The time it takes for the country's population to double is 1000 years. The total population would be 10 million people.
How to calculate the population growth?We can calculate the population growth by
P = P₀ × r × t
Where
P = population growthP₀ = current populationr = growth raten = number of periodsSuppose that immigration is the only factor of population growth. We have
Net immigration rate, i = r = 1/1000The current population, P₀ = 5 million peopleFind the time that takes the country's population to double!
To make the country's population double, the population growth should be also 5 million people.
The formula would be
5,000,000 = 5,000,000 × 1/000 × t
t = 1,000/1
t = 1,000 years
Hence, the country's population will be double after 1,000 years.
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Rectangle URST undergoes a dilation centered at the origin. The result is rectangle U'R'S'T'. Which rule describes the dilation? A) (x, y) → (2x, 2y) B) (x, y) → (3x, 3y) C) (x, y) → ( 1 2 x, 1 2 y) D) (x, y) → (− 1 2 x, − 1 2 y)
Option A, (x,y) → (2x,2y) This rule describes an origin-centered stretch with a factor of 2. That is, the image doubles its original size in both the x and y directions.
The new rectangle is similar to the original, but with larger dimensions, so the correct rule is A) (x, y) → (2x, 2y).
In this case, the rule described in option A) (x, y) → (2x, 2y) specifies that the image is twice the size of the original rectangle in both the x and y directions increase. This means that the scale factor is 2. This will result in a similar shape but with larger dimensions. This is the correct rule describing stretching the rectangle URST to the rectangle U'R'S'T'.
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43 centigrams ? 31.7 milligrams
>. <. =. Please pick a symbol for the question mark
Answer:
43 centigrams > 31.7 milligrams
Step-by-step explanation:
Since 43 centigrams is equal to 430 milligrams, it is therefore greater that 31.7 milligrams.
In the parallelogram above, AE = 7x+4, BE=15x-12, and DE= 9x. What is the length of BD?
Answer:
BD = 36
Step-by-step explanation:
• the diagonals of a parallelogram bisect each other , so
BE = DE , that is
15x - 12 = 9x ( subtract 9x from both sides )
6x - 12 = 0 ( add 12 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Then
BD = BE + ED
= 15x - 12 + 9x
= 24x - 12 ( substitute x = 2 )
= 24(2) - 12
= 48 - 12
= 36
Andrew goes to the school by bus.
The probability that the bus is late is 0.1.
If the bus is late, the probability that the Harris is late to the school is 0.8.
If the bus is not late, the probability that Andrew is late to school is 0.05.
i) Draw a tree diagram to show the above information with all the probabilities.
Answer: I am not able to create images such as tree diagrams. But I can explain to you how it could be done.
A tree diagram is a visual representation of the possible outcomes and their probabilities.
The tree diagram to show the above information would have two branches: one representing the event that the bus is late and the other representing the event that the bus is not late.
The first branch, "Bus is Late", would have a probability of 0.1 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.8) and the other representing the event that Andrew is not late to school (with a probability of 0.2).
The second branch, "Bus is not Late", would have a probability of 0.9 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.05) and the other representing the event that Andrew is not late to school (with a probability of 0.95).
This tree diagram will help you to understand the relationship between the different events and their probabilities, as well as the overall probability of Andrew being late to school.
Step-by-step explanation:
An airplane is headed for the airport, 15 miles away. If the airplane is at an altitude of 5000 feet, what is the angle of depression, to the nearest tenth of a degree, from the airplane to the airport? (1 mile = 5280 feet)
The angle of depression of the airplane is 3.6⁰.
What is the angle of depression of the airplane?
The angle of depression of the airplane is calculated by forming a triangle with base displacement of the airplane and the altitude.
base of the right triangle = 15 miles = 79,200 ft
height of the right triangle = 5,000 ft
The angle of depression is calculated as follows;
θ = arc tan ( h / b )
θ = arc tan ( 5000 / 79,200 )
θ = 3.6⁰
Thus, the angle of depression of the airplane is a function of the altitude and base displacement of the airplane.
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find the measure of each interior angle and each exterior angle of a regular 45-gon.
The measure of each interior angle is calculated to be 172° and each exterior angle is calculated to be 8°.
