability that the dictionary is selected is 0.417, 3 novels and 2 books of poems are selected is 0.707. The probability that 4 novels are selected is 0.354.
The probability that the dictionary is selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select the dictionary and 4 other books.
The total number of ways to select 5 books from the shelf is:
C(12,5) = 12! / (5! * 7!) = 792
The number of ways to select the dictionary and 4 other books is:
C(1,1) * C(11,4) = 11! / (4! * 7!) = 330
Therefore, the probability that the dictionary is selected is:
P(dictionary) = 330/792 = 0.417
The probability that 3 novels and 2 books of poems are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 3 novels and 2 books of poems.
The total number of ways to select 5 books from the shelf is:
C(12,5) = 12! / (5! * 7!) = 792
The number of ways to select 3 novels and 2 books of poems is:
C(8,3) * C(3,2) = (8! / (3! * 5!)) * (3! / (2! * 1!)) = 560
Therefore, the probability that 3 novels and 2 books of poems are selected is:
P(3 novels, 2 books of poems) = 560/792 = 0.707
The probability that 4 novels are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 4 novels and 1 other book.
The total number of ways to select 5 books from the shelf is:
C(12,5) = 12! / (5! * 7!) = 792
The number of ways to select 4 novels and 1 other book is:
C(8,4) * C(4,1) = (8! / (4! * 4!)) * (4! / (1! * 3!)) = 280
Therefore, the probability that 4 novels are selected is:
P(4 novels) = 280/792 = 0.354
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_____ The given question is incomplete, the complete question is given below:
If 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that a. the dictionary is selected? b. 3 novels and 2 books of poems are selected? c. 4 novels are selected?
Use the substitution method to solve the system of linear equations.
y = x - 4
4x + y = 26
Answer:
y = 2 and x = 6
Step-by-step explanation:
Let y = x - 4 be equation a
Let 4x + y = 26 be equation b
Substitute a into b:
4x + (x-4) = 26
5x - 4 = 26
5x = 30
x = 6
Substitute the value of x into a:
y = x - 4
y = 6 - 4
y = 2
CHECK:
4x + y = 26
4*6 + 2 = 26
24 + 2 = 26
26 = 26
LHS = RHS
Therefore, y = 2 and x = 6
Can you please answer the question???
The volume of given triangular prism is 24,000 cubic yards.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, the dimensions of base are 30 yards and 20 yards.
Here, area = 1/2×30×20
= 300 yd²
Volume of a triangular prism = Area of base triangle × Length of the prism.
= 300×80
= 24,000 yd³
Therefore, the volume is 24,000 yd³.
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Find the volume of a rectangular prism with the following dimensions: V = lwh Length:
4m Width
: 0.3 m Height
: 1.5 m
Answer:
1.8 m³
Step-by-step explanation:
You want the volume of the rectangular prism with dimensions L=4 m, W = 0.3m, H = 1.5 m.
VolumeThe volume formula is given in the problem statement:
V = LWH
Substituting the given values of L, W, H, we find the volume to be ...
V = (4 m)(0.3 m)(1.5 m)
V = 1.8 m³
The volume of the rectangular prism is 1.8 cubic meters.
Parallelogram CDEF is shown below.
Find the length of the segments and the measure of the angles: CF, FE, ∠D, and ∠
Length of the segments are 11 units and 10 units and measures of the angles are 54° and 126°.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Since, CDEF is a parallelogram, opposite angles are equal.
(9y)° = (7y + 28)°
9y - 7y = 28
2y = 28
y = 14
∠C = ∠E = 9y = 126°
Sum of the angles of a quadrilateral is 360°.
∠D = ∠F = (360° - (126°×2)) / 2 = 54°
Opposite sides are also equal for a parallelogram.
2x = x + 5
2x - x = 5
x = 5
CF = DE = 2x = 10 units
CD = FE = 3x - 4 = 11 units
Hence opposite sides are equal with lengths 10 units and 11 units and opposite angles are equal with measures 54° and 126°.
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8 in x 3 in x 2 in. of 8 inches x 10 inches
Answer: imma say do 8x3x2= the answer you get then 8x10= the answer you get then multiply the two answer you get that should be you answer.
Step-by-step explanation: hope this helps
jack's favorite number is 836. jill subtracts a secret number from 836 and her answer is the smallest possible combination of all the digits from jack's favorite number. what is the secret number?
The secret number is 564 as we solve it by given question.
jack's favorite number is 836 so here we have number 836 and
jill subtracts a secret number from 836 and her answer is the smallest possible combination of all the digits from jack's favorite number
so here we have a number 836
let we subtract x from 836 to get a number which is smallest number by using 836
the number which we can make by using these 3 degits are
368, 386, 638, 683, 836, 863 anf from all these numbers the smallest number which can be using 836 is 368
as given in question we have 836 and we will subtract x and get 368 so
836 - x = 368
x = 836 - 368
x = 564
the secrets number is 564.
