The distance between points (2, 3) and (-4, 5) is 6.3 units.
As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,
[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]
Here we have been given points (2,3) and (-4,5)
Let us assume that (x₁, y₁) = (2, 3)
and (x₂, y₂) = (-4, 5)
Let d represents the distance between points (2,3) and (−4,5)
Using above distance formula the distance d between given points would be,
[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-4 - 2)^2 + (5 - 3)^2]}\\\\\Rightarrow d = \sqrt{[(-6)^2 + (2)^2]}\\\\\Rightarrow d = \sqrt{36+4}\\\\\Rightarrow d = \sqrt{40}\\\\\Rightarrow d = 6.3~units[/tex]
Therefore, the distance is 6.3 units.
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The complete question is:
What is the distance between points (2,3) and (−4,5) ?
Where would the point (-1,3) be if it wa rotated 270 degree counterclockwie about the point (1,0) ?
The point (-1,3) would be located at the point (3,-1) after a 270 degree counterclockwise rotation about the point (1,0).
To rotate a point in a 2D space, we can use the rotation matrix formula:
[x'] = [cos(Ф) -sin(Ф)][x]
[y'] [sin(Ф) cos(Ф)][y]
Where x' and y' are the coordinates of the point after rotation, x and y are the coordinates of the point before rotation, and theta is the angle of rotation in radians.
In this case, the point to be rotated is (-1,3) and the point of rotation is (1,0). The angle of rotation is 270 degrees, which is equivalent to 3/2π radians.
Plugging in the values:
[x'] = [cos(3/2π) -sin(3/2π)][-1]
[y'] [sin(3/2π) cos(3/2π)][3]
[x'] = [0 1][-1]
[y'] [-1 0][3]
x' = 3 and y' = -1
Therefore, the point (-1,3) is located at the point (3,-1) after a 270 degree counterclockwise rotation about the point (1,0).
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Kwame and Olivia each combine orange juice and mango juice. Kwame makes a
total of 12 cups, and Olivia makes a total of 20 cups. Kwame uses less orange
juice than Olivia, but his orange-mango juice tastes more like oranges than hers
does. Give an example of the number of cups of each ingredient each person
could have used. Explain your thinking.
The number of cups of each ingredient Kwame and Olivia could have used is 6 cups and 10 cups respectively.
What do you mean by possible combinations?In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter. For example, the combination of three fruits from a basket containing apples, oranges, and bananas would be the set {apple, orange, banana}, {apple, banana, orange}, {orange, apple, banana}, {orange, banana, apple}, {banana, apple, orange}, and {banana, orange, apple}. The number of possible combinations is often represented using the combination formula, which is often written as "nCr", where "n" is the total number of items in the collection.
It's not possible to give an exact example of the number of cups of each ingredient each person used, as there are infinitely many ways that Kwame and Olivia could have combined orange juice and mango juice to make 12 and 20 cups respectively.
However, one example of the number of cups of each ingredient each person could have used is:
Kwame: 6 cups orange juice, 6 cups mango juice Olivia: 10 cups orange juice, 10 cups mango juice
This satisfies the constraints that Kwame uses less orange juice than Olivia and his orange-mango juice tastes more like oranges than hers does.
This is an example of the possible combination, but it might not be the only one. Also, it's possible that there are other combinations that could satisfy the given information, but this is one example.
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Write the fraction that repreent the colored part of each hape. Then, anwer and urround the larger fraction of each pair
The fraction that represents the colored part of each shape is i) ½ ii) 8/9 iii) ½ iv) ¼ v) 3/7 vi) ¼ vii) 1 viii) 4/9 ix) ½ x) 1/2.
Fractions refer to the parts of a whole. A fraction is a ratio between specified parts of a figure to all parts of a figure. The numerator indicates the parts of the whole and the denominator indicates the total number of equal parts. In the given shapes, as everything is equally divided, the fraction of shaded region is equal to the number of shaded parts divided by the number of total parts.
i) The number of shaded regions = 2
The total number of regions = 4
Fraction = 2/4 = 1/2
ii) The number of shaded regions = 8
The total number of regions = 9
Fraction = 8/9
iii) The number of shaded regions = 4
The total number of regions = 8
Fraction = 4/8 = ½
iv) The number of shaded regions = 1
The total number of regions = 4
Fraction = 1/4
v) The number of shaded regions = 3
The total number of regions = 7
Fraction = 3/7
vi) The number of shaded regions = 3
The total number of regions = 12
Fraction = 3/12 = 1/4
vii) The number of shaded regions = 10
The total number of regions = 10
Fraction = 10/10 = 1
viii) The number of shaded regions = 4
The total number of regions = 9
Fraction = 4/9
ix) The number of shaded regions = 4
The total number of regions = 8
Fraction = 4/8 = 1/2
x) The number of shaded regions = 1
The total number of regions = 2
Fraction = 1/2
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There are 14 dogs at the dog park on a busy Saturday. 2 of them are springer spaniels.
