Let R be the region in the first quadrant bounded by the graph of y = 2 \sqrt x, the horizontal line y = 6, and the y-axis, as shown in the figure.
a) Find the area of R.
b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y = 7.
c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the y-axis.

Tyler's age when he was inaugurated is given as follows:

50.3 years old.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 54.6, \sigma = 6.3[/tex]

The z-score associated with the 25th percentile is given as follows:

Z = -0.675.

Hence Tyler's age is obtained as follows:

-0.675 = (X - 54.6)/6.3

X - 54.6 = -0.675 x 6.3

X = 50.3.

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4to9, 4:9, and 4\9 are all different ways to  the same ratio of 4 to 9. Ratios are a fundamental concept in mathematics, and they are used in various fields such as finance, physics, and engineering.

"Reio" is not a known mathematical term or concept. However, the three expressions you provided, 4to9, 4:9, and 4\9, represent different ways to write a ratio.

A ratio is a mathematical comparison of two or more quantities, often written in the form of a fraction or with a colon. It is used to describe the relationship between the quantities being compared.

The expression 4to9, also written as 4:9, represents a ratio of 4 to 9. This means that there are 4 units of one quantity for every 9 units of another quantity. The ratio can be simplified by dividing both the numerator and denominator by their greatest common factor, if any.

The expression 4/9, written with a forward slash, represents the same ratio as 4 to 9. This is because a ratio can be expressed as a fraction, where the numerator represents one quantity and the denominator represents the other quantity.4to9, 4:9, and 4\9 are all different ways to write the same ratio of 4 to 9. Ratios are a fundamental concept in mathematics, and they are used in various fields such as finance, physics, and engineering.

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According to the description, element a21 will represent B. 100.

According to the question, the rows represent the type of music while the columns represent the weeks. Now the element that we have is a21. The 2 in the element stands for the rows which is the type of music and this is R and B.

The column is the weeks and since we have the column as 1, we will look at week 1 and the second bar in that week which is R and B. So, the correct description is option B.

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If the number of research papers in Dr. Carey's area of expertise is increasing by 3% every year and 34,176 research papers were published this year, then approximately 35,168 research papers will be published two years from now.

To calculate the number of research papers that will be published two years from now, we need to apply the 3% annual increase for two consecutive years to the initial count of 34,176 papers.

First, we calculate the increase for the first year:

Increase = 34,176 * 3% = 34,176 * 0.03 = 1,025.28 (approximately)

Next, we add this increase to the initial count to get the count after one year:

Count after one year = 34,176 + 1,025.28 = 35,201.28 (approximately)

Now, we calculate the increase for the second year based on the count after one year:

Increase = 35,201.28 * 3% = 35,201.28 * 0.03 = 1,056.04 (approximately)

Finally, we add this increase to the count after one year to get the count after two years:

Count after two years = 35,201.28 + 1,056.04 = 36,257.32 (approximately)

Therefore, approximately 36,257 research papers will be published two years from now.

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Therefore, the projectile goes approximately 6.9 × 10^6 meters or 6,900 kilometers high.

Let's first convert the initial speed from km/hr to m/s to be consistent with the unit of acceleration due to gravity.

1.30×10^4 km/hr = (1.30×10^4 × 1000 m/km) / (3600 s/hr) = 3611.11 m/s

We can use the kinematic equation: Δy = v0t + 1/2at^2 to determine the maximum height reached by the projectile. At the highest point, the velocity is zero, so we can use the fact that v = v0 + at = 0 to find the time it takes to reach the maximum height.

v0 = 3611.11 m/s (initial velocity)

a = -9.81 m/s^2 (acceleration due to gravity)

t = -v0/a = -3611.11/(-9.81) = 367.97 s (time to reach maximum height)

Now we can use the time to find the maximum height reached:

Δy = v0t + 1/2at^2 = 3611.11 × 367.97 + 1/2 × (-9.81) × (367.97)^2 ≈ 6.9 × 10^6 meters

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Using the tangent of the angle from trigonometric ratio, the value of x is 4.0

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

sin θ = opposite / hypothenuse

cos θ = adjacent / hypothenuse

tan θ = opposite / adjacent

To solve this problem, we can use the tangent of the angle.

tan θ = opposite / adjacent

tan 20 = x / 11

Cross multiply both sides;

x = 11 tan 20

x = 4.0

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The correlation between average 2007 price and number of 2007 is 0.207

To compute the correlation between the average 2007 price and the number of 2007 wins for the 16 National League baseball teams, we can use the formula for Pearson's correlation coefficient.

