Using proportion, the number of liters of soda needed would be 52.5 liters.
How to Use Proportion to Solve Word Problem?Proportion can be described as an equation that relates two equal ratio to each other.
If you need 7 liters of soda for every 12 guests, and you have 90 guests, you can use the proportion:
7 liters / 12 guests = x liters / 90 guests.
To find the number of liters of soda you need, you can cross-multiply and solve for x:
12x = 7(90)
12x = 630
x = 630/12
x = 52.5
So, you need 52.5 liters of soda for 90 guests.
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Please help me find the value and what kind of angle is this?
Answer: consecutive interior angles and x=66°
Step-by-step explanation:
The angles are consecutive interior angles. The property is consecutive interior angles are supplementary.
2x+24+24=180 [combine like terms]
2x+48=180 [subtract both sides by 48]
2x=132 [divide both sides by 2]
x=66
Therefore, the angle is consecutive interior angles and x=66°.
In a recent student government election, the ratio of students who voted for the winner to all the students who voted was 0.85. The number of students who voted was 60. How many votes did the winner get?
In a recent student government election, the number of vote of the winner is 51
How to determine the ratioAn ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
In a proportion, two ratios are specified to be equal to one another in an equation.
The number of votes of the winner is calculated by writing the ratio
= number of the students who voted / total number of students
let x be the number of students that voted the winner
85 / 100 = x / 60
100x = 60 * 85
x = 5100 / 100
x = 51
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a fire station is to be located along a road of length a, where a is a fixed positive real number. if fires will occur at points uniformly chosen on (0, a), where should the station be located so as to minimize the expected distance from the fire?
If fires occur at points uniformly chosen on (0, A), then [tex]a = \frac{A}{2}[/tex] is the second derivative where should the station be located so as to minimize the expected distance from the fire.
From the question, a fire station is to be located along a road of length A, A < ∞.
If fires occur at points uniformly chosen on (0, A), then we have to find where should the station be located so as to minimize the expected distance from the fire.
E∣X−a∣ = [tex]\int^{A}_{0}|x-a| \frac{1}{A} dx[/tex]
E∣X−a∣ = [tex]\int^{a}_{0}|a-x| \frac{1}{A} dx+\int^{A}_{a}|x-a| \frac{1}{A} dx[/tex]
Now integrating.
E∣X−a∣ = [tex]\frac{1}{A}\left(\frac{a^2}{2}+\frac{A^2}{2}-aA-\left(\frac{a^2}{2}-a^2\right)\right)[/tex]
E∣X−a∣ = [tex]\frac{a^2}{A}-a+\frac{A}{2}[/tex]
If we set the derivative to zero, we get [tex]\frac{2a}{A}-1=0[/tex], where [tex]a = \frac{A}{2}[/tex] is the derivative. One can look at the second derivative, which is always positive, to see if this is the minimizer.
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The complete question is:
A fire station is to be located along a road of length A, A < ∞. If fires occur at points uniformly chosen on (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[∣X−a∣] when X is uniformly distributed over (0, A).
The mean weight of adult man is US is 190 lb and SD 59lb. An elevator in our building has a weight limit of 2500lb. what is the probability that if 10 men on the elevator, they will overload its weight limit
Answer: no it will not overload it's weight limit
Step-by-step explanation: 190 x 10 = 1900
i'm sorry if i am wrong
then i think i do/ 59 x 10 = 590 so then 1900 + 590 = 2490
A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 47 type I ovens has a mean repair cost of $75. 51, with a standard deviation of $23. 53. A sample of 54 type II ovens has a mean repair cost of $71. 32, with a standard deviation of $18. 43. Conduct a hypothesis test of the technician's claim at the 0. 01 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens
The value of test statistics z=1.04
First, state the null and alternative hypotheses:
[tex]H_o=u_1=u_2\\H_a=u_1 > u_2[/tex]
Use z-statistics:
[tex]z=\frac{x_1-x_2}{y} ------(1)[/tex]
where x₁ and x₂ are the means and:
[tex]y=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }[/tex]
Calculating the value of test statistics:
[tex]y=\sqrt{\frac{(23.53)^2}{47}+\frac{(71.32)^2}{54} }[/tex]
[tex]y=\sqrt{\frac{533.6609}{47}+\frac{5086.542}{54} }[/tex]
[tex]y=\sqrt{11.780+7.460}[/tex]
[tex]y=\sqrt{19.24}[/tex]
y = 4.386
Now substitute the y value in equation (1)
[tex]z=\frac{75.57-71.32}{4.386}[/tex]
z = 1.04
The test statistics is z = 1.04
The decision rule for rejecting the null hypothesis is: α≤ test statistics
Using the z-score table, it is possible to determine the p-value, which is:
value = 0.877
Comparing the p-value with the level of significance (α = 0.05):
0.877 > 0.05
Therefore, we fail to reject the null hypothesis.