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When the data is asymmetrical, you use _ (IQR/SD) to measure the spread.
Fοr distributions with a nοrmal shape or symmetry, the mean and standard deviation are emplοyed; for asymmetrical distributiοns, the median and interquartile range are used.
Do you calculate spread using IQR or standard deviation?Because it is unaffected by οutliers, the IQR is frequently regarded as a mοre accurate measure of spread than the range. The variance and standard deviatiοn are indicators of hοw widely the data are dispersed from the mean. Each οbserved data value's prοximity to the mean is summarised.
Why are skewed data sets used for IQR?The strοngest indicator of variability in data sets with οutliers or skewed distributions is the interquartile range. It's unlikely to be impacted by οutliers because it's based οn numbers that come frοm the centre half of the distribution.
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let |q|=5 at angle at 45° and |r|=16 at an angle of 300°. what is |q-r|?
Answer:
18.0
Step-by-step explanation:
this is correct!
how many ways can baseball players and basketball players be selected from baseball players and basketball players?
There are many ways that baseball players and basketball players can be selected from a group of athletes who play both sports.
One way is to use a selection process that allows for both players to be chosen based on their individual merits. For example, a team could use a combination of criteria such as previous performance, physical fitness, athleticism, and skill level to select the most suitable players for each sport. This could be done by assigning each player a score based on these criteria and then selecting the highest scoring players for each position.Another way to select players from a group of athletes playing both sports is to use a draft system. This system would allow teams to choose players based on the team's needs, rather than individual merits. This could be done by assigning each player an overall ranking and then allowing teams to select players in order of their ranking. A third way to select players from a group of athletes playing both sports is to have a tryout or combine where players can showcase their skills and abilities. This allows teams to evaluate players in a more comprehensive way and make sure they are selecting the best players for their team. Finally, teams can also use a combination of the above methods to select players. For example, they could use a combination of a draft system, individual merit selection, and a tryout/combine to get a better idea of which players are the best fit for their team. Overall, there are many different ways that teams can select baseball players and basketball players from a group of athletes playing both sports. The method chosen will depend on the team's individual needs and preferences.
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How many different combinations of baseball players and basketball players can be selected from a group of baseball players and basketball players?
Given that P=1.80 and Q=2.91, find ghe relative error in the computation of 1/P-1/Q
Answer:
±1.007%
Step-by-step explanation:
You want the relative error in the computed value of 1/P -1/Q when P=1.80 and Q=2.91.
Maximum and minimumEach of P and Q is specified to the hundredths place, so the errors in each of P and Q will be half of a hundredth, or 0.005. The maximum value of P or Q will be 0.005 more than the given value, and the minimum will be 0.005 less.
The maximum and minimum of the computation will be had when P and Q are at their opposite extremes: one is a maximum when the other is a minimum.
Max difference = 1/1.795 -1/2.915 ≈ 0.21404
Min difference = 1/1.805 -1/2.905 ≈ 0.20978
Relative errorThe relative error in the computed value can be found a couple of ways. One is to compare the maximum and minimum computed values with the nominal computed value.
Here, we choose to compare half the difference in the computed values to the average of the computed values. That way, we can describe the error as symmetrical about that average;
((0.21404 -0.20978)/2) / ((0.21404 +0.20978)/2) = relative error
= (0.21404 -0.20978) / (0.21404 +0.20978) ≈ 0.01007
The relative error is about ±1.007%.
__
Additional comment
Another way to compute the error is by looking at the derivatives. The relative error found that way is ...
RE = -∆P(Q/P(Q -P)) +∆Q(P/Q(Q -P))
where ∆P and ∆Q are ±0.005.
The maximum relative error found this way is about ±1.00686% compared to the ±1.00685% computed above.
If you compare the possible error to the nominal value, it is not symmetrical: -1.00532% to 1.00841%.
Looking at the above expression for RE, you see that the multiplier of the relative error in P is Q/(Q-P), while the multiplier of the relative error in Q is P/(Q-P). That is, errors in P have a much larger effect than errors in Q.
Four children are playing a card game. The chart shows the number of cards each child has in his or her stack.
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Which is equivalent to Mike’s portion of the total number of cards?
A.) 2/25
B.) 16%
C.) 8/25
D.) 80%
(PLEASE EXPLAIN HOW YOU GOT THIS ANSWER)
The requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
From the given data,
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Total cards = 50
Now equivalent to Mike’s portion of the total number of cards is given as ,
= Mike cards/total card
= 8 / 50 × 100%
= 4/25×400%
= 16%
Thus, the requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
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Find the lengths of the diagonals of rectangle WXYZ.
