In a study of television viewing habits, it is desired to estimate the average number of hours teenagers spend watching per week. If it is reasonable to assume σ = 3.2 hours, how large a sample is needed so that it will be possible to assert with 95 percent confidence that the sam mean is off by at most 20 minutes?

The formula for X's cumulative distribution function (CDF) is

a. Probability P(X≤3) = P(X=1) + P(X=2) + P(X=3) = 1/7 + 1/14 + 3/14 = 5/14

b. P(X<3) = P(X=1) + P(X=2) = 1/7 + 1/14 = 3/14

c. P(X<4.12|X>1.638) = P(2<X<4.12)/P(X>1.638) = [P(X=3)+P(X=4)]/[1-P(X=1)] = (3/14)/(11/14) = 3/11

d.  The cumulative distribution function of X, for x = 5, F(5) = 1

a. Probability P(X≤3) = P(X=1) + P(X=2) + P(X=3) = 1/7 + 1/14 + 3/14 = 5/14

b. P(X<3) = P(X=1) + P(X=2) = 1/7 + 1/14 = 3/14

c. P(X<4.12|X>1.638) = P(2<X<4.12)/P(X>1.638) = [P(X=3)+P(X=4)]/[1-P(X=1)] = (3/14)/(11/14) = 3/11

d. The formula for X's cumulative distribution function (CDF) is

F(x) = P(X < x)

For x = 1, F(1) = 1/7

For x = 2, F(2) = 1/7 + 1/14 = 3/14

For x = 3, F(3) = 1/7 + 1/14 + 3/14 = 5/14

For x = 4, F(4) = 1/7 + 1/14 + 3/14 + 2/7 = 11/14

For x = 5, F(5) = 1

As a result, X's CDF is:

F(x) = {1/7, x < 1

3/14, 1 ≤ x < 2

5/14, 2 ≤ x < 3

11/14, 3 ≤ x < 4

1, x ≥ 4}

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The approximate measure of angle G.The correct answer is a. 41.4 degrees.

The measure of angle G in triangle EFG can be calculated using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In right triangle EFG, the two legs are EF and EG and the hypotenuse is FG. This can be expressed mathematically as [tex]8^2 + 10^2 = 12^2.[/tex] Simplifying the expression, the equation becomes 64 + 100 = 144. Solving this equation yields 64 = 144, which is true. To calculate the measure of angle G, we will use the inverse tangent function, which is written as [tex]tan^-1[/tex]. In this function, the inverse tangent of the ratio of the opposite side to the adjacent side is equal to the angle. This can be expressed mathematically as [tex]tan^-1 (8/10)[/tex] = G. Using a calculator, the inverse tangent of 8/10 is approximately 41.4 degrees. Therefore, the correct answer is a. 41.4 degrees.

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The account with the greater principle is Account B

First, find the principle on Account A to be :

= Interest earned in 14 months / Interest rate for 21 months

= 14 / ( 4 % / 12 months x 21 months )

= 14 / 7 %

= $ 200

Then find the principle on Account B using the same method :

= Interest earned in 14 months / Interest rate for 21 months

= 15.75  / ( 3 % / 12 months x 21 months )

= 15. 75 / 5. 25 %

= $ 300

Account B has the greater principal.

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The approximate population in Italy in 2012 was about 60,045,678.74.

We mean close in value or amount but not precise. an approximate solution. a rough date.

We can begin by establishing a ratio between the number of mobile phones and the population:

code:

147.4% = 1.474 (because 147.4% is the decimal equivalent of 1.474)

1.474 = number of mobile phones / population

We can solve for the population by substituting the given values:

code:

88,600,000 / population = 1.474

88,600,000 / 1.474 = population

The population is 60,045,678.74 people.

As a result, the approximate population of Italy in 2012 was 60,045,678.74.

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The two sets of lengths that do not form a triangle are the options B and C.

For a triangle with side lengths x, y, and z we know the triangular inequality, it says that the sum of any two sides must be larger than the other side, so we can write 3 inequalites:

x + y > z

x + z > y

z + y > x

So if for one of the given sets, one of these inequalities is false, then the set does not form a triangle.

For the second set:

12 yd, 25 yd, 13 yd

The inequality:

12 yd + 13yd > 25yd

25 yd> 25 yd

is false, so that set does not form a triangle.