Each interior angle in a polygon can be calculated using the formula, (n - 2) ×180°/n
where, n is the polygon's number of vertices.
So, each exterior angle can be calculated as, 180 - (n - 2) 180°/n
Now, let us put the number of vertices into these formulae,
Each interior angle = (45 - 2)×180°/45 = 43×180°/45 = 172°
Each exterior angle = 180 - (45 - 2) 180°/45 = 8°
So, the interior angle is 172° and the exterior angle is 8°.
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The post office’s human resources manager wants to determine an optimal hiring plan. Day Number of full-time employees required 1 = Monday 17 2 = Tuesday 13 3 = Wednesday 15 4 = Thursday 19 5 = Friday 14 6 = Saturday 16 7 = Sunday 11 Union rules state that each full-time employee must work 5 consecutive days and then receive 2 days off. Formulate an IP to minimize the number of fulltime employees who must be hired, and solve it using Excel Solver to find the optimal solution
Here is a simple framework to model the problem as an Integer Programming (IP) problem and solve it using Excel Solver:
Define decision variables:Let x(i,j) be the number of full-time employees assigned to work on day i (1 <= i <= 7) and given day off on day j (1 <= j <= 7).
Set constraints:a. Work days constraint: For each day i, the number of employees working must meet the demand:
∑(j=1 to 7) x(i,j) = demand(i) (1 <= i <= 7)
b. Availability constraint: Each employee can work only 5 consecutive days, so for each day j (1 <= j <= 7), the number of employees given day off on day j must be less than or equal to the number of employees working on day j-5:
∑(i=1 to 7) x(i,j) <= ∑(i=j-5 to j-1) x(i,j-5) (1 <= j <= 7)
Set objective:The objective is to minimize the total number of full-time employees hired, so the objective function is:
minimize: ∑(i=1 to 7) ∑(j=1 to 7) x(i,j)
Solve using Excel Solver:Excel Solver can be used to find the optimal solution to the IP problem. The constraints and objective function should be set up in the spreadsheet, and Solver should be configured to use the integer constraint option. The solution will give the optimal number of full-time employees hired and their assignment on each day.
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the average weekly work hours of full-time u.s. workers have approximately a normal distribution with mean 37 hours and standard deviation hours. suppose 200 u.s. citizens are randomly chosen. find an approximate probability that less than 10 of them are working more than 50 hours a week on average (round off to third decimal place).
The approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.019
We can use the normal distribution to approximate the probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average.
To do this, we have to standardize the variable by subtracting the mean and dividing by the standard deviation.
In this case, X = (50 - 37) / hours = 1.83
We know that for a standard normal distribution, the probability of X being less than a certain value can be found using a standard normal table or a calculator with a built-in standard normal cumulative distribution function (CDF).
Now, we will use the cumulative distribution function to find the probability of less than 10 out of 200 working more than 50 hours a week on average. Using a standard normal table or calculator, we can find the probability of having X < -2.04.
P(X < -2.04) = 0.0188
So the approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.0188 which rounding it off to the third decimal place we get 0.019.
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Tank A has a capacity of 9.5 gallons. 6 1/3 gallons of the tanks water are poured out. How many gallons of water are left in the tanks
The volume of water that are left in the tank is equal to 3.2 gallons.
How to calculate the volume of a geometric figure?Mathematically, the volume of a cuboid tank is a measure of its capacity and it can be calculated by using this following formula:
Volume of a tank = L × W × H
Where:
L represents the length of a cuboid tank.W represents the width of a cuboid tank.H represents the height of a cuboid tank.In order to determine the quantity (volume) of water that are left in the tank, we would use this mathematical expression:
Volume of water left = capacity of tank A - volume of water poured
Volume of water left = 9.5 gallons - 6 1/3 gallons
Volume of water left = 9.5 gallons - 6.3 gallons
Volume of water left = 3.2 gallons.
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Fill in the table using this function rule.
y=2x-3
X Y
-6 ?
-3 ?
0 ?
3 ?
The table is filled considering the numeric values of the function, as follows:
x = -6, y = -15.x = -3, y = -9.x = 0, y = -3.x = 3, y = 3.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The numeric value in this problem is found replacing the lone instance of x by it's value, hence the numeric value at x = -6 is given as follows:
y = 2(-6) - 3
y = -12 - 3
y = -15.