First, we need to calculate the following sums:

Sum of prices (ΣX) = 19.68 + 17.07 + 34.30 + 17.90 + 14.72 + 16.70 + 26.66 + 20.09 + 18.11 + 25.28 + 26.73 + 17.08 + 20.83 + 24.53 + 29.78 + 20.88 = 387.47

Sum of wins (ΣY) = 90 + 84 + 85 + 72 + 90 + 71 + 73 + 82 + 83 + 88 + 89 + 68 + 89 + 71 + 78 + 73 = 1296

Sum of products of prices and wins (ΣXY) = (19.68 * 90) + (17.07 * 84) + (34.30 * 85) + (17.90 * 72) + (14.72 * 90) + (16.70 * 71) + (26.66 * 73) + (20.09 * 82) + (18.11 * 83) + (25.28 * 88) + (26.73 * 89) + (17.08 * 68) + (20.83 * 89) + (24.53 * 71) + (29.78 * 78) + (20.88 * 73) = 24839.87

Sum of squared prices (ΣX^2) = (19.68)^2 + (17.07)^2 + (34.30)^2 + (17.90)^2 + (14.72)^2 + (16.70)^2 + (26.66)^2 + (20.09)^2 + (18.11)^2 + (25.28)^2 + (26.73)^2 + (17.08)^2 + (20.83)^2 + (24.53)^2 + (29.78)^2 + (20.88)^2 = 19151.7899

Sum of squared wins (ΣY^2) = (90)^2 + (84)^2 + (85)^2 + (72)^2 + (90)^2 + (71)^2 + (73)^2 + (82)^2 + (83)^2 + (88)^2 + (89)^2 + (68)^2 + (89)^2 + (71)^2 + (78)^2 + (73)^2 = 94518

Using these sums, we can calculate the correlation coefficient (r):

r = (n * ΣXY - ΣX * ΣY) / sqrt((n * ΣX^2 - (ΣX)^2) * (n * ΣY^2 - (ΣY)^2))

where n is the number of data points, which in this case is 16.

Substituting the values:

r = (16 * 24839.87 - 387.47 * 1296) / sqrt((16 * 19151.7899 - (387.47)^2) * (16 * 94518 - (1296)^2))

Calculating this expression gives us:

r ≈ 0.207

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Answer:

A: area of one additional plan exceeds 624 square feet ...... it does not

Step-by-step explanation:

let's lay out the six additional plans:

plan                         width                  length                  area

6                                26                       24                          624

7                                 28                      22                           616

8                                30                       20                           600

9                                32                       18                             576

10                              34                         16                            544

11                                36                       14                             504

A: one additional plan (plan 6) does not exceed 624. so this incorrect

B: one of the plans (plan 11) is less than 544. this is correct.

C: area of plan 6 = area of plan 5. this is correct.

D: Plan 7 area (616) is less than area of plan 6 (624). this is correct.

So, A is incorrect

In the item procurement importance matrix, the item described as low risk, low value is referred to as a non-critical item.

The item procurement importance matrix is a tool used in procurement management to categorize items based on their importance and risk. It helps in determining the appropriate procurement strategies and allocation of resources. The matrix typically categorizes items into four quadrants based on their value and risk levels: critical, strategic, non-critical, and bottleneck.

A non-critical item is characterized by low risk and low value. These items are generally of lesser importance in terms of their impact on the overall procurement process. They may include non-essential or low-cost items that are easily replaceable or have minimal consequences if they experience delays or disruptions in the supply chain.

Therefore, in the item procurement importance matrix, the item described as low risk, low value is categorized as a non-critical item.

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The minor arc is QS and the measure of the arc is 98°

An arc is a smooth curve joining two endpoints. It can also be defined as the portion of a circumference of a circle. The circumference of a circle will be divided into minor arc and major arc.

The major arc is the arc that bounds the big sector and the minor arc is the arc that bounds the small sector.

A sector is an area bounded radii and an arc

Therefore the minor arc is arc SQ and the measure of the arc is also 98°. This is because the angle substended by the arc is equal to the measure of the arc.

