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Part 1

Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to 6 if she rolls the two number cubes 252 times?

Answer: geometric because it has a steady rate of multiplying by 4.5.

Step-by-step explanation:

Answer:

(x,y) = (-5,-8)

Answer:

Step-by-step explanation:3x+7=x-3. 3x-x=-3-7. 2x=-10. X=-5. but y=x-3. So. Y=-5-3=-8

The area of the sidewalk of the circular flower bed is approximately 251.2 square meters.

All points on a plane that are equally spaced from a fixed point known as the center make up a circle, which is a geometric object. The diameter of a circle is the distance through its center; the radius is the distance from any point on the circle to that point. One of the many significant characteristics of circles is the constant ratio of circumference to diameter, indicated by the mathematical constant (pi).

Given, the diameter of the flower bed is 16m, thus:

radius = 16/2 = 8m.

Now,

Area of the flower bed = π(8m)^2 = 64π square meters

Area of the outer circle (sidewalk) = π(12m)^2 = 144π square meters

Area of the sidewalk = Area of the outer circle - Area of the flower bed

= 144π - 64π

= 80π square meters

≈ 251.2 square meters

Hence, the area of the sidewalk is approximately 251.2 square meters.

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The measure of angle B is 24 degrees. We can calculate it in the following manner.

When two angles lie along a straight line, they form a straight angle which measures 180 degrees. Let's call the measure of angle B as x, then the measure of angle A can be expressed in terms of x as:

m∠A = 5(x + 7.2)

We can now use the fact that the sum of the measures of angles A and B is equal to 180 degrees, and substitute the expression for m∠A to get:

m∠A + m∠B = 180

5(x + 7.2) + x = 180

Simplifying the equation:

6x + 36 = 180

Subtracting 36 from both sides:

6x = 144

Dividing both sides by 6:

x = 24

Therefore, the measure of angle B is 24 degrees.

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Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, what is m∠B?

Binomial expansion of the given algebraic expression is:

729x⁶ − 1458x⁵y + 1215x⁴y² - 540x³y³ + 135x²y⁴ - 18xy⁵ + y⁶

The binomial theorem is one that states the principle for expanding the algebraic expression (x + y)ⁿ and expresses it as a sum of the terms involving individual exponents of variables x and y.

Thus, for example (x + y)³ will be expressed as:

1(x³)(y⁰) + 3(x²)(y¹) + 3(x¹)(y²) + 1(x⁰)(y³)

Similarly, for (3x - y)⁶, using pascals triangle, we have:

1(3x)⁶ + 6(3x)⁵(-y)¹ + 15(3x)⁴(-y)² + 20(3x)³(-y)³ + 15(3x)²(-y)⁴ + 6(3x)¹(-y)⁵ + 1(-y)⁶

= 729x⁶ − 1458x⁵y + 1215x⁴y² - 540x³y³ + 135x²y⁴ - 18xy⁵ + y⁶

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Answer: 0.09m > 56.60 + 0.07m, where m > 2830.

Step-by-step explanation:

Let's assume that Plan A costs more than Plan B for monthly phone use greater than some value m, where m is the number of minutes of phone use in a month.

For Plan A, the monthly cost can be expressed as:

Cost_A = 0 + 0.09m = 0.09m

For Plan B, the monthly cost can be expressed as:

Cost_B = 56.60 + 0.07m

To find the value of m for which Plan A costs more than Plan B, we need to set the two costs equal to each other and solve for m:

0.09m = 56.60 + 0.07m

0.02m = 56.60

m = 56.60 / 0.02

m = 2830

Therefore, for monthly phone use greater than 2830 minutes, Plan A will cost more than Plan B.

In mathematical notation, we can express this as:

0.09m > 56.60 + 0.07m, where m > 2830.

The final answer is "2.2" < x  < 6.4 which is the pοssible length οf x.