The same procedure is applied for x = -3, x = 0 and x = 3.
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A polynomial function is represented by the data in the table.
Choose the function represented by the data.
f(x) = −14x − 11
f(x) = −12x + 1
f(x) = 2x2 + 1
f(x) = x2 − 6x + 1
Convert 4 liters into gallons. Round your answer to the nearest hundredth.
*Note: you must use these exact conversion factors to get this question right.
1 cup (cup) = 8 fluid ounces (fl oz)
1 liter (L) 1000 milliliters (mL)
1 pint (pt) = 2 cups (cups)
1 cubic meter (m³) = 1000 liters (L)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 3.785 liters (L)
1 gallon (gal) = 4 quarts (qt)
1 fluid ounce (fl oz) = 29.574 milliliters (ml)
1 cubic foot (ft³) = 7.481 gallons (gal)
Answer:
= (blank) gallons
how many 6-digit numbers (leading zeros are allowed) contain exactly one 3, one 4, and one 5 as digits? g
246960 6-digit numbers contain exactly one 3, one 4, and one 5 as digits.
There are a total of 6 digits that make up any of the numbers in 0 to 999999 with the given condition
The total numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
This can be represented as UVWXYZ
Digit 3 can occupy any of the 6 positions
Digit 4 can occupy any of the (6 - 1) positions
Digit 5 can occupy any of the (6 - 2) positions
The remaining 7 digits will occupy the last 3 positions in the following ways:
The first of the 7 digits can be selected from any of 7 ways
The second can be selected from any of 7 ways
The third can be selected from any of 7 ways
So, the total number of selection is:
= 6 × 6 × (6 - 1) × (6 - 2) × 7 × 7 × 7
= 36 × 5 × 4 × 343
= 246960
Therefore there are 246960 numbers.
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in a sample of 2000 people, 430 people have their ears pierced. two unrelated people are selected at random without replacement, find the probability that neither of the people have their ears pierced.
The probability that neither of the people have their ears pierced is 0.6157
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The probability of A happening is the number of people who do not have their ears pierced divided by the total number of people in the sample, which is:
P(A) = (2000 - 430) / 2000 = 1570 / 2000 = 0.785
The conditional probability of B given A is the number of people who do not have their ears pierced and are still available to be selected as the second person divided by the total number of people available to be selected as the second person, which is:
P(B|A) = (2000 - 430 - 1) / (2000 - 1) = 1569 / 1999 = 0.7845
Therefore, the probability that neither of the people have their ears pierced is:
P(A) * P(B|A) = 0.785 * 0.7845 = 0.6157
Hence, the probability that neither of the people have their ears pierced is 0.6157
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translate the image (x+7,y-19)
The translation rule (x + 7, y - 19) has the meaning given as follows:
Translation 7 units right.Translation 19 units down.What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.The meaning of each translation in this problem is given as follows:
x + 7: 7 units right.y - 19: 19 units down.Missing InformationThe problem asks for the meaning of the translation (x + 7, y - 19).
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Answers for this problem?
Note that the square feet of carpet that will be required for this area is: 42 Square Feet of Carpet.
This is solved using the knowledge of the area of rectangles and right-angled triangles.
What is a right-angled triangle?A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees.
Note that the area of a right-angled triangle is given as:
A = (½)×b×h square units
Where b is breath and h is height.
Note as well that the area of the rectangle is given as Lx B
To solve the above problem, we must create one more right-angled triangle beside the one already created, then solve for the areas of the respective shapes.
Now that the shape has been divided in to two Right-angled Triangles and one rectangle (See the attached) their respective dimensions are given as follows:
1) Right Angled triangled A
B = 2ft
H = 3ft
Area = 1/2 2 * 3 = 3ft
2) Right-Angled Triangle B
B = 4ft
H = 3ft
A = 1/2 * 4 * 3
A = 6ft
3) Rectangle - C
L = 11ft
B= 3ft
A = 11 * 3 = 33 Ft.
Thus total square feet of outdoor carpet required is:
3 + 6 + 33
= 42 Square Feet of Carpet.