And the last set:

5 ft, 9 ft, 16 ft​

The inequality:

5ft + 9ft > 16ft

14ft > 16 ft

Is also false,

So B and C are the correct options.

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Answer:

(n - 8)(n + 7)

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

Given trinomial:

Apply Viet's theorem.

The sum of the roots is 1 and the product of the roots is - 56.

This is achieved when the roots are 8 and - 7.

The part of the expression x(5 + y) that goes to the parentheses is 5 + y.

The correct option is 4.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:
A phrase: “x times the quantity 5 plus y.”

5 plus y 5 + y

x times the quantity 5 plus y = x(5 + y)

The complete expression is,

x(5 + y).

Therefore, 5 + y is the required expression.

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This function y = 6x + 50 has a graph that is a straight line with a 50-point y-intercept.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is its graph or the rate of change is large.

Given, The radius y after x days is represented by the equation y = 6x + 50.

Here, The initial radius was 50 mm and it is growing at a rate of 6 mm per day.

The graph of this function will be a straight line having a y-intercept at 50.

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The volume of the solid is 72π. of the x-axis, the volume of the solid is 72π of y axis, the volume of the solid is 192π of the line x=6 and the volume of the solid is 99π of the line x=9.

(a) Spinning the locale about the x-hub will make a strong with a round and hollow shape. The volume of the strong can be tracked down utilizing the equation:

[tex]V = ∫[a,b] πy^2 dx[/tex]

where an and b are the x-directions of the marks of convergence of the bends y=x and y=0.

The convergence focuses are (0,0) and (6,6). In this way, the restrictions of coordination are 0 and 6.

V = [tex]V = ∫[a,b] πy^2 dx[/tex]

=[tex]π(6^3)/3[/tex]

= 72π

The volume of the strong is 72π.

(b) Spinning the locale about the y-hub will make a strong with a round and hollow shape. The volume of the strong can be tracked down utilizing the equation:

V = [tex]∫[a,b] πx^2 dy[/tex]

where an and b are the y-directions of the marks of convergence of the bends y=x and y=0.

The convergence focuses are (0,0) and (6,6). In this way, the restrictions of coordination are 0 and 6.

V = [tex]∫[0,6] πy^2 dy[/tex]

= [tex]π(6^3)/3[/tex]

= 72π

The volume of the strong is 72π.

(c) Rotating the district about the line x=6 will make a strong with a washer shape. The volume of the strong can be tracked down utilizing the recipe:

V = [tex]∫[a,b] π(R^2 - r^2) dx[/tex]

where an and b are the x-directions of the marks of convergence of the bends y=x and y=0, R is the separation from the line of upheaval to the external edge of the strong (y=x), and r is the separation from the line of transformation to the internal edge of the strong (y=0).

The convergence focuses are (0,0) and (6,6). R=6 and r=0, since the strong stretches out from the line of insurgency to the bend y=x.

V =[tex]∫[0,6] π(6^2 - x^2) dx[/tex]

= [tex]π(6^3 - 2(6^3)/3)[/tex]

= 32π(6)

The volume of the strong is 192π.

(d) Rotating the locale about the line x=9 will make a strong with a washer shape. The volume of the strong can be tracked down utilizing the recipe:

V =[tex]∫[a,b] π(R^2 - r^2) dx[/tex]

where an and b are the x-directions of the marks of convergence of the bends y=x and y=0, R is the separation from the line of upheaval to the external edge of the strong (y=x), and r is the separation from the line of transformation to the internal edge of the strong (y=0).

The convergence focuses are (0,0) and (6,6). R=3, since the separation from the line x=9 to the bend y=x is 3 units. r=0, since the strong reaches out from the line of transformation to the bend y=x.

V = [tex]∫[0,6] π(3^2 - x^2) dx[/tex]

= [tex]π(3^3 - 2(6^2)(3) + 6^3/3)[/tex]

= 18π(6) - 27π

= 99π

The volume of the strong is 99π.

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The probability that a randomly selected student plays a sport, given

that the student is a senior is A. 0.32

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

This is a case of conditional probability and we know,

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Given, At a high school, the probability that a student is a senior is 0.25

and the probability that a student is a senior and plays a sport is 0.08.

Therefore, The probability that a randomly selected student plays a sport, given that the student is a senior is,

= 0.08/0.25.

= 0.32

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The perimeter of the rectangular bedroom is: A. 116 feet.

