Given the triangle below...
30°
B
79
A
What is the measure of angle B?

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

1257.6 g

Step-by-step explanation:

1 m = 100 cm

1.6 m = 1.6 * 100 cm = 160 cm

Use a proportion.

196.5/25 = x/160

25x = 196.5 * 160

25x = 31,440

x = 1,257.6

Answer: 1257.6 g

Answer:

The answer is "A mean of 0 and a standard deviation of 1".

Step-by-step explanation:

The standard answer of its following formula is calculated by:

\(\to z=\frac{X-\mu}{\sigma}\)

Its standard score relates to the sampling distribution with the normal distribution average standard variation of 0 and 1, correspondingly. The mean for a standard scoring is 0, and the normal deviation is 1. that's why the mean=0, standard deviation=1.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

x+1/2=21/14

x = ?

Step 02:

14 (x + 1 ) = 2 * 21

14x + 14 = 42

14x = 42 - 14

x = 28 / 14

x = 2

The answer is:

The value of x is 2

There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

Answer:

Some answers to the reducing fraction sheet

Q14 = 4/5 because divide 12 and 15 by 3

Q15=can't be reduced because 11 is a prime number so it can't be divided by anything

Q17=can't be reduced because 17 is a prime number

Q18=can't be reduced because 13 is a prime number

Q19=38/9 because 114 and 27 would be divided by 3

Q20= -1/1 because you would divide both 14,529 by itself would equal to - 1/1

I can only help you with this sheet I can't help you with the other one hope this was helpful! :)

Answer:

$42.50

Step-by-step explanation:

15% = .15

50 x .15 = 7.5

50 - 7.5 = 42.5

Answer: The correct answer is A)

The distance between points ( -5 , -3 ) and ( -10 , -8 ) is AB = \(5\sqrt{2}\) Units

The Pythagorean theorem is used to calculate the distance between two points using the distance formula. Rewriting the Pythagorean theorem as d = \(\sqrt{(x_{1} - x_{2}) ^{2} + (y_{1}-y_{2} ) ^{2} }\) to calculate the separation between any two locations.

According to the given information

Let one point be \((x_{1},y_{1})\) = ( -5 , -3 )

Let second point be \((x_{2} , y_{2})\) = ( -10 , -8 )

According to the distance formula

AB = \(\sqrt{(x_{1} - x_{2}) ^{2} + (y_{1}-y_{2} ) ^{2} }\)

AB = \(\sqrt{(-5 + 10) ^{2} + (-3+8 ) ^{2} }\)

AB = \(\sqrt{5^{2}+5^{2} }\)

AB = \(\sqrt{50}\)

AB = \(5\sqrt{2}\) Units

The distance between points ( -5 , -3 ) and ( -10 , -8 ) is AB = \(5\sqrt{2}\) Units

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the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

To find the probability that the claim will be rejected assuming the manufacturer's claim is true, we need to calculate the probability of having 70 or fewer patients cured out of 100.

First, we need to determine the mean (μ) and standard deviation (σ) of the binomial distribution.

For a binomial distribution, the mean (μ) is given by μ = n * p, where n is the number of trials (100 patients) and p is the probability of success (0.73).

μ = 100 * 0.73 = 73

The standard deviation (σ) of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).

σ = sqrt(100 * 0.73 * (1 - 0.73)) = sqrt(100 * 0.73 * 0.27) = sqrt(19.71) ≈ 4.44

Next, we will use the normal distribution to approximate the binomial distribution. Since the sample size is large (n = 100) and both np (100 * 0.73 = 73) and n(1 - p) (100 * 0.27 = 27) are greater than 5, the normal approximation is valid.

We want to find the probability of having 70 or fewer patients cured, which is equivalent to finding the cumulative probability up to 70 using the normal distribution.

Using the z-score formula:

z = (x - μ) / σ

For x = 70:

z = (70 - 73) / 4.44 ≈ -0.6767

Now, we can use a standard normal distribution table or a calculator to find the cumulative probability up to z = -0.6767.

The cumulative probability P(X ≤ 70) is approximately 0.2489.

Therefore, the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

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Design of Experiments (DOE) is a statistical methodology that is used to systematically change input variables or process parameters to discover the effect of these changes on the output variables.

DOE is a critical tool used in the manufacturing industry, pharmaceuticals, and many other sectors. The cake making process is a simple example of how DOE is used. Consider a case where we want to optimize a recipe for a cake mix.