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Consider absolute value function f
f(x) = -2/3|x + 4|
The vertex of the function is a (minimum/maximum) at (0,4)(0,-4)(4,0)(-4,0)
For the absolute value function, the vertex is at its maximum at (-4,0).
What is function?A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences. A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output.
Here,
The vertex for the absolute value function is at its maximum at (-4,0).
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Let S(t) be the number of students enrolled in a school district in terms of the number of years, t, after 2000.
Which statements regarding function S are true? Select TWO that apply.
Answer:
S(t) is a function, because there is a unique output value (number of students) for each input value (number of years after 2000)
S(t) can be represented by a graph, where the horizontal axis represents the number of years after 2000, and the vertical axis represents the number of students
Step-by-step explanation:
The statements regarding function S are true are:
S(5) = 2024 means there were 2024 students in 2005.
S(10)= S(5) there same number of students in 2005 and 2010.
We have function,
S(t)= 2000t
First, S(0) in 2000 means that there were 2000 students in starting.
Second, S(5) = 2024 means there were 2024 students in 2005.
Third, S(10)= S(5) there same number of students in 2005 and 2010.
Fourth, S(15)- S(10)= -40 means that there were 40 less students in 2015 than in 2010.
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a hardware store sells toolboxes. The table shows the types of tools in each toolbox. Becca says that for every 14 tools in a toolbox, there are 2 hammers. Is Becca correct? EXPLAIN
Type l # of tools
Hammer l 2
Plies l 5
Screwdriver l 6
Wrench l 3
Becca is not correct because her probability of 2/14 is not equal to the true experimental probability of 2/16.
How to find the probability of selection?We are given the tools in the box as;
Hammer = 2 nos
Pliers = 5 nos
Screw drivers = 6 nos
Wrench = 3 nos
Thus;
Total number of tools in the box = 2 + 5 + 6 + 3
= 16
Probability of selecting a hammer = 2/16
Now, Becca says that for every 14 tools in a toolbox, there are 2 hammers. This means she is suggesting a probability of 2/14.
This is wrong because it is different from the experimental probability that we got.
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∠TWP≅
∠HGD
∠DGH
∠GHD
∠GDH
Californians use 75 BTU of energy per home per year which is 25% less than the national average.
How many BTU does an average American household use? Show Work
Proportionately, an average American household uses 100 BTU of energy per home per year while Californians use 75 BTU, which is 25% less than the national average.
What is the proportion?Proportion refers to the ratio or relative size of a value or number compared to another.
Proportions are fractional values equated to each other.
Generally, proportions may be depicted as fractions, decimals, or percentages.
The level of energy per home per year in California = 75 BTU
The national average of BTU use = 100%
California's use = 75% (100 - 25)
Proportionately, if 75% = 75 BTU, 100% = 100 BTU (75/0.75)
Thus, the national average use of energy is expected to be 100 BTU.
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how to graph y=2x+1
-2x=y=-2
Answer:
For y=2x+1
The line y=2x+1 has a y-intercept of +1, so begin with a point at (0,1)
and its slope is 2/1, which means from there you go Up 2 and Right 1.
Follow that pattern until you can draw a straight line through all the points.
For -2x=y=-2
In this point it only passes (0,2) and (1.0)
Have a wonderful day! :-)
The scale drawing of the rectangular garden has an area of `2` ft². If Mai used a scale factor of `\frac{1}{3}`, what is the actual area of the garden?
The actual area of the garden without the scale factor is 6 square feet.
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.
What is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. Depending on the size and number of sides, different forms have varying areas.
Let the original area of the garden be x.
Given that the scale factor used is 1/3, thus we have:
x (1/3) = 2
x = (2)(3)
x = 6
Hence, the actual area of the garden without the scale factor is 6 square feet.
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Step by step. Integrated 2 Checkpoint 4 Picture Below
The value of 'x' in the equation 8 - x/x = 3/2 is x equal to [tex]3\frac{1}{5}[/tex].
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, An equation in 8 - x/x = 3/2 fractions.
Now, The LCM of both the denominators is 2x, So we'll multiply each term by 2x.
2(8 - x) = 3x.
16 - 2x = 3x.
- 2x - 3x = - 16.
- 5x = - 16.
5x = 16.
x = 16/5.
x = [tex]3\frac{1}{5}[/tex].