The triangle inequality theοrem is a cοrnerstοne οf geοmetry and states that any triangle's sum οf its first twο sides is always greater than its third side. Fοr a triangle with sides a, b, and c, a + b > c, b + c > a, and a + c > b.

Accοrding tο the Triangle Inequality Theοrem, the length οf the third side must be greater than the sum οf the lengths οf the triangle's twο sides.

Therefοre, the pοssible length οf a triangle is equal tο the prοduct οf the sum οf the twο sides and the difference οf the twο sides.

Therefοre,

4.3 - 2.1 <  x < 4.3 + 2.1

2.2 < x < 6.4

Since "2.2" x 6.4 is a pοssible length fοr f x, that is the final answer.

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Complete Question:

What is the range of possible sizes for side xxx? < x <

Answer:

Step-by-step explanation:

Its 4.24 to the nearest hundredth because I input the square root of 18 in my caclulator.

The area of the square is increasing at a rate of 8 cm²/s when the area of the square is 16 cm².

When the side length of a square increases, the area of the square also increases. The formula for area of a square is side length multiplied by itself.

Therefore, when the side length of a square increases at a rate of 2 cm/s, the area of the square increases at a rate of 2 cm/s multiplied by 2 cm/s, or 4 cm²/s.

However, since the side length of the square is 16 cm when the area of the square is 16 cm², the rate at which the area of the square increases is 2 cm/s multiplied by 16 cm, or 8 cm²/s.

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The answer is C. To Solve i just used desmos.

The prοbability that the prοpοrtiοn οf red marbles in the sample frοm bin a is greater than the prοpοrtiοn οf red marbles frοm bin b is 0.1573.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here by using probability calculator for sampling distribution of [tex]p_1-p_2[/tex].

[tex]z=\frac{\hat p_1-\hat p_2}{\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}}[/tex]

Here [tex]\hat p_1=p_1[/tex] = 40% = 0.40 and [tex]\hat {p_2}=p_2[/tex] = 52% = 0.52 and [tex]n_1=0 , n_2=40[/tex]

=> [tex]z=\frac{0.40-0.52}{\sqrt{\frac{0.40(1-0.40)}{0}+\frac{0.52(1-0.52)}{40}}}[/tex]

=> z = -1.00561

Here [tex]\hat p_1 > \hat p_2[/tex]

=> [tex]\hat p_1 - \hat p_2 > 0[/tex]

Then , P(x<z) = 0.1573.

Hence  the prοbability that the prοpοrtiοn οf red marbles in the sample frοm bin a is greater than the prοpοrtiοn οf red marbles frοm bin b is 0.1573.

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The Practice Operations with radical expressions is simplified using the basic of the Algebra:

Algebraic expressions incorporating radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root might be an nth root, a square root, or a cube root. Radical expressions can be made simpler by taking them down to their most basic form and, if feasible, getting rid of all of the radicals.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. An algebraic expression's numerator and denominator are multiplied by the appropriate radical expression if the denominator contains a radical expression.

Practice Operations with radical expressions are:

1) [tex]\sqrt{540}[/tex] = [tex]\sqrt{36 * 15 }[/tex]

= 6√15

2) [tex]\sqrt[3]{432}[/tex] = [tex]\sqrt[3]{216*2}[/tex]

= [tex]6\sqrt[3]{2}[/tex]

3) [tex]\sqrt[3]{128}[/tex] = [tex]\sqrt[3]{64*2}[/tex]

= [tex]4\sqrt[3]{2}[/tex]

4) [tex]-\sqrt[4]{405}[/tex] = [tex]-\sqrt[4]{81*5}[/tex]

= [tex]-3\sqrt[4]{5}[/tex]

5) [tex]\sqrt[3]{-5000}[/tex] = [tex]-\sqrt[3]{1000*5}[/tex]

= [tex]-10\sqrt[3]{5}[/tex]

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For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?