What is the probability that a randomly selected dog is a springer spaniel?
Write your answer as a fraction or whole number.
Answer:1/7
Step-by-step explanation: You take the amount that are springer spaniels and you put them with the whole of the dogs in the park 14 so you would have 2/14. You can reduce this fraction to 1/7 by dividing both the top and bottom of the fraction by 2.
there is 2 worker, one can make a house in 2 days, while the other one make a house in 3 days, how much days it take them to make a house
Answer:
5 days to make a house for both of them
Answer: 6/5 days
Step-by-step explanation:
If a worker can make a house in 2days, it can make 1/2 of the house in 1 day.
Similarly, the other worker can make 1/3 of the house in 1 day.
So, in 1 day, together, they will make 1/2 + 1/3 = 5/6 of the house.
So, it will take them 6/5 days to complete the house together.
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What are the zeroes of f/x x2 − X − 2?.
The zeros of function f(x) = x² -x - 2 are: x = 2 and x = -1
Consider given polynomial function f(x)=x² -x - 2
As we know the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.
To find the zeros of function f(x), we need to equate f(x) to zero then solve it for x.
⇒ f(x) = 0
⇒ x² -x - 2 = 0
using the Quadratic Formula where
a = 1, b = -1, and c = -2
[tex]\Rightarrow x=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow x = \frac{1\pm \sqrt{9} }{2}\\\\\\\Rightarrow x = \frac{1\pm 3 }{2}[/tex]
Thus x = 2 and x = -1 are zeros.
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The complete question is:
What are the zeros of f(x)=x² -x - 2 ?
What percentage profit did she make on costs
Answer:21
Step-by-step explanation:
Prepaid off-peak call cost = R41,67 (rounded off) + R1.30 x airtime used. O 1 Time (in min) Prepaid costs Contract costs 0 41,67 108,42 10 54,67 108,42 20 30 67.67 80.67 108.42 C 40 50 93,67 107 108,42 108.42 60 B D 10214 . Use your completed table to draw a graph of the airtime in minutes versus the prepaid contract call costs on different sets of axes.
Answer: I can provide you with the data in tabular format if you want to create the graph with the provided data.
Airtime (min) | Prepaid costs | Contract costs
0 | 41.67 | 108.42
10 | 54.67 | 108.42
20 | 67.67 | 108.42
30 | 80.67 | 108.42
40 | 93.67 | 108.42
50 | 102.14 | 108.42
60 | 114.64 | 108.42
This table shows the airtime (in minutes) used, and the corresponding costs for both prepaid and contract call plans. The prepaid costs are calculated using the formula: R41.67 + R1.30 x airtime used, whereas the contract costs are fixed at R108.42.
It's worth noting that the costs for the contract call plan is fixed and doesn't change with the airtime used, while for the prepaid plan the costs increase as the airtime increases.
Step-by-step explanation:
you want to sell 1/lb jars of mixed peanuts and cashews for five dollars . you paid three dollars per pound for peanuts and six dollars per pound of cashews . you plan to combine four parts peanuts and one part cashews to make your mix . you have spent $70 on materials to get started . how many jars must you sell to break even ?
Answer:
To calculate the number of jars you need to sell to break even, we can use the following formula:
(Cost of materials + Cost of ingredients per jar) / Price per jar = Number of jars needed to break even
We know that the cost of materials is $70, the cost of ingredients per jar is $18 ( $12 for peanuts + $6 for cashews) and the price per jar is $5.
Plugging in these values into the formula we get:
($70 + $18) / $5 = (88/5) = 17.6 jars
So, you need to sell at least 17.6 jars to break even.