Perimeter of a rectangle = 2(length + width)

To find the perimeter of the rectangular bedroom, we need to calculate the sum of the lengths of its four sides.

Let's start by finding the length of the horizontal sides of the rectangle. The two horizontal sides are defined by the points (21, 18) and (21, −7), which are 25 feet apart in the vertical direction (18 − (−7) = 25). Therefore, the length of each horizontal side is 25 feet.

Next, let's find the length of the vertical sides of the rectangle. The two vertical sides are defined by the points (21, 18) and (−12, 18), which are 33 feet apart in the horizontal direction (21 − (−12) = 33). Therefore, the length of each vertical side is 33 feet.

Now we can add up the four side lengths to get the perimeter:

Perimeter = 2(Length of horizontal sides) + 2(Length of vertical sides)

= 2(25 feet) + 2(33 feet)

= 50 feet + 66 feet

Perimeter = 116 feet

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The distance from the pitching rubber to first base is 98.7ft, B - the distance from the pitching rubber to first base is 96.6ft and C - A pitcher must pivot to face in a 45-degree angle if he is facing home plate.

(a) To find the distance from the pitching rubber to first base, we can use the Pythagorean theorem, since the distance forms the hypotenuse of a right triangle with legs of length 80ft (the length of a side of the square) and 55.5ft (the distance from the pitching rubber to home plate along a diagonal line). Thus, we have:

distance to first base = [tex]\sqrt{ 80^{2} + 55.5^{2}[/tex] =  98.7ft

(b) To find the distance from the pitching rubber to second base, we can use the fact that second base is located at a distance of 80ft from home plate along a line perpendicular to the line connecting the pitching rubber and home plate. Using the Pythagorean theorem, we have:

distance to second base = [tex]\sqrt{55.5^{2} + 80^{2} }[/tex] = 96.6ft

(c) If a pitcher faces home plate, he needs to turn through an angle of 45 degrees to face second base. This is because second base is located at one corner of the square, and the angle formed by the lines connecting the pitching rubber to home plate and second base is a right angle (since the sides of the square are perpendicular).

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The Mean Absolute Deviation (MAD) for actual sales is 300 and for forecast is 600.

Mean Absolute Deviation evaluates the absolute difference between each data point to its mean. Mean Absolute Deviation can be calculated using formula:

MAD = ∑|x - x bar|

                n

where:

x = data point

x bar = data mean

n = number of data

Based on the given data, we know that:

Mean Actual sales = (1,000 + 1,600 + 2,000 + 1,800) / 4

Mean actual sales = 1,600

MAD = |1,000 - 1,600| + |1,600 - 1,600| + | 2,000 - 1,600| + |1,800 - 1,600|

                                                4

MAD = (600 + 0 + 400 + 200) / 4

MAD = 300

Mean Forecast = (600 + 2,500 + 1,500 + 2,000) / 4

Mean forecast = 1,650

MAD Frc = |600 - 1,650| + |2,500 - 1,650| + |1,500 - 1,650| + |2,000 - 1,650|

                                                                4

MAD Forecast = (1,050 + 850 + 150 + 350) / 4

MAD Forecast = 600

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Answer: 60 = 1/√3.

Step-by-step explanation:

The cotangent of 60 degrees is equal to the x-coordinate of the point of intersection divided by the y-coordinate of the point of intersection. In this case, the x-coordinate is 0.5 and the y-coordinate is √3/2. Therefore, cot 60 = 0.5 / √3/2 = 1/√3.

So, cot 60 = 1/√3.

The length of Stephen's rug is 3 feet.

To find the length of Stephen's rug, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In this case, we know that the perimeter of the rug is 16 feet and the width is 5 feet. So, we can plug in these values into the formula and solve for L:

Let's use the formula for the perimeter of a rectangle to solve the problem:  Perimeter = 2 x (Length + Width)

We know that the perimeter of the rug is 16 feet and the width is 5 feet. Plugging those values into the formula, we get: 16 = 2 x (Length + 5)

Simplifying the equation, we can divide both sides by 2:

8 = Length + 5

16 = 2L + 2(5)

16 = 2L + 10

2L = 6

L = 3

Therefore, the length of Stephen's rug is 3 feet.

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No, it is not safe to stop the addition of terms when their magnitude falls below s, even if the desired absolute error is less than e.