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Given cot A = 8 5 cotA= 5 8 and that angle A A is in Quadrant I, find the exact value of csc A cscA in simplest radical form using a rational denominator.
The exact value of csc A is (√89) /5
How to find the exact value of csc A?Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.
Since cot A = 8 /5 and that angle A is in Quadrant I.
tan A = 5/8 (Remember: tan = 1/cot and tan = opposite/adjacent)
opposite = 5 and adjacent = 8
hypotenuse = √(5² + 8²) = √89
sin A = 5/(√89) (sin = opposite/hypotenuse)
csc A = (√89) /5 (csc = 1/sin)
Thus, the exact value of csc A is (√89)/5
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A three-column table is given.
Part A C D
Part 14 28 63
Whole 50 40 B
What is the value of B in the table?
12
36
68
90
The value of B in the table will be D. 90
How to explain the proportional relationship!The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.
The ratios between the two variables should be considered in order to determine whether a relationship is proportional. The relationship is proportional if the ratio remains constant. The relationship is not proportional if the ratio changes.
In this case, the relationship between part and whole is 7:10.
Therefore, the value of B will be:
= 10 / 7 × 63
= 10 × 9
= 90
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megan collects stamps.she keeps her stamps ina abook that can hold 17 on each page. she has 56 pages full of stamps, and 14 pages that are only half full.how many stamps does megan have?
Megan have total 1,071 stamps.
The concept used in this problem is multiplication, specifically using it to find the total number of stamps by multiplying the number of pages by the number of stamps per page. Additionally, it also uses the concept of addition to find the total number of stamps by adding the number of stamps on full pages to the number of stamps on half-full pages.
as given, Megan keeps her stamps in a book that can hold 17 on each page. she has 56 pages full of stamps. So,
Megan has 56 pages * 17 stamps per page = 952 stamps on full pages.
and 14 pages that are only half full. So,
She has 14 pages * (half of 17 stamps per page) = 14 pages * 8.5 stamps per page = 119 stamps on half-full pages.
Therefore, Megan has 952 stamps + 119 stamps = 1,071 stamps in total.
hence, Megan have total 1,071 stamps.
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a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 34 cm to 18 cm in 30 minutes. at what rate, in cubic cm per minute, is the volume of the snowball changing at the instant the radius is 6 cm?
The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.
The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.
dV/dt = 4/3π(3r²) dr/dt
We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:
dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min
Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.
We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:
dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min
So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.
Note that the negative sign indicates that the volume is decreasing.
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true or false: if the median of a data set is larger than the mean, then the histogram of the data will likely have a longer right tail.
The given statement about Histogram that , " if median of a data set is larger than mean, then the histogram of data will likely have a longer right tail" is FALSE .
A histogram is a graph in which most of data falls to the right of graph's peak and is known as a right-skewed histogram. This type of histogram is also known as a positively skewed histogram.
The relation between the mean , median and mode in a right-skewed histogram is denoted as : mean > median > mode .
A distribution is called skewed Right if, in histogram , the right tail (smaller values) is much longer than the left tail (larger values).
Therefore , For histogram to have longer right tail , the median should be less than the mean .
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What’s a system of equations that can be entered into a graphing calculator to solve 16.9x-2.3=3.2x+18
The system of equations that can be entered is y = 16.9x - 2.3 and y = 3.2x + 18
How to determine the system of equationsFrom the question, we have the following parameters that can be used in our computation:
16.9x-2.3=3.2x+18
Express the equation properly
So, we have the following representation
16.9x - 2.3 = 3.2x + 18
Next, we split the equation and introduce the variable y
So, we have
y = 16.9x - 2.3
y = 3.2x + 18
The above is the system of equations
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two people are picked at random from a group of 50 and given $10 each. after that, independently of what happened before, three people are picked from the same group - one or more people could have been picked both times - and given $10 each. what is the probability that at least one person received $20?
The probability that at least one person received $20 is 0.3
In math the term called probability is defined as a number that reflects the chance or likelihood that a particular event will occur.
Here we know that two people are picked at random from a group of 50 and given $10 each.
Here we have also know that three people are picked from the same group - one or more people could have been picked both times - and given $10 each.
Then the probability is calculated based on the binomial distribution is written as,
=> P = (50 3) 10³ (1 - 10) ⁵⁻³
When we simplify this one then we get the value of p as 0.3.
Then the following values are calculated through it,
μ = 15
σ = 3.24
σ² = 10.5
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) Lea plots a point at a number on this number line. The number rounded to the nearest thousand is 30,000. What must be true about the point? +) 31:000 28,000 29. 000 30,000 ?) It is closer to 30. 000 than 29,000. D)) It is between 30,000 and 31,000. It is closer to 28,000 than 31,000. It is between 29,000 and 30,000.