--------------------
Cost of materials / (Price per jar - Cost of ingredients per jar) = Number of jars needed to break even
We know that the cost of materials is $70, the cost of ingredients per jar is $18 ( $12 for peanuts + $6 for cashews) and the price per jar is $5.
Plugging in these values into the formula we get:
$70 / ($5 - $18) = 70 / -13 = -5.38 jars
It is not possible to sell -5.38 jars, which means you are making a loss. This indicates that your cost of materials and ingredients is higher than the price you are selling the jars for. To break even, you will have to lower your costs or increase the price of the jars.
The corporate team-building event will cost $44 if it has 11 attendees. If there are 12 attendees, how
much will the corporate team-building event cost? Solve using unit rates.
Answer: 12 attendees can attend the corporate team-building event, with a budget of $48.
How to calculate event cost?
step1:
First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4
11÷11=1
So for every 1 attendee it is $4.
Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12
And whatever you do to one number you have to do for the other.
Step2:
so $4*12= $48
So for every 12 attendees it costs $48.
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12 attendees can attend the corporate team-building event, with a budget of $48.
How to calculate event cost?step1:
First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4
11÷11=1
So for every 1 attendee it is $4.
Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12
And whatever you do to one number you have to do for the other.
Step2:
so $4*12= $48
So for every 12 attendees it costs $48.
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Express the product (√2 – √3) (√2 – √3) in simplest form.
Answer:
The expression (√2 – √3) (√2 – √3) simplifies to 2 - 2√6 + 3, which can be further simplified to 3 - 2√6.
What is a cube of 12?.
1728 is the cubic of the number 12.
Cube of given number = [tex]12^{3}[/tex] which is equal to 1728.
The cubes are made up of values that are obtained by multiplying integers by themselves three or four times. The cube's original number can be found by raising any natural number to the power of three.
Cubes are the numbers that are produced when an integer is multiplied by itself three times. We can find cubes for any number, whether it be an integer or a fraction. In order for the cube of a whole number (x) to produce a perfect cube, the cube root of x3 must equal x. The procedure of locating cubes is thus the opposite of locating the cube root.
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El producto de
97
×
8
97×897, time, 8 e igual a
776
776776. Ua el dato anterior para reolver como un decimal. 9. 7
×
0. 08
=
9. 7×0. 08=9, point, 7, time, 0, point, 08, equal
La fórmula para multiplicar dos números decimales es la misma que para multiplicar números enteros.
Primero, muestra los números en forma de dígitos y coloca un punto decimal entre los números. Luego, multiplica los dígitos del número de la izquierda a la derecha, como si fueran números enteros. Después, añade los resultados, teniendo en cuenta la regla de los puntos decimales. Por último, contar el número de dígitos que hay después del punto decimal, y coloca el punto decimal en el resultado.
En este caso, se multiplican los números 9.7 y 0.08. Primero, se muestran los números en forma de dígitos: 9.7 y 0.08. Luego, se multiplican los dígitos de la izquierda a la derecha, como si
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What is 8 and 4/8 as a simplified number? And what is 4 and 1/6 + 7 and 1/6, and also try and simplify the number if possible.
A worker spent 2 hours and 40 minutes making 20 products. If he works at the same productivity, how long will it take the worker to make 30 units?
Answer:
Step-by-step explanation:
The Time Taken to make 20 products = 2hours and 40 minutes = 160 minutes
Time taken to make 10 units = 80 minutes
Time taken to make 30 units = time taken to make 20 units + time taken to make 10 units
= 160 minutes + 80 minutes
= 240 minutes or 4 hours.
The worker needs 4 hours to make 30 units.
The ratio can be calculated as follows:
The first is to convert hours to minutes
2 hours 40 minutes = (2×60)+40 = 120+40 = 160 minutes
The next step is to compare worth comparison
[tex]\frac{a1}{b1}[/tex] = [tex]\frac{a2}{b2}[/tex]
[tex]a_{1} = 160 minutes\\a_{2} = X\\b_{1} = 20 products\\b_{2} = 30 products[/tex]
So,
[tex]\frac{160}{20} = \frac{X}{30}[/tex]
X = [tex]\frac{(160.30)}{20}[/tex]
X = [tex]\frac{4800}{20}[/tex]
X = 240 minutes
The next is to convert minutes into hours
240 minutes ÷ 60 minutes
= 4 hours
The worker needs 4 hours to make 30 units.