This is because the magnitude of the terms in the series may not decrease monotonically, and there may be large fluctuations in the magnitudes of the terms.
Therefore, it is necessary to use convergence tests, such as the ratio test or the root test, to determine if the series converges absolutely.

For the series ∑ (0.99)^n, we can use the ratio test to check for absolute convergence:

lim (n → ∞) |(0.99)^(n+1)/(0.99)^n| = 0.99 < 1

Since the limit is less than 1, the series converges absolutely. However, we cannot simply stop adding terms when their magnitude falls below a certain value s, as the magnitude of the terms in the series may not decrease monotonically.

Instead, we need to use the convergence test to determine the number of terms required to achieve the desired absolute error e.

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The domain and the range for the function in this problem are given as follows:

For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.

The range is obtained as follows:

Hence the composition of these three intervals is given as follows:

(∞, -2] U {-1} U [2, ∞).

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Answer: 1/9

Step-by-step explanation:

2/2=1

18/2=9

Answer:

Given: Find the standard for of 59 × 10^-7 ( 0.0000059 ).

= 5.9 × 10-6.

Step-by-step explanation:

Rotation, reflection, translation

Hope this helps :)

Yes, The ratios 8/16 and 3/6 form a proportion.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The ratios are,

⇒ 8/16 and 3/6

Now, We know that;

Two ratio are equivalent to each other then, it is form a proportional relation.

Hence, We can check as;

⇒ 8 / 16 = 1/2

⇒ 3/6 = 1/2

Thus, The ratios 8/16 and 3/6 form a proportion.

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The burgers is sold each for 3.75 dollars , while the fries is solde for 1.25 dollars each

We would have to solve for the price of each of the items using the simultaneous linear equation method

2 burgers and 3 fries for $11.25

we would have:

Use the elimination method to solve the system of equations:

2 x+ 3 y = 11.25

7 x + 5 y = 32.50

Step 1 - Multiply Equation 1 by 7:

7 * (2x+3y=11.25) --> 14x + 21y = 78.75

Step 2 - Multiply Equation 2 by 2:

2 * (7x+5y=32.50) --> 14x + 10y = 65

Step 3 - s

14x + 21y = 78.75

-(14x + 10y = 65)

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

21y - 10y = 78.75 - 65

Step 4 - simplify and solve for y:

11y = 13.75

y  = 13.75 / 11

y = 1.25

Step 5 - now that we have solved for y, let's rearrange Equation 1 to solve for x:

2x = 11.25 - 3y

Divide each side by 2

2x / 2 = 11.25 - 3y / 2

x  =  11.25 - 3y / 2

Step 6 - we determined y = 1.25. Plug it into our Rearranged equation 1:

x  =  11.25 - 3(1.25) / 2

x  =  11.25 - 3.75 / 2

x  =  7.5 / 2

x = 3.75

Since x is the burgers which is 3.75 dollars while y is the fries which is 1.25 dollars

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Answer: The frequency (f) of a wave is related to its wavelength (λ) and velocity (v) by the equation:

f = v/λ

Given the wavelength range of 100 m to 1000 m for the medium radio wave band, we can calculate the frequency range as follows:

For the lower wavelength of 100 m:

f = v/λ = 299.8 × 10^6 m/s / 100 m = 2.998 × 10^6 Hz

For the higher wavelength of 1000 m:

f = v/λ = 299.8 × 10^6 m/s / 1000 m = 299.8 × 10^3 Hz

Therefore, the frequency range for the medium radio wave band is approximately 2.998 × 10^6 Hz to 299.8 × 10^3 Hz.

Step-by-step explanation:

The mean of the number of eagles spotted is 7.8

In our daily life, we encounter a lot of information in the form of numbers, tables, graphics, etc. This information can refer to goals, temperatures in different cities, most popular articles in student classes, etc. Data is collected information  

Order refers to the frequency with which an event or value occurs. A frequency table is a table that lists items and indicates how often they occur.

Then, find the sum of all frequencies and multiply each class frequency by the midpoint for that class. Then find the mean of the frequency distribution using the formula where the mean of the clustered frequency distribution is given as ¯x=∑fixi∑fi.

here for rage 3-6 first find mean = (3+6)/2= 4.5 frequency =13

here for rage 7-10 first find mean =(7+10)/2=8.5 frequency =21

here for rage 11-14 first find mean =(11+14)/2=12.5 frequency 6

mean = (4.5*13+8.5*21+12.5*6)/(13+21+6)

=7.8

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Lola used 15/4 cups of rice to make rice pudding.