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To test these hypotheses, appropriate statistical methods such as a t-test or z-test can be employed, depending on the sample size and whether the population standard deviation is known

In this scenario, the appropriate null and alternative hypotheses can be formulated based on the objective of the hypothesis test. Let's consider the mean running time of the flashlight battery as the parameter of interest.

Null Hypothesis (H0): The mean running time of the flashlight battery is equal to 8 hours.

Alternative Hypothesis (Ha): The mean running time of the flashlight battery has changed, either increased or decreased, as a result of the production method change.

Symbolically, the hypotheses can be represented as:

H0: μ = 8 (mean running time is equal to 8 hours)

Ha: μ ≠ 8 (mean running time is not equal to 8 hours)

Here, μ represents the population mean running time of the flashlight battery. The null hypothesis assumes that the mean running time remains unchanged at 8 hours, while the alternative hypothesis allows for any deviation from this value.

. These tests would help analyze the sample data and provide evidence to either accept or reject the null hypothesis in favor of the alternative hypothesis.

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in the past, the mean running time for a certain type of flashlight battery has been 8 hours. the manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. what are the appropriate null and alternate hypotheses?

If those two given angles combined = 180, then u and v are parallel.

(91 + x) + 95 = 180

186 + x = 180

x = 180-186

x = -6

When x = -6, lines u and v are parallel.

Therefore, the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is 11/15, or about 0.733.

We can approach this problem by finding the probability of Sergio's number being less than or equal to the sum of Tina's numbers, and then subtracting this probability from 1.

The total number of ways for Tina to select two distinct numbers from the set is 6 choose 2, which is 15. Each pair of numbers has an equal chance of being selected, so we can assume that each pair has probability 1/15 of being selected.

Now, for each pair of numbers Tina selects, there is a range of numbers that Sergio can select such that his number is greater than the sum of Tina's numbers. Specifically, Sergio's number must be greater than the smaller of Tina's numbers and less than or equal to the largest number in the set.The length of this shaded region is 6 - 2 = 4. Therefore, the probability of Sergio's number being greater than the sum of Tina's numbers for a given pair of numbers is 4/6 = 2/3.

The probability of Tina selecting any particular pair of numbers is 1/15, so the probability of Sergio's number being greater than the sum of Tina's numbers for that pair is (2/3)(1/15) = 2/45.

To find the total probability, we sum up the probabilities for all pairs of numbers:

(2/45) + (2/45) + (2/45) + (2/45) + (2/45) + (2/45) = 12/45 = 4/15

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Answer:

If the hummingbird is filmed at 140 frames in one second, and the film is played at 10 frames per second, then the film would play for 14 seconds.

Step-by-step explanation:

Using dimensional analysis:

140 frames / (10 frames /sec)  =  14 seconds

The value of b in Rhombus UVWX is 86 degrees.

In a rhombus, opposite angles are congruent, so we have:

Angle W = Angle U = 90 degrees (since UVWX is a rhombus)

Angle V = Angle X (opposite angles are congruent)

Using the fact that the sum of the angles in a quadrilateral is 360 degrees, we can write an equation in terms of b:

Angle U + Angle V + Angle W + Angle X = 360 degrees

Substituting the known values, we get:

90 + Angle V + 90 + Angle X = 360

Simplifying, we get:

Angle V + Angle X = 180

Substituting Angle V = 2b - 62 and Angle X = b - 16, we get:

2b - 62 + b - 16 = 180

Simplifying, we get:

3b - 78 = 180

Adding 78 to both sides, we get:

3b = 258

Dividing by 3, we get:

b = 86

Therefore, the value of b in rhombus UVWX is 86 degrees.

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a) The probability that a patient testing positive for HIV with this test is infected with it is approximately 73.96%

b) With this test, there is a 26.04% chance that a patient who tests positive for HIV is not actually infected.

c) The probability that a patient testing negative for HIV with this test is infected with it is approximately 0.18%.

d) The probability that a patient testing negative for HIV with this test is not infected with it is approximately 99.82%.