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How do I convert improper fractions into mixed numbers?
Answer:
Step-by-step explanation: Divide the numerator by the denominator.
Write down the whole number part of the quotient.
Take the remainder and write it over the original denominator.
Kevin bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $305. How much did each computer cost before finance charges?
The cost of the desktop is $2083.8 and the cost of the laptop is $1783.8.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Kevin bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different financing plans. For the desktop, the interest rate was 7% per year, and for the laptop, it was 9.5% per year.
The cost will be calculated as:-
305 = 0.06x + 0.095( x + 300 )
305 = 0.06x + 0.095x + 28.5
276.5 = 0.155x
x = $1783.8
Desktop cost = x + 300
Desktop cost = 1783.8 + 300= $2083.8
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In Triangle RMC, RM = 19. MC = 27. and CMR = 27°. What is the area of RMC? Round to the nearest tenth.
the area of the triangle RMC will be 116.44 unit²
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. There are different types of triangles such as isosceles, right-angled, equilateral etc.
The sum of all angles of triangle = 180
In Triangle RMC, RM = 19. MC = 27. and CMR = 27°.
Area is = A*B*sin(M)/2
= 19*27*sin(27)/2
=116.44856
Hence the area of the triangle RMC will be 116.44 unit²
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Triangle PQR is similar to Triangle XYZ. If PQ = n + 2, QR = n - 2, and XY = n^2 - 4,
what is the value of YZ, in terms of n?
Note that if Triangle PQR is similar to Triangle XYZ, and If PQ = n + 2, QR = n - 2, and XY = n²- 4, then the value of YZ, in terms of n is: (n-2)²
What is the justification for the above expression?
Where triangle PQR is similar to triangle XYZ, then;
PQ/QR =XY/YZ
Given
PQ = n + 2,
QR = n - 2 and
XY=n² - 4,
Substitute
n+2/n-2 = n²-4/YZ
n+2/n-2 = (n+2)(n-2)/YZ
1/n-2 = n-2/YZ
Cross multiply
YZ = (n-2)(n-2)
YZ = (n-2)²
Hence the value of YZ in terms of n is (n-2)²
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Draci sets up a room for a banquet. She has 54 chairs. She places 9 chairs at each table. How many tables have 9 chairs?
Draci sets up a room for a banquet with 6 tables.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=15x+7. Where:
m= the slope.
b= the constant term that represents the y-intercept.
The problem is a literal math question, that you can convert into a linear equation. Where:
x= number of tables
y= number of chairs
From the information of the question, you can write:
y=mx+b, where:
y= total number of chairs= 54
m= number of chairs in each table = 9
b=0 , because you have a constant function since Draci places 9 chairs at each table. Thus:
54=9x
x=54/9
x=6
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Mihka i on a long road trip, and he average 65 mph for 3 hour while he' driving on the highway. While he' driving on ide road for 1 hour, he only average 45 mph. What i the total ditance that he cover on her road
trip?
Mishka travels 230 kilometres in total on her road trip.
Mishka travels at a 65 km/hr average speed on the highway.
Mishka's time spent driving at this speed on the highway is 3 hours.
Mishka travels at an average rate of 35 km/h on the side road.
Driving at this speed on a side road took Mishka one hour.
Mishka travelled a total distance.
Having said that,
Speed equals Distance/Time
Or, Distance = Speed X Time.
Mishka travelled a total of Mishka miles on the roadway =
= Highway Speed X Highway Travel Time
= 65 X 3
= 195 km
Mishka travelled the following distance via side roads:
= Speed on side street X Travel time
= Speed on side road X Time taken on side road
= 35 X 1
= 35 km
Total distance travelled by Mishka = Distance travelled on highway + Distance travelled on side road
= 195 + 35
= 230 km
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y - 3x = 1
2y - x = 12
Answer:
x = 2, y = 7
Step-by-step explanation:
y - 3x = 1 |*2
2y - x = 12
2y - 6x = 2
2y - x = 12 | - Ist equation
2y-x-2y+6x = 12-2
5x = 10
x = 2
Insert x to first equation:
y - 3*2 = 1
y = 7
Madelyn earns $159.25 for 7 hours of work. If she makes a constant hourly wage, which table represents the relationship between the number of hours she works and her total earnings?
Answer: She makes around $22 dollars per hour.