The following are some input factors that might affect the quality of the cake mix:

The response variable for the experiment is cake texture, as it will be measured using the following factors:

After determining the response and input variables, the next step is to identify levels and ranges for the input factors. As an example, we may use the following levels for the input variables:

Amount of butter: 25, 50, 75, 100

Sugar concentration: 20, 30, 40, 50

Egg yolk quantity: 1, 2, 3, 4

Amount of flour: 100, 200, 300, 400

Baking temperature: 150, 160, 170, 180

Mixing time: 5, 10, 15, 20

In a standard DOE, a full factorial experiment is carried out in which every possible combination of the different levels of input variables is tested. The output of each test run is then recorded, and statistical analysis is performed to identify which input variables have the greatest effect on the output variables.

By using DOE, we can optimize the recipe for a cake mix by finding the ideal combination of input variables that result in the best cake texture.

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The combination is the way to find a number of different committees. The different number of committees is 120.

What is the combination?

A combination is a method of selecting items from a collection where the order of selection is irrelevant.

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

Given that the total number of teachers is 10.

The number of members of the committee is 3.

The formula of combination is nCr = n!/[r!(n-r)!]

Where n is the total number of objects and r is the number of objects those are selected.

In the question, n=10, r=3

The different committees is ₁₀C₃

=10!/3!(10-3)!

=10!/3!7!

=120

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Answer: 288

Step-by-step explanation: the number of songs downloaded this year will be x

x/12=30-6

= x/12=24

12*24= 288

x=288

The correct option is (C) The graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Option (C) gives a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.

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Answer:

see photo

be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.

Step-by-step explanation:

Plato/Edmentum

Answer:

-2

a open bracket

and then a and - a negate each other to give -2

The derivative of \\(( f(x) = \ln \left(\frac{x^{2}(x^{3}-7)}{(x-9)^{2}}\right) \) is \( f'(x) = \frac{2}{x} + \frac{3x^2}{x^3-7} - \frac{2}{x-9} \).\)

To expand \(\( f(x) = \ln \left(\frac{x^{2}(x^{3}-7)}{(x-9)^{2}}\right) \)\), we can use the properties of logarithms:

1. Product Rule:\(\( \ln(ab) = \ln(a) + \ln(b) \)\)

2. Quotient Rule:\(\( \ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b) \)\)

3. Power Rule: \(\( \ln(a^b) = b \ln(a) \)\)

Let's expand the expression step by step:

\(\( f(x) = \ln \left(\frac{x^{2}(x^{3}-7)}{(x-9)^{2}}\right) \)\)

Using the product rule:

\(\( f(x) = \ln(x^{2}) + \ln(x^{3}-7) - \ln((x-9)^{2}) \)\\\)

Using the power rule:

\(\( f(x) = 2\ln(x) + \ln(x^{3}-7) - 2\ln(x-9) \)\)

Now, let's differentiate \( f(x) \) using the chain rule and the derivative rules of logarithmic functions:

\(\( f'(x) = 2 \cdot \frac{1}{x} + \frac{1}{x^3-7} \cdot 3x^2 - 2 \cdot \frac{1}{x-9} \)\)

Simplifying further:

\(\( f'(x) = \frac{2}{x} + \frac{3x^2}{x^3-7} - \frac{2}{x-9} \)\)

So, the derivative of \\(( f(x) = \ln \left(\frac{x^{2}(x^{3}-7)}{(x-9)^{2}}\right) \) is \( f'(x) = \frac{2}{x} + \frac{3x^2}{x^3-7} - \frac{2}{x-9} \).\)

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Answer:

FH = 24

Step-by-step explanation:

just use this formula incase of next time

FH= FG - HG

FG = FH +HG

HG = FG - FH

The answer is 33

Step-by-step explanation:

56-23=33

Answer:

FG=33

Step-by-step explanation:

If the whole line is 56 and GH is 23, you could subtract those to get FG which is 33

The probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%. The 15th percentile of the population is 2.57.

To find the probability that the sample mean will be between 8 and 14, we need to calculate the standard error of the mean (SEM) first. The SEM is the standard deviation of the sampling distribution of the mean, and it is given by the formula SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

In this case, σ = 12 and n = 75, so SEM = 12/√75 ≈ 1.386.