Gonna determine how likely something is gonna occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

Let's denote the events as follows:

A = Patient is infected with HIV

B = Patient tests positive for HIV

Given information:

P(A) = 0.08 (probability of a patient being infected with HIV)

P(B|A) = 0.98 (probability of testing positive given the patient is infected with HIV)

P(B|A') = 0.03 (probability of testing positive given the patient is not infected with HIV)

We need to find:

a) P(A|B) = Probability that a patient testing positive for HIV is infected with it.

b) P(A'|B) = Probability that a patient testing positive for HIV is not infected with it.

c) P(A|B') = Probability that a patient testing negative for HIV is infected with it.

d) P(A'|B') = Probability that a patient testing negative for HIV is not infected with it.

We can use Bayes' theorem to find these probabilities:

a) P(A|B)=P(B|A)*P(A)/P(B)

b) P(A'|B)=P(B|A')*P(A')/P(B)

c) P(A|B') = P(B'|A) * P(A) / P(B')

d) P(A'|B') = P(B'|A') * P(A') / P(B')

To find P(B), we can use the law of total probability:

P(B)=P(B|A)*P(A)+P(B|A')*P(A')

First, let's calculate P(B):

P(B)=P(B|A)*P(A)+P(B|A')*P(A')

     = 0.98 * 0.08 + 0.03 * (1 - 0.08)

     = 0.0784 + 0.0276

     = 0.106

Now, we can calculate the probabilities:

a) P(A|B)=P(B|A)*P(A)/P(B)

          = 0.98 * 0.08 / 0.106

          = 0.0784 / 0.106

          ≈ 0.7396 (or 73.96%)

b) P(A'|B)=P(B|A')*P(A')/P(B)

           = 0.03 * (1 - 0.08) / 0.106

           = 0.0276 / 0.106

           ≈ 0.2604 (or 26.04%)

c) P(A|B') = P(B'|A) * P(A) / P(B')

          = (1 - P(B|A)) * P(A) / (1 - P(B))

          = (1 - 0.98) * 0.08 / (1 - 0.106)

          = 0.02 * 0.08 / 0.894

          ≈ 0.0018 (or 0.18%)

d) P(A'|B') = P(B'|A') * P(A') / P(B')

           = (1 - P(B|A')) * (1 - P(A)) / (1 - P(B))

           = (1 - 0.03) * (1 - 0.08) / (1 - 0.106)

           = 0.97 * 0.92 / 0.894

           ≈ 0.9982 (or 99.82%)

Therefore:

a) The probability that a patient testing positive for HIV with this test is infected with it is approximately 73.96%

b) The probability that a patient testing positive for HIV with this test is not infected with it is approximately 26.04%.

c) The probability that a patient testing negative for HIV with this test is infected with it is approximately 0.18%.

d) The probability that a patient testing negative for HIV with this test is not infected with it is approximately 99.82%.

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A graph of the system of inequalities is shown on the set of axes below

No, (6, 3) is not a solution to the system of inequalities.

In order to graphically determine the solution for this system of linear inequalities on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear inequalities while taking note of the point of intersection;

y ≤ -3x/4 + 5            ......equation 1.

3x - 2y > 4       ......equation 2.

Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them, which is represented by this ordered pair (3, 2).

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Answer: Credit cards

Step-by-step explanation:

(you can search it up as well)

The distance between two points a and b on the real line is given by the absolute difference between the two points, which is calculated as the positive difference between the values of a and b regardless of their order.

The distance function, denoted as d(a, b), is a metric that satisfies the properties of non-negativity, symmetry, and the triangle inequality. It is used to quantify the distance between two points in one-dimensional space, and is an important concept in geometry, analysis, and other fields of mathematics. The distance formula can be extended to higher dimensions and is used in various applications such as optimization, clustering, and machine learning.

The distance between two points a and b on the real line is given by the absolute difference between the two points: d(a, b) = |a - b|

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There is no meaningful difference in the weights of the two types of rings

From the question, we have the following parameters that can be used in our computation:

Platinum = 8.21 grams

Gold = 8.61 grams

The difference in these weights is

Difference = 8.61 grams - 8.21 grams

Evaluate the difference

Difference = 0.4 grams

This value approximates to 0

This means that there is no meaningful difference in the weights

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The data in the table represent a direct variation

The equation is y = 5x

From the question, we have the following parameters that can be used in our computation:

x  1 3 4 7

y 5 15 20 35

In the above table of values, we can see that

As the x values, the y values increase

This means that the table of values represent a direct variation

The equation is a direct variation

So, we have

y = kx

The value of k is calculated as

k = 5/1

So, we have

k = 5

This means that

y = 5x

Hence, the equation is y = 5x

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The parallel vectors to CD are:

Here we have the vector:

CD = 4a - 3b

Where a and b are vectors.