Step-by-step explanation:
You can divide her wage by the amount of hours she works.
Combine the two congruent trapezoid at the right to make new polygon. Draw your new polygon and claify them
A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. It is formed by combining two congruent trapezoids, which results in a quadrilateral with two pairs of opposite sides that are parallel and equal in length. All four angles of the parallelogram are also equal.
1. Draw the two congruent trapezoids.
2. Line up the two trapezoids, making sure that the corresponding sides are parallel and the same length.
3. Connect the two trapezoids with lines to form the parallelogram.
4. Check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length.
A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. To make a parallelogram, two congruent trapezoids are combined. This can be done by lining up the two trapezoids, making sure that the corresponding sides are parallel and the same length. Then, the two trapezoids can be connected with lines to form the parallelogram. It is important to check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length. If these criteria are met, then the shape is a parallelogram.
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what is the difference of (-2x+9) and (3x-4)
Answer:
-5x + 13
Step-by-step explanation:
Difference = subtraction
[tex](-2x+9) - (3x-4)\\-2x - 3x + 9 + 4\\-5x + 13[/tex]
a hot airballoon rises 120 feet every 3 seconds. which equation represents the relationship bettween time and height
y = 30x
y = 40x
y = 120x
y = 3x + 120
Answer:
y = 40x
Step-by-step explanation:
How much is a 90 angle?.
A 90-degree angle, also known as a right angle, is an angle that measures exactly 90 degrees.
A 90-degree angle is an angle that measures exactly 90 degrees. It is also known as a right angle, since it is an angle that forms a right angle.
In geometry, angles are measured in degrees, and a full rotation is equal to 360 degrees. The angle formed by two intersecting lines is measured by the amount of rotation needed to bring one line to overlap the other. A 90-degree angle is formed by rotating one line by exactly 90 degrees, so that the two lines form a right angle.
A right angle is an angle that measures 90 degrees and it is represented by a small square at the angle's vertex. This square is a symbol of the angle's measure. In addition, the right angle is the only angle that can be used in geometry to create perpendicular lines which are lines that meet at 90 degrees.
In real-world applications, right angles are found in many things such as the corners of a room, the corners of a square or rectangle, and the corners of tools like a square, a ruler, and a protractor.
Therefore, In short, a 90-degree angle, also known as a right angle, is an angle that measures exactly 90 degrees. It's represented by a small square at the angle's vertex, and it's the only angle that can be used in geometry to create perpendicular lines.
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2x^5 different from (2x)^5
The difference between the two expressions:
2x^5 and (2x)^5
Is the coefficient that multiplies the variable.
How are the two expressions different?We want to see how the expressions:
2x^5 and (2x)^5
Are different.
Remember that the exponents can be distributed, then we can write the rule:
(a*b)^n = (a^n)*(b^n)
Then we can rewrite the second expression as:
(2x)^5 = (2^5)*x^5 = (2*2*2*2*2)*x^5 = 32x^5
So the difference between the two expressions is the coefficient that is multiplying the variable x.
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How much water do you add to make each concentration? 25% sugar syrup using 15 grams of sugar pls help.
Answer:
25% sugar syrup means in a mixture of 100g sugar syrup, sugar should be 25g
so, when sugar is 25g , mixture is 100g
when sugar is 1g, mixture is 100/25 = 4g
when sugar is 15g, mixture is 15*4 =60g
So, amount of water to be added=60-15= 45g
Step-by-step explanation:
9. A water tank already contain 55 gallon of water when Baxter begin to fill it. Water flow into the tank at a rate of 8 gallon per minute. Write a linear equation to
model thi ituation. Find the volume of water in the tank 25 minute after Baxter
begin filling the tank
So, 25 minutes after Baxter began filling the tank, the volume of water in the tank is 255 gallons.
A linear equation can be used to model the situation where water is flowing into a tank at a constant rate. The equation would be in the form:
V = 55 + 8t
Where V is the volume of water in the tank (in gallons), t is the time (in minutes) that has passed since Baxter began filling the tank, and 55 and 8 are the y-intercept and slope respectively
To find the volume of water in the tank 25 minutes after Baxter began filling it, you would substitute 25 for t in the equation above:
V = 55 + 8(25) = 55 + 200 = 255 gallons
So, 25 minutes after Baxter began filling the tank, the volume of water in the tank is 255 gallons.
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