WY = 24x-8
XZ = -18x+13
The length of each diagonal is ___ units.
In rectangle WXYZ, the length of each diagonal are 40.97 units and 39.98 units.
To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem.
The diagonal WX is the hypotenuse of right triangle WXY, so we have:
WX^2 = WY^2 + XY^2
Similarly, the diagonal YZ is the hypotenuse of right triangle XYZ, so we have:
YZ^2 = XY^2 + XZ^2
Substituting the given values for WY and XZ, and x = 2, we get:
WY = 24(2) - 8 = 40
XZ = -18(2) + 13 = -23
Plugging these values into the equations above and simplifying, we get:
WX^2 = 40^2 + XY^2
YZ^2 = XY^2 + (-23)^2
Since XY is a common side of both triangles, we can solve for it by setting the two expressions for XY^2 equal to each other:
40^2 + XY^2 = XY^2 + (-23)^2
Simplifying, we get:
40^2 + 23^2 = 2XY^2
XY^2 = (40^2 + 23^2) / 2 = 1039
Substituting this value for XY^2 in the equations for WX^2 and YZ^2, we get:
WX^2 = 40^2 + 1039 = 1679
YZ^2 = 1039 + (-23)^2 = 1598
Taking the square roots, we get:
WX = sqrt(1679) ≈ 40.97
YZ = sqrt(1598) ≈ 39.98
Therefore, the length of each diagonal of Rectangle are approximately 40.97 units and 39.98 units.
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_____The given question is incomplete, the complete question is given below:
Find the lengths of the diagonals of rectangle WXYZ.
WY = 24x-8
XZ = -18x+13
x= 2
The length of each diagonal is ___ units.
#10
USING STRUCTURE The shipping container is a rectangular prism. Write a
olume of the container. Express the answer in standard form.
(4x-3) ft
(x+1) ft
(x+2) ft
The volume is cubic feet.
4x³ + 9x² - x - 6 is a volume of the container.
What does volume mean in plain terms?
Any three-dimensional solid's volume is just the amount of space it takes up. These solids can have the shape of a cube, cuboid, cone, cylinder, or sphere.
The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units. A derived measure called the cubic meter (m3) serves as the SI unit of volume.
= (4x-3) . (x+1) . (x+2)
= [ 4x .x + 4x . 1 - 3x - 3] . ( x + 2)
= ( 4x² + 4x - 3x - 3 ) ( x + 2 )
= ( 4x² + x - 3 ) ( x+ 2 )
= 4x³ + x² - 3x + 8x² + 2x - 6
= 4x³ + 9x² - x - 6
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sara is making punch. she has 15 cups of sugar. each batch of punch needs 1.25 cups of sugar. how many batches of punch can sara make?
Answer: 12
she has 15 cups of sugar and needs 1.25 cup for a batch so we say 15/1.25 to get 12
Answer:
12
Step-by-step explanation:
15 / 1.25 = 12 she can make 12 batches
which expression is equivalent to 2(a-3)+4a
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The expression is given below.
⇒ 2(a -3) + 4a
Simplify the expression, then we have
⇒ 2(a -3) + 4a
⇒ 2a - 6 + 4a
⇒ 6a - 6
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
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The missing options are given below.
A. 6a - 6
B. 6a - 1
C. a - 6
D. None of the above
a researcher records the change in weight (gain or lost) during the first semester of college for each individual in a sample of 25 freshmen, and calculates the average change in weight. this average is an example of a . group of answer choices
The average change in weight calculated by the researcher for the sample of 25 freshmen is an example of a statistic.
A statistic is a numerical summary of a sample that is used to make inferences about a population. In this case, the sample is the 25 freshmen, and the population could be all freshmen entering college.
The average change in weight is a statistic because it summarizes the data collected from the sample, and is used to make conclusions about the population.
It represents the typical or average amount of weight gained or lost by the freshmen in the sample during their first semester in college.
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Transformation Question
Translate point (5, -6) based on vector V.
V:(-2,10)
The updated positions are (5, -6) + (-2, 10) = (3, 4)
Describe vector.A vector is a mathematical concept that has both magnitude and direction. The vector's size is determined by size. An arrow-depicted line serves as this representation. The vector's magnitude is represented by the line's length, and its direction is shown by the arrow. additionally referred to as geometric, Euclidean, spatial, or just "vectors."
You can add the components of the vector to the corresponding components of the point to translate point (5, -6) based on vector V:(-2,10).
The updated positions are (5, -6) + (-2, 10) = (3, 4)
Thus, the translated message is (3, 4).