A vector V will be parallel to CD if we can find a scalar number k such that we can write the vector as:

V = k*CD

The second option:

V = 20a - 15b

We can rewrite this as:

V = 20a - 15b = 5*(4a - 3b)   this vector is parallel.

The third one is:

V'  =10a - 20b + 2a + 11b

V' = 12a - 9b = 3*(4a - 3b)  this vector is parallel.

V'' = (-8a + 6b) = -2*(4a - 3b)  this vector is parallel.

V''' = a - (3/4)b = (1/4)*(4a - 3b)  this vector is parallel.

These are all the parallel vectors.

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Mean for start of school year is 6.5; Mean for end of school year is 7.2.

Median for start of school year is 6.5; Median for end of school year is 7.

To find the means, list out each data value given for each dot plot and calculated the mean.

Mean for start of school year:

We have, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9

Mean = ( 4 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 9)/14

= 91/14

Mean ≈ 6.5

Mean for end of school year:

We have, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9

Mean = ( 5 + 5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 9 + 9 + 9)/14

= 101/14

Mean ≈ 7.2

Median represents the middle data value in a data set, therefore:

Median for start of school year = ( 6 + 7)/2 = 6.5

Median for end of school year = ( 7 + 7)/2 = 7

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Answer:

$0.96

Step-by-step explanation:

ok so 30.72 divided by 2 is 15.36. So 1 gallon is $15.36.

there are 16 cups in a gallon.

So there are 32 cups.

$15.36 dollars in gallons converted to that of 16 cups, or $30.72 dollars in gallons to 32 cups..

30.72 divided by 32 is 0.96. 15.36 divided by 16 is 0.96.

So, $0.96 is the price per cup

The vertex of the function f(x)=(x-3)²-2 is (3, -2).

13) The given function is f(x)=x²+1.

Rewrite in vertex form and use this form to find the vertex (h, k).

(0, 1)

14) The given function is f(x)=(x-3)²-2.

Rewrite in vertex form and use this form to find the vertex (h, k).

(3, -2)

15) The given functions are f(x)=x² and f(x)= -1/2 x²

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: Reflected

Reflection about the y-axis: None

Vertical Compression or Stretch: Compressed

16) The given functions are f(x)=x² and f(x)= x²-1

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: None

Vertical Shift: Down 1 Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

Therefore, the vertex of the function f(x)=(x-3)²-2 is (3, -2).

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The requried measures of DEF and x are 82° and 90° respectively.

In a quadrilateral, the sum of the opposite angle is 180°,
So,
98 + y = 180
y = 180 - 98
y =  82°

Similarly,
x + x = 180
2x = 90
x = 90°

Thus, the requried measures of DEF and x are 82° and 90° respectively.

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Step-by-step explanation:

Depends on how you read it :

x = the number

1/2 x -2 = 4

x = 12             <==== I suspect this is the answer wanted

or  

1/2 ( x-2)  = 4

x = 10  

The probability of taking 2 different types of sandwiches is 0.691

From the question, we have the following parameters that can be used in our computation:

The total number of sandwiches is

4 + 5 + 2 = 11

So, the probability of taking the same types of sandwiches is

P(Same) = (4/11 * 3/10) + (5/11 * 4/10) + (2/11 * 1/10)

This means that the probability of taking 2 different types of sandwiches is

P(Different) = 1 - [(4/11 * 3/10) + (5/11 * 4/10) + (2/11 * 1/10)]

Evaluate

P(Different) = 0.691

Hence, the probability is 0.691

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The number of tickets were sold are; 150 for adult tickets and 250 for child tickets

There are 400 seats in the auditorium which means that there are 400 tickets to be sold and the total ticket sales were 2600 dollars.

Since there were adult tickets for 9 each and child tickets for 5 dollars each.

9x + 5y = 2600

x + y = 400

Solving;

9x + 5(400-x) = 2600

9x + 2000 - 5x = 2600

4x = 600

x = 150

Then y = 250

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