Answer: find an alength times a weight

Step-by-step explanation:

What is the Area of a Rectangle?

a Definition: The area of the rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area. But in the case of a square, since all the sides are equal, therefore, the size of the court will be equal to the court of side length.

the

1. Find the length of the rectangle. In most cases, you will be given the length; if not, you can find it using a ruler.

Note that the double hash marks on the long sides of the rectangle mean that the lengths of the two sides are the same.

2. Find the width of the rectangle. Use the same methods to find it.

Note that the single hash marks on the wide sides of the rectangle mean that the two widths have equal lengths.

3. Write the length and width next to each other. In this example, the length is 5 cm and the width is 4 cm.

4. Multiply the length times the width. Your length is 5 cm and your width is 4 cm, so you should plug them into the equation A = L * W to find the area.

A = 4 cm * 5 cm

A = 20 cm^2

5. State your answer in square units. Your final answer is 20 cm^2, which means "twenty centimeters squared.

You can write your final answer in one of two ways: either 20 cm. sq. or 20 cm^2.

a) The residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

b) the equation y = 2x + 3 may not be a good fit for the given data.

What is the linear equation?

A linear equation is an equation that describes a straight line in a two-dimensional space. It is a mathematical expression that relates two variables, usually x and y, such that one variable is a function of the other. The general form of a linear equation is:

y = mx + b

a. To calculate the residuals, we need to find the predicted values of y using the given equation and then subtract them from the actual values of y.

For x = 1, y = 2(1) + 3 = 5, residual = 5 - 5 = 0

For x = 2, y = 2(2) + 3 = 7, residual = 8 - 7 = 1

For x = 3, y = 2(3) + 3 = 9, residual = 4 - 9 = -5

For x = 4, y = 2(4) + 3 = 11, residual = 5 - 11 = -6

For x = 5, y = 2(5) + 3 = 13, residual = 6 - 13 = -7

For x = 6, y = 2(6) + 3 = 15, residual = 16 - 15 = 1

For x = 10, y = 2(10) + 3 = 23, residual = 11 - 23 = -12

So, the residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

We can plot these points (x, residual) on a scatter plot.

b. The points on the scatter plot show a random pattern, which suggests that the model may not be a good fit.

The negative residuals for x = 3, 4, and 5 indicate that the actual values of y are lower than the predicted values, while the large negative residual for x = 10 indicates a much larger error.

Additionally, the residual for x = 6 is positive, which means the actual value of y is higher than the predicted value.

Therefore, the model may not be a good fit for the given data.

The points (1, 0), (2, 1), (3, -5), (4, -6), (5, -7), (6, 1), and (10, -12) show a random pattern on the scatter plot, which suggests that the model may not be a good fit.

Thus, the equation y = 2x + 3 may not be a good fit for the given data.

Hence, a) the residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

b) the equation y = 2x + 3 may not be a good fit for the given data.

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Step-by-step explanation:

Box volume = 2880  cm^3    <=====correct

Cylinder volume = pi * r^2 * h = 3.14 * (6^2) (20) = 2260.8 cm^3

                 (radius, r = 1/2 diameter = 6 cm)

Box can hold this much more:  2880 - 2260.8 = 619.2 cm^3

Answer and explanation:

Background info:

y = mx + b, where,

 If we look at the y-values in the table, we see that 4 ounces is added each time (16 + 4 = 20 + 4 = 24...).  Similarly, if we look at the x-values in the table, we see that 0.5 hours is added each time (0 + 0.5 = 0.5 + 0.5 = 1 ...).

Therefore, since the change in y is 4 (oz) and the change in x is 0.5 (hr), we divide 4 by 0.5 to find the slope:

4 / 0.5 = 8 = m

As we can see on the table, when x is 0, y = 16.  Thus, 16 is our y-intercept.

Thus, the general equation for the table is y = 8x + 16

Interpreting the slope and y-intercept:  When we consider our units, slope in context of this problem is change in ounces / change in hours.  We can think of 8 as the fraction 8 over 1.  