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Mrs. Norris is planting a vegetable garden with tomatoes and beans. She wants to have 20 more potato plants than beat plants. She will plant 100 plants altogether. How many bean plants should she plant?
Solve using system of equations by elimination. Show your work
PLEASE help me with this question. Will name the BRAINLIEST for whoever gets it right!
The number of bean plants should she plant will be 60
t = tomato plants
b = beans
To Solve by using system of equations
Clear any fractional coefficients if there are any. Alternate the coefficients of a single variable. Select the variable you want to remove. Multiply one or both equations to make the variable's coefficients opposite.
Total plants = 100
t + b = 100 {equation 1}
20 more tomatoes than beans
t = b + 20 {equation 2}
b + 20 + b = 100
2b + 20 = 100
Finish solving for b to find a number of beans.
Then tomatoes will be b+20
Putting this in equation 1
b+20+b=100
2b+20=100
b=40
then t= b+20 {equation 2}
t=60
Hence the number of bean plants should she plant will be 60
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please help me with this.
Answer:
1: 5/10, square root of 2, 2.5, square root of 25 3: 4.5
Step-by-step explanation:
2.5
5 divided by 10 comes to 0.5
25 square rooted is 5
2 square rooted is 1.4
the biggest number is 5 and the smallest is 0.5
subtract 0.5 from 5 and you get 4.5
on a drive from your home to town, you wish to average 64 mph. the distance from your home to town is 88 miles. however, at 44 miles (half way), you find you have averaged only 48 mph. what average speed must you maintain in the remaining distance in order to have an
The average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph is 50.39 mph.
We have to find the average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph.
Let the speed be x.
The total average we want = 33.6 mph
The distance from your home to town = 90 miles
Time = Distance/Speed
Time = 90/33.6
At 45 miles (half way), you find you have averaged only 25.2 mph. So
Time first leg = 45/25.2
Time second leg= 45/x
Now the average speed;
45/25.2 + 45/x = 90/33.6
Subtract 45/25.2 on both side, we get
45/x = 90/33.6 - 45/25.2
After solving the ratio, we get
45/x = 0.893
Multiply by x on both side, we get
0.893x = 45
Divide by 0.893 on both side, we get
x = 45/0.893
x = 50.39 mph
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The complete question is:
On a drive from your home to town, you wish to average 33.6 mph. The distance from your home to town is 90 miles. However, at 45 miles (half way), you find you have averaged only 25.2 mph. What average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph?
What is the perimeter of parallelogram WXYZ?
W
X
Y
Z
34
34
34
34
60
Answer: The perimeter of a parallelogram is the sum of all its sides.
In this case, since all sides of the parallelogram WXYZ are given as 34 units, the perimeter of parallelogram WXYZ is the sum of all its four sides.
So the perimeter of parallelogram WXYZ = 34 + 34 + 34 + 34 = 136 units
It's important to notice that the given value of perimeter = 60 is not correct.
The perimeter of parallelogram WXYZ is 136 units, not 60 units.
Step-by-step explanation:
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The difference between two positive numbers is 50. One number is four times the other number. What are the two numbers?
The two missing positive numbers are; 50/3 and 200/3
How to solve algebra word problems?The difference between two positive numbers is 50. Let the two numbers be x and y and as such we have;
x - y = 50 -----(1)
One number is four times the other number. Thus;
x = 4y -----(2)
Put 4y for x in eq 1 to get;
4y - y = 50
3y = 50
y = 50/3
Thus;
x = 4(50/3)
x = 200/3
We conclude that x and y above are the two positive numbers.
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8112 equals 2 ^ 4 times 3 times 13 ^ 2 find the value of the smallest square number that is a mutiple of 8112
The factor 3 does not occur in pair. Thus, ‘3’ is the smallest number by which 8112 should be divided to get a perfect square.
What is the lowest square number?The LCM of 8, 15, and 20 is 120. Prime factors 2, 3, and 5 do not have a pair in this case. To construct a perfect square, 120 must be multiplied by 2 x 3 x 5. As a result, the least square number divisible by 8, 15, and 20 is 3600.
The smallest square matrix is 2 2 2 2 ; there is no theoretical limit to the highest size square matrix, however anything larger than 10 10 10 10 becomes impossible to manage numerically.4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961
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