Next, we need to standardize the sample mean using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We do this by calculating the z-score for each endpoint of the interval:

z1 = (8 - 10) / 1.386 ≈ -1.441

z2 = (14 - 10) / 1.386 ≈ 2.882

We then use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. Alternatively, we can use the formula for the cumulative distribution function (CDF) of the standard normal distribution:

P(-1.441 < Z < 2.882) ≈ Φ(2.882) - Φ(-1.441) ≈ 0.985 - 0.204 ≈ 0.785

So, the probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%.

To find the 15th percentile of the population, we use the inverse of the CDF of the standard normal distribution. That is, we find the z-score that corresponds to a cumulative probability of 0.15:

Φ(z) = 0.15

z ≈ -1.036

Finally, we use the formula for the sample mean in terms of the standard normal distribution to find the corresponding value in the original units:

X = μ + z(σ/√n)

X = 10 + (-1.036)(12/√75)

X ≈ 2.57

Therefore, the 15th percentile of the population is 2.57

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10k^3 , 6k^3

k^3 ( 10, 6 )

2k^3 (5, 3)

so 2k^3 is the greatest common factor of both the numbers .

Answer:

greatest common factor: 2k³

Step-by-step explanation:

given 10k³ and 6k³

for gcf just simply break them down:

10k³ = 2 * 5 * k * k * k

6k³ =  2 * 3 * k * k * k

-------------------------------------------------------------------------------------------------------------

Analyse both of them and find similarities:

the similarities are: 2 * k * k * k

so the greatest common factor is 2k³

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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To find the points on the curve y = 3x^4 - 30x^2 + 2 where the tangent line is horizontal, we need to find the values of x where the derivative of the curve is equal to zero.

The derivative of the given curve y = 3x^4 - 30x^2 + 2 can be found by taking the derivative of each term with respect to x. The derivative is given by dy/dx = 12x^3 - 60x.

To find the points where the tangent line is horizontal, we set the derivative equal to zero and solve for x: 12x^3 - 60x = 0. Factoring out the common factor of 12x, we get 12x(x^2 - 5) = 0.

Setting each factor equal to zero, we find x = 0 and x^2 - 5 = 0. Solving for x^2 - 5 = 0, we get x = ±√5.

Therefore, the points on the curve where the tangent line is horizontal are (0, 2) and (√5, -13) and (-√5, -13).

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To find the points on the curve y = 3x^4 - 30x^2 + 2 where the tangent line is horizontal, we need to determine where the derivative of the function is zero.

The derivative of the function y = 3x^4 - 30x^2 + 2 can be found by applying the power rule of differentiation:

dy/dx = 12x^3 - 60x

To find the points where the tangent line is horizontal, we set the derivative equal to zero:

12x^3 - 60x = 0

Factoring out a common factor of 12x, we get:

12x(x^2 - 5) = 0

This equation is satisfied when either 12x = 0 (which gives x = 0) or x^2 - 5 = 0 (which gives x = ±√5).

Therefore, the points on the curve where the tangent line is horizontal are (0, 2), (√5, -23), and (-√5, -23).

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\((42 \times 51) + 14 = \)

Answer:

All of them demonstrate the distributive property, except for number 4. 1-3 all have a number on the outside of the parenthesis to distribute itself to the number and variable within the parenthesis, while #4 has a plus sign outside each pair of parenthesis, making you unable to distribute those numbers.

Answer:

{y l y > 9}

Step-by-step explanation:

Given function:

\(f(x)=3^x+9\)

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s).  Therefore, the parent function of the given function is:

The range of the parent function is restricted to positive real numbers as it never takes a negative value.  Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞).  Therefore, the range of the parent function is {y | y > 0}.

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up.  So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

y=2x-2 is the equation of the graph.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given figure the points are (2, 2)(3,4)(4, 6)

m=6-4/4-3

m=2/1

slope =2

Now let us find the y intercept

4=2(3)+b

4=6+b

b=-2

y=2x-2

Hence, y=2x-2 is the equation of the graph.

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Answer:

b. 40m

Step-by-step explanation:

\(length \: of \: x \\ {x}^{2} = {8}^{2} + {6}^{2} \\ {x}^{2} = 64 + 36 \\ {x}^{2} = 100 \\ \sqrt{ {x}^{2} } = \sqrt{100} \\ x = 10m\)

\(x = 10m \\ 4x = 4 \times 10 \\ 4x = 40m\)

Using the given linear function, it is found that the expressions are given by:

It is:

4x - 3y = 12.

To find y in terms of x, we isolate y, hence the expression is given by:

\(3y = 4x - 12\)

\(y = \frac{4x}{3} - 4\)

To find x in terms of y, we isolate x, hence the expression is given by:

\(4x = 12 + 3y\)

\(x = \frac{3y}{4} + 3\)

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The inequality best representing the trial numbers in which Hannah feels 2 points is t > 7.

In the question, we are given that Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 1, Hannah closes her eyes while Arianna gently touches 2 paperclip points 3 millimeters (mm) apart on Hannah's forehead. Then Hannah reports whether she could feel 1 or 2 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 2 more mm apart. Hannah reports feeling 1 point until the points are 15mm apart, when she begins reporting that she feels 2 points.

We are asked for the inequality that best represents the trial numbers in which Hannah feels 2 points.

We know that for trial 1, the paperclip points are 3 mm away.

After that the gap between the paperclips are exceeded by 2 mm.

Thus, for trials:

2 we have paperclips at 5 mm gap.

3 we have paperclips at 7 mm gap.

4 we have paperclips at 9 mm gap.

5 we have paperclips at 11 mm gap.

6 we have paperclips at 13 mm gap.

7 we have paperclips at 15 mm gap.

8 we have paperclips at 17 mm gap.

9 we have paperclips at 19 mm gap.

and so on.

We are informed that until the gap is 15 mm, she reports 1 points and after that she reports 2 points.

15 mm is for trial 7.

Thus, after 7th trial, she reports 2 points.

Thus, the inequality best representing the trial numbers in which Hannah feels 2 points is t > 7.

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The provided question is incomplete. The complete question is:

"Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 1, Hannah closes her eyes while Arianna gently touches 2 paperclip points 3 millimeters (mm) apart on Hannah's forehead. Then Hannah reports whether she could feel 1 or 2 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 2 more mm apart. Hannah reports feeling 1 point until the points are 15mm apart, when she begins reporting that she feels 2 points. Which inequality best represents the trial numbers in which Hannah feels 2 points?

a. t > 6

b. t < 6

c. t < 7

d. t > 7"

Answer: The inequality best represents the trial numbers in which Hannah feels 2 points is t>7

Step-by-step explanation:

Given: Ariana and Hannah are conducting an experiment to test the difference threshold for sense of touch on forehead.

Initially, the 2 paperclips are 3 mm apart on Hannah’s forehead.

To be more clear about the two points where the paperclips are touched on Hannah’s forehead, let us assume circle C to be Hannah’s forehead and A and B are the two points (as shown in the image).

Hannah feels only 1 point

For trail 1, the paperclips are 3mm apart.

Given, for each next trail, the gap is increased by 2mm.

So, for trail 2, the gap (Distance between 2 points A and B) is 3mm + 2mm = 5mm.

For trail 3, gap is 5mm + 2mm = 7mm

For trail 4, gap is 7mm + 2mm = 9mm

For trail 5, gap is 9mm + 2mm = 11mm

For trail 6, gap is 11mm + 2mm = 13mm

For trail 7, gap is 13mm + 2mm = 15mm

And so on.

According to the question, for a distance greater than 15mm, Hannah starts reporting that she is feeling two points.

Thus, till the 7th trail, Hannah reports 1 point on her forehead and after it she reports 2 points.

Hence,

The inequality best represents the trial numbers in which Hannah feels 2 points is t>7 (where t is the trial number).

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Disclaimer: The question is incomplete. Given below is the complete question.

Question:  Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 1, Hannah closes her eyes while Arianna gently touches 2 paperclip points 3 millimeters (mm) apart on Hannah's forehead. Then Hannah reports whether she could feel 1 or 2 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 2 more mm apart. Hannah reports feeling 1 point until the points are 15mm apart, when she begins reporting that she feels 2 points. Which inequality best represents the trial numbers in which Hannah feels 2 points?

a. t > 6

b. t < 6

c. t < 7

d. t > 7

The 3 represent the degree of the freedom in the given equation.

According to the statement

we have to find that the in the given statement the digit is 3 is represented the term and we have to find that term.

So, For this purpose, we know that the

The given statement is:

X^2(3) = 8.4, p < .05,

From this it is clear that the

Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.

This represent the independent values in the given statement also.

So, The 3 represent the degree of the freedom in the given equation.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

In the result X^2(3) = 8.4, p < .05, what is 3 represent from the given questions?

a. the observed value

b. the critical value

c. the significant level

d. degrees of freedom

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