Given is that Lola has 4[tex]\frac{1}{2}[/tex] cups of rice. She uses 3/4 of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert.

Amount used by Lola for the rice pudding -

{x} = 4[tex]\frac{1}{2}[/tex] - 3/4

{x} = 9/2 - 3/4

{x} = 18/4 - 3/4

{x} = 15/4

Therefore, Lola used 15/4 cups of rice to make rice pudding.

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{Complete question -

Lola has 4[tex]\frac{1}{2}[/tex] cups of rice. She uses 3/4 of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert. How much rice does Lola use for the rice pudding?}

The required probability that events A and B both occur is 0.15.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

The probability that events A and B both occur is given by the product of their individual probabilities if they are independent. Independence means that the occurrence of one event does not affect the probability of the other event.

In this case, the probability that events A and B both occur is given by:

0.3 × 0.5 = 0.15

So, the probability that events A and B both occur is 0.15.

It's important to note that without further information, we cannot determine if events A and B are independent. The probabilities of 0.3 and 0.5 are the individual probabilities of each event, but we would need to know if their occurrence affects each other to determine if they are independent.

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According to the distribution shown above, the heights of female is taller according to the gender based distribution of heights.

What exactly is normal distribution?

The normal distribution, also called the Gaussian distribution, is a probability distribution that is symmetric about the mean, demonstrating that data close to the mean occur more frequently than data distant from the mean. The normal distribution looks like a "bell curve" when represented graphically.

Considering the information provided,

The United States' average male population is 69.

In the US, men's standard deviation is 2.25.

In the US, the average gender distribution is 64.

Women in the US experience a 2 standard deviation.

Now z-score for,

Female players = [tex]\frac{74-64}{2}[/tex] = 5

Playing men =  [tex]\frac{74-69}{2.25}[/tex] = 2.22

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The system of equations are solved

a) The train will reach at 2:00 PM if it leaves at 11:25 AM

b) The train will reach at 21:20 PM if it leaves at 18:45 PM

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A train journey from London to Leed takes 2h 35min

So , the total journey time is 155 minutes

a)

The time when the train reaches Leeds when it leaves at 11:25 AM is given by the equation A = 11:25 AM + 155 minutes

On simplifying the equation , we get

The train will reach at 2:00 PM if it leaves at 11:25 AM

b)

The time when the train reaches Leeds when it leaves at 18:45 PM is given by the equation A = 18:45 PM + 155 minutes

On simplifying the equation , we get

The train will reach at 21:20 PM if it leaves at 18:45 PM

Hence , the equations are solved

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The price of burger is  $3.75 and the fries cost $1.25

On Monday, Jack bought 2 burgers and 3 fries for $11.25

On Tuesday he bought 7 burgers and 5 fries for $32.50

Let a represent the cost of the burger

Let b represent the cost of the fries

2a + 3b= 11.25..........equation 1

7a + 5b= 32.50..........equation 2

Solve by elimination method
Multiply equation 1 by 7 and multiply equation 2 by 2

14a + 21b= 78.75

14a + 10b= 65

11b= 13.75

b= 13.75/11

b = 1.25

Substitute 1.25 for b in equation 2

7a + 5(1.25)= 32.50

7a + 6.25= 32.50

7a= 32.50-6.25

7a= 26.25

a= 26.25/7

a= 3.75

Hence the price of burger is $3.75 and the price of fries is $1.25

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Javier contribute $12,000 of his balance in the bank account.

Compound interest is the interest which is calculated on both the initial principal and the accumulated interest from previous periods. It can be easily understood as interest on interest.

                                    [tex]A= P(1+\frac{r}{n})} ^{nt}[/tex]

Javier has been saving to purchase a beach home for 20 years.

Monthly deposits of $500 are made into an annuity that earns 3.5% annual interest, compounded monthly.

Javier contribute= monthly deposit* number of months* time period

Javier contribute = 500*12*20

                            = $12000

Hence, Javier contribute $12,000.

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Answer:

Step-by-step explanation:

Javier contributes $500 each month, for 20 years. To find the amount that was contributed, we multiply those pieces together (12 months in each year).

500⋅12⋅20=$120,000