Table B has inputs 6, 7, and 8, and each input has a unique output, so table B does represent a function.

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range) with the property that each input is related to exactly one output. Functions are used to model various real-world situations, from the growth of populations to the movement of celestial bodies. They play a central role in many areas of mathematics, including calculus, differential equations, and number theory. Functions are often represented using equations, graphs, and tables, and are studied in depth in the field of mathematical analysis.

Here,

A function is a relationship between an input set (usually called the domain) and an output set (usually called the range) such that for each input, there is exactly one output. To determine if a table represents a function, we need to check if each input has only one corresponding output.

Table A has inputs 1, 2, 3, and 4, but the output for input 2 is 9 and the output for input 3 is also 9. Therefore, table A does not represent a function.

Table B has inputs 6, 7, and 8, and each input has a unique output, so table B does represent a function.

Therefore, only table B represents a function, and the answer is "Only B".

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In terms of journey times, Bus 14 is more reliable than Bus 47, as seen by its lower IQR and narrower range of travel times based on the line plot.

We must examine the data's variability to ascertain which bus is the most reliable. The interquartile range (IQR), which is the range of the middle 50% of the data, is one way to measure variability.

The line plot for Bus 47 reveals a range of trip times of 4 to 28 minutes, with an IQR of 8 minutes (from 10 to 18 minutes). This reflects a reasonable degree of consistency in journey times, as it shows that half of the students on Bus 47 have trip times that are within 8 minutes of one another.

With an IQR of six minutes, the line plot for Bus 14 reveals a travel time range of 8 to 28 minutes (from 14 to 20 minutes). This demonstrates that journey times on Bus 14 are more consistent than on Bus 47, with half of the students' travel times being within 6 minutes of one another.

We may also have a look at the data range, which is the range of numbers between the maximum and minimum. Bus 14 has a range of 20 minutes, while Bus 47 has a range of 24 minutes (from 4 to 28 minutes) (from 8 to 28 minutes). The conclusion that Bus 14 is more reliable is further supported by the suggestion that its range of travel times is lower.

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The quadratic equation 2x^2 - x + 10 = 0 can be solved using the quadratic formula, which is:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Here, a = 2, b = -1, and c = 10. Substituting these values, we get:

x = [-(-1) ± sqrt((-1)^2 - 4(2)(10))] / 2(2)

x = [1 ± sqrt(1 - 80)] / 4

x = [1 ± sqrt(-79)] / 4

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is "No solution".

Mr. Nelson took 35 students on the trip.

The equation that can be used to solve this problem is:

100 + 6.50n = 327.50

Where n is the number of students. To solve this equation, we need to subtract 100 from both sides of the equation:

6.50n = 227.50

Next, we need to divide both sides by 6.50:

n = 35

Therefore, Mr. Nelson took 35 students on the trip.

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Using graphs, the measure of the angle XYZ after the rotation on the coordinate plane about its origin is option E, 150°.

An ordered set of facts or values is shown visually in a graph, which is a diagram in mathematics. Often, the points on a graph serve as a representation of the relationships between two or more things.

An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. The numerical information gleaned via observation is referred to as data.

The Latin word Datum, which means "something delivered," is where the word data originated originates.

Following the formulation of a study question, data are continuously gathered through observation. The information is subsequently categorised, organised, and visually portrayed.

Here in the question,

When the given angle of 60° is rotated 90° on its origin:

The angle created = 60+90 = 150°

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Answer:

82.8 in.

Step-by-step explanation:

Keelin's hourly rate increased by 7.89%. To calculate the percentage increase in Keelin's hourly rate, we need to determine the difference between the new and old rates and express that difference as a percentage of the old rate.

First, we find the difference between the two rates:

$10.25 - $9.50 = $0.75

This means that Keelin's hourly rate increased by $0.75 per hour.

Next, we need to express this increase as a percentage of the old rate:

($0.75 / $9.50) x 100% = 7.89%

Therefore, Keelin's hourly rate increased by 7.89%.