As number is rounded off to 30,000, the correct option is A i.e, it is closer to 30,000 than 29,000.
We look at the last three digits and round to the closest thousand. If these digits total 500 or more, the thousands digit is rounded up; if they total less than 500, the thousands digit is rounded down while remaining the same.
For example, to solve this question we have to check whether 16796 is closer to 16000 or 17000 in the counting. In this case, 16796 is closer to 16000, hence 17000 is the round figure of 16796.
In this problem, as the number is said to be rounded off to the nearest thousand is 30,000, this means that, the number is closer to 30,000 than 29,000.
The question is incomplete. The picture of number line is missing. It is placed in the attachment below.
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Select the inequality that models the problem.
The sum of two consecutive odd integers is at least 76. Find the least possible pair of integers.
A) n + n + 2 > 76
B) n + n + 1 ≥ 76
C) n + n + 2 ≥ 76
D) n + n + 1 > 76
By resolving the inequality, we discovered that the least possible pair of numbers is (37,39) if the total of two consecutive odd integers is at least 76.
The sum of two consecutive odd integers is at least 76.
First we let the two consecutive odd integers.
The first consecutive odd integer = n
The second consecutive odd integer = n + 2
The sum is at least 76. So the inequality that models the problem is
n + n + 2 ≥ 76
Now we determine the least possible pair of integers by solving the inequality.
2n + 2 ≥ 76
Subtract 2 on both side, we get
2n ≥ 74
Divide by 2 on both side, we get
n ≥ 37
If the least value of x is 37. So
The second odd integer = x + 2 = 37 + 2 = 39
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Solve log x = 4. (5 points) 10,000 1,000 40 4
log(x) = 4 can be restated as an exponential statement: 10^4 = x
x = 10000
The height of a vase is 45. 7 centimeters when rounded to the nearest tenth of a centimeter. What is the shortest possible height of the vase?
The shortest possible height of the vase would be 45.650 centimeters.
Rounding to the nearest tenth of a centimeter, the height of a vase is 45.7 centimeters. The vase's height can be as short as possible. Include three digits in your response.
Rounding to the nearest tenth, the vase's height is 45.7.The vase's smallest possible height will be 45.65 due to the fact that the figure is rounded to a tenth digit of 7 after the tenth digit.Using the, we can determine that the tenth digit is 7 - 1 = 6 before rounding.In order for the hundredth digit to be rounded to 1, the smallest value that could be assigned to it is 5.The value placed at 1,000 could take the smallest digit value up to three decimal places.To know more about height of vase here
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Please Help me On this Question thank you if you do!
Answer:
3rd one
Step-by-step explanation:
Answer:
3rd one
Step-by-step explanation:
3/4 x +3-2x = -1/4 +1/2x+5
step by step pleasz lets me know what to add sub etc...
The value of x from the expression 3/4 x +3-2x = -1/4 +1/2x+5 can be simplified as 45/29.
What is simplification?The concept that will be used is simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
3/4x +3-2x = -1/4 +1/2x+5
We can simplify by collecting the like terms,
3/4x - 1/2x - 2x = -1/4 + 5 -3
Then we can simplify further as:
-29x/20 = - 9/4
29x = (20*9)/4
29x= 45
x= 45/29
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Henry Heavyfoot was just arrested for speeding by Officer O'Rourke for traveling 65 mph in a 55 mph zone. Henry claimed his speedometer said 55 mph not 65 mph. What could Henry claim as his percent error?
Henry can claim 15.38% as his percent error.
We know that the formula for the percent error is:
Percent Error = (Absolute Error ÷ Actual Value) × 100
where, Absolute Error = ∣Actual Value - Estimated Value|
In this situation, the actual value is 65 mph and the Estimated value is 55 mph.
So, using above formula for absolute error,
Absolute Error = ∣Actual Value - Estimated Value|
Absolute Error = ∣65 - 55|
Absolute Error = 10
Now we find the percent error using above formula for the percent error.
Percent Error = (10 ÷ 65) × 100
Percent error = 15.38%
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Basil has 5 numbered cards. Two of the numbers are hidden. The mode of the 5 is 8. The mean of the 5 is 6. Work out the two hidden numbers
Two hidden cards out of five numbered cards with 8 as mode and 6 as mean of five numbers is equal to 8 and 1.
Total number of numbered cards is equal to 5
Number of hidden cards are two.
Let us consider two hidden cards be 'a' and 'b'.
Mode of the five numbered cards is 8
Three numbers are 4 , 9 , a, b, 8.
Mode represents the number with higher frequency.
4, 9, 8 only one time as 8 is the mode one of the number should be equal to 8.
let b = 8
Mean of five numbers is 6
Mean = ( Sum of all the numbers ) / total numbers
⇒ 6 = ( 4 + 9 + a + 8 + 8 ) / 5
⇒ 30 = 29 + a
⇒ a = 30 -29
⇒ a = 1
Therefore, two hidden numbers for the given mode and mean is equal to 8 and 1.
The above question is incomplete , the compete question is:
Basil has five numbered cards.
Two of the numbers are hidden. 4 9 ? ? 8
The mode of the five numbers is 8.
The mean of the five numbers is 6
c) Work out the two hidden numbers.
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Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
Answer:
-2x + y = 25
Step-by-step explanation:
just add them together by columns. X-3x = -2x
3y-2y = y
5+20 =25.
done.
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
-6x^{2}-582=−60x
The result of completing the square for the equation -6x² - 582 = −60x will be (x - 5)² = - 72.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The equation is given below.
-6x² - 582 = −60x
Simplify the equation, then we have
-6x² - 582 = −60x
-6(x² + 97) = - 60x
x² + 97 = 10x
x² - 10x = - 97
x² - 10 + 25 = 25 - 97
(x - 5)² = - 72
The result of completing the square for the equation -6x² - 582 = −60x will be (x - 5)² = - 72.
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Banana Inc. is producing batches of smartphones. The company's quality control department randomly picks a sample phone from each batch for testing. Which of the following percentages is possible as the percentage of the samples that pass?
Answer:
It is not possible to determine the percentage of samples that pass without additional information.
-10 + 17 < 2x - 10
solve the equality
Answer: x>17/2
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
7<2x−10
Step 2: Flip the equation.
2x−10>7
Step 3: Add 10 to both sides.
2x−10+10>7+10
2x>17
Step 4: Divide both sides by 2.
2x/2 > 17/2
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
Let's solve your inequality step-by-step.
−10+17<2x−10
Step 1: Simplify both sides of the inequality.
7<2x−10
Step 2: Flip the equation.
2x−10>7
Step 3: Add 10 to both sides.
2x−10+10>7+10
2x>17
Step 4: Divide both sides by 2.
[tex]\frac{2x}{2} > \frac{17}{2} \\\\ x > \frac{17}{2}[/tex]
Hope this helped :0
John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Which inequality shows the constraint on the amount of flour John has to make pies and cobblers?
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
An inequality which shows the constraint on the amount of flour John has to make pies and cobblers is: B. 3x + 3y ≤ 16
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:
3x + 3y ≤ 16
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Rewrite in simplest form -10(2g-7)+6g
Answer:
70-14g
Step-by-step explanation:
-20g+70+6g = 70-14g
According to the 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino. A political party wants to know how much impact the Hispanic and Latino vote will have, so they wonder if the percentage has changed since then. They take a random sample of 853 adults in Oregon and ask, among other things, their race. 110 of the people surveyed were Hispanic or Latino. Can the party conclude that the Hispanic or Latino proportion of the population has changed since 2010
The test hypothesis for the 2010 U. S. Census is H0 = Oregon < Latino.
In math the term called hypothesis is defined as an idea that is suggested as the possible explanation for something but has not yet been found to be true or correct.
Here we know that in 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino.
And here we have also know that random sample of 853 adults in Oregon and 110 of the people surveyed were Hispanic or Latino.
Then the sample proportion is calculated as,
=> sample proportion=113/853=0.1325
And the value of Test statistic is,
=> z = (0.1325-0.117)/√(0.117*(1-0.117)/853)
=> z = 1.41
So, the hypothesis is written as,
=> H0 = Oregon < Latino.
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Find X and Y.
TEACHING TEXTBOOKS GEOMETRY
The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
The equations are given below.
2y = 180° - 126°
2y = 54°
y = 27°
2x + 1 = 180° - 85°
2x + 1 = 95°
2x = 94°
x = 47°
The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.
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The complete question is attached below.
Use logarithms to solve: 9x=4
The value of given expression 9x=4 equals to 4/9.
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.
Given expression ,
log 9x = log 4
log 9 + log x = log 4
log x = log 4 - log 9
log x = log 4 / 9
x = 4 /9.
Hence, The value of given expression 9x=4 equals to 4/9.
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You buy a 562. 75 mL of dish soap. You already have some at home. How many mL do you have? 224. 14 at home
The total amount of dish soap added to both amounts will be 786.89 ml.
Describe addition.
In math, addition is the process of adding two or more integers together.
Since you currently have 224.14 mL of dish soap at home, you decide to buy a 562.75 ml container of it.
We will combine the two amounts together to get the total amount of dish soap.
Dish soap is 786.89 ml total (562.75 ml plus 224.14 ml).
Consequently, there is 786.89 ml of dish soap in total.
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