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To estimate the percentage of a state's voters who support the current governor for reelection, three newspapers each survey a simple random sample of voters. Each paper calculates the percentage of voters in its sample who support the governor and uses that as an estimate for the population parameter. Here are the results:
Answer:
No OK so A. is the correct answer I think
similarity help for math please
The triangles that do not follow the similarity statement and therefore are not similar triangle are ACT and CAR
What is similar triangleSimilar triangles are triangles that have the same shape, but may have different sizes. Their corresponding angles are congruent, and the corresponding sides are proportional. In other words, if you were to enlarge or shrink one triangle uniformly, it would overlap exactly with the other triangle.
In this problem, we can find two triangles that are similar and that implies that they must be equal to one another.
In this case, we have
1. ART ≈ CAT
2. CAR ≈ CTA
Only ACT ≠ CAR
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four students, tamika, arianys, jin, and mohal, line up one behind the other. how many different ways can they stand in line?
There are 24 different ways they can stand in line.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.
There are four students, and each one can be in any one of the four positions in the line. Therefore, the total number of different ways they can stand in line is:
4 × 3 × 2 × 1 = 24
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5. Rajah 2 menunjukkan sebuah silinder dan sebuah kuboid. Diagram 2 shows a cylinder and a cuboid. Guna / Use = 271 30 cm Rajah 2/ Diagram 2 Diberi bahawa isi padu silinder dan kuboid adalah sama. Cari nilai x dan berikan jawapan anda betul kepada dua tempat perpuluhan. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Jawapan / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us
who can help me pls
Answer:
Step-by-step explanation:
5. Diagram 2 shows a cylinder and a cuboid. Diagram 2 shows a cylinder and a cuboid. Fold / Use = 271 30 cm Find the value of x and give the correct answer to the multiple of two places. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Answer / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us
what is the period of the function f(x) shown in the graph?
Answer:
8π
Step-by-step explanation:
The period of a function f(x) is the x-distance between two repeating points of the function
Looking at the function graph given we see that the function reaches a peak value(called amplitude) at x = -6π and then again reaches this value at x = 2π
So the x-distance is 2π - (-6π) = 2π + 6π = 8π
From 2π, the function reaches its maximum value again at 10π giving the period once again as 10π - 2π = 8π
what is the probability of getting a number less than 2 or a prime number upon rolling a six-sided die? a.) 1 half b.) 2 over 3 c.) 1 third d.) 5 over 6
Answer:
b) 2/3
Step-by-step explanation:
For a 6-sided die
total number of numbers: 6
numbers less than 2: 1
prime numbers: 2, 3, 5
total number of desired outcomes: 1 + 3 = 4
p(less than 2 or prime) = 4/6 = 2/3
a steel plate contains 20 bolts. assume that five bolts are not torqued to the proper limit. four bolts are selected at random, without replacement, to be checked for torque. (a) what is the probability that all four of the selected bolts are torqued to the proper limit?
The probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.
To calculate the probability that all four of the selected bolts are torqued to the proper limit, we need to find the number of combinations of 4 bolts out of 20 that have been torqued to the proper limit.
Let's call the number of proper bolts n = 20 - 5 = 15.
The number of combinations of 4 proper bolts out of 15 is given by the binomial coefficient nCk, where n is the number of bolts and k is the number of bolts selected.
nCk = n! / (k! (n - k)!).
So, the number of combinations of 4 proper bolts out of 15 is:
15C4 = 15! / (4! (15 - 4)!) = 15! / (4! 11!) = 1365.
Therefore, the probability of selecting all 4 proper bolts out of 20 is:
P = number of combinations of 4 proper bolts / number of combinations of 4 bolts = 1365 / 20C4 = 1365 / 4845 = 0.28
So, the probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.
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Use the Slope Formula to calculate the slope of a line with these two points. Find the slope of the line that passes through (5, 11) and (9, 2).
The percentage B(t) of women ages 25 and older in the United States who hold a bachelor's degree or higher t years after 1990 can be approximated by
B(t) = 0.48t + 18.
Using an inequality, determine those years for which more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher.
Please help!!
Answer:
he inequality to determine the years in which more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher is:
0.48t + 18 > 40
Subtracting 18 from both sides:
0.48t > 22
Dividing both sides by 0.48:
t > 45.83
So, for years t greater than 45.83, more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher.
Step-by-step explanation:
Two urns contain white balls and yellow balls. The first urn contains 5 white balls and 4 yellow balls and the second urn contains 3 white balls and 2 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
The probability that the both balls would be white when drawn at random from each urn would be = 1 7/45
How to calculate the probability that both balls are white?The number of colour that is found in two urns = 2( white and yellow).
The first urn contains the following:
5 white balls
4 yellow balls
The total number of balls = 9 balls.
The probability of getting a white ball = 5/9
The second urn contains the following:
3 white balls
2 yellow balls
The total number of balls = 5 balls
The probability of getting a white ball = 3/5
Therefore the probability that both balls are white;
= 5/9 + 3/5
= 25+27/45
= 52/45
= 1 7/45
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