A percent increase is a measure of the increase in a quantity compared to the original value. In this case, the original value is Keelin's hourly rate of $9.50, and the new value is $10.25. The percentage increase is calculated by finding the difference between the new and old values and expressing that difference as a percentage of the original value.

A percentage increase is useful in analyzing changes over time or comparing changes in different variables. In this case, knowing the percentage increase in Keelin's hourly rate can help her understand how much her pay has increased and plan for future financial goals. It can also be helpful for an employer to calculate percentage increases in employee salaries when determining raises or promotions.

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The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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The volume of the region outside the cone phi = pi /4 and inside the sphere rho = 4 cos phi. The volume is 63.717

The limits of integration for ρ are 0 and 4 cos∅, since the sphere has a radius of 4 cos phi. The limits for phi are π/4 and π/2 because we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of the point. Finally, the limits for theta are 0 and 2π because theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.

The volume of the region is therefore given by:

V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos∅) ρ²

Simplifying the integral using the base number, we get:

V = 8 x (64/3 - 16/3√2π) = 63.717

Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere ρ = 4 cos∅ is 8 (64/3 - 16/3√2π), which is the exact answer using π as needed.

Complete Question:

Use spherical coordinates to find the volume of the region outside the cone phi = pi /4 and inside the sphere rho = 4 cos phi. The volume is?

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The match can be scheduled in 900 different ways.

Here, the number of players from each school = 3.

Let us assue that the players of the first school be A, B, and C.

And the players of the second school be X, Y, and Z.

Here, each player from the first school has to play twice with each player from the second school.

We can organize the schedule into six different rounds, i.e.,

R1 : AX BY CZ

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BY CX

So, the number of possible ways to do this would be : 6! = 720 ways.

Now, three rounds are played simultaneously in each round.

R1 : AX BZ CY

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BX CZ

R5 : AZ BY CX

R6 : AZ BY CX

And R1 : AX BY CZ

R2 : AX BY CZ

R3 : AY BZ CX

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BX CY

The total number of possible ways for the second case would be twice of  6! / (2! 2! 2!), which is equal to 90+ 90 = 180.

Therefore, the total number of ways in which the match can be scheduled is 720 + 180 = 900.

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The complete question is:

central high school is competing against northern high school in a backgammon match. each school has three players, and the contest rules require that each player play two games against each of the other school's players. the match takes place in six rounds, with three games played simultaneously in each round. in how many different ways can the match be scheduled?

The equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

To find the equation of the line passing through the two given points (–6, 1) and (6, –9) in slope-intercept form, we need to first find the slope of the line.

The slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]

Substituting the values of the given points, we get:

m = (-9 - 1) / (6 - (-6))

m = -10 / 12

m = -5 / 6

Now that we know the slope of the line, we can use the point-slope form of the equation of a line to find its slope-intercept form. The point-slope form of a line passing through a point [tex](x_1, y_1)[/tex] with slope m is given by:

[tex]y - y_1 = m(x - x_1)[/tex]

Substituting the values of the slope and one of the given points (–6, 1), we get:

y - 1 = (-5 / 6)(x - (-6))

y - 1 = (-5 / 6)(x + 6)

Simplifying this equation, we get:

y = (-5 / 6)x - 1/6

Therefore, the equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

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The best unit of measure for the liquid in family-sized container of apple cider is the liter - True.

The metric unit of volume is known as the litre (international spelling) or liter (American English spelling) (SI symbols L and l,[1] with another symbol also used: ℓ). It is equivalent to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3). A litre or cubic decimetre fills a space of 10 cm × 10 cm × 10 cm (see figure) and is therefore equal to one-thousandth of a cubic metre. One litre of liquid water has a weight of almost precisely one kilogram, because the kilogram was initially defined in 1795 as the weight of one cubic decimetre of water at the temperature of melting ice (0 °C). However, subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.

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Answer:

Step-by-step explanation: