The mass of a cube, M (kg), is
proportional to the cube of the length of
its edge, L (m).
The mass of the cube is 100 kg when
the length of its edge is 20 cm.
Work out L (to 2 DP) when M = 1900
kg

Thanks

Addition is commutative because the order in which two numbers are added does not affect the result.

Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers.

Addition is commutative because the order in which two numbers are added does not affect the result. For example, 1 + 2 = 2 + 1 = 3. In contrast, subtraction is not commutative because the order in which two numbers are subtracted does affect the result. For example, 1 - 2 = -1, but 2 - 1 = 1. The operation is different when the order of the numbers are changed.

so, addition is commutative because the order in which two numbers are added does not affect the result.

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This kind of evidence is an example of a claim. Hence, the correct answer is option 1.

A claim is a statement or assertion that is made about a particular topic or issue. In this case, the statement is being made by "doctors" and is being presented as evidence of a causal relationship between lack of sleep and negative health outcomes. The statement is not an argument, which would include reasoning or logic to support the claim, nor is it a testimony or excerpt, which would be a statement or quote from a specific person or source.

Option 2, "an argument," is incorrect because it suggests that reasoning or logic is being provided to support the claim. However, in the sentence provided, there is no indication that any reasoning or logic is being presented to support the claim that many people who do not get enough sleep each night suffer from illness and stress. Usually, an argument has a claim and evidence or reasoning to back up that claim.

Option 3, "a testimony or an excerpt," is incorrect because it suggests that a statement or quote is being provided from a specific person or source. However, in the sentence provided, there is no indication of a specific person or source providing the statement. Instead, the statement is being attributed to "doctors" in general rather than any specific individual. A testimony would typically include a statement or quote from a specific person or source, given under oath or affirmation in a formal legal setting.

This question should be provided as:

Use the sentence to answer the question. Most doctors say many people who don't get enough sleep every night struggle with illness and stress. Which kind of evidence is this an example of? Responses:

 The correct answer is option 1.

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The complete table to find all the factor pairs of 50 is. First factor Second factor. 1 and 50. 2 and 25. 5 and 10.

The complete table to find all the factor pairs of 50 is

First factor    Second factor

1             and      50

2            and      25

5             and    10

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

How to find all the factor pairs of 50

From the question, we have the following parameters that can be used in our computation:

Factor pairs

The number is then given as

Number = 50

The given table of values is incomplete

So, we fill them one after the other

The number 50 can be expressed as

50 = 1 * 50

So, the factor pairs are 1 and 50

The number 50 can also be expressed as

50 = 2 * 25

So, the factor pairs are 2 and 25

Lastly, the number 50 can also be expressed as

50 = 5 * 10

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The equation for g(x) would be g(x) = 9cos(x-1) ^3 + 4.

This is because the function M(x) = 9cos(x)^3 represents a cosine function cubed, which results in a three-dimensional graph that oscillates and has multiple local maxima and minima. By translating the function one unit left, represented by the subtraction of 1 from the x value inside the cosine function, the entire graph is shifted one unit to the left.

The translation of 4 units up is represented by the addition of 4 to the overall function. This means that the entire graph of g(x) is now 4 units higher than the original function M(x).

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It depends on the specific nonlinear system of equations. Generally speaking, there could be one or multiple solutions, or there could be no solutions.

A nonlinear system is a system of equations or functions which does not yield a linear relationship or linear solution when solved. A nonlinear system is often difficult to solve due to its inherently complex nature. Nonlinear systems can be found in multiple areas, such as engineering, economics, and mathematics.

If the equations are linear, then there will be exactly one solution. If the equations are nonlinear, then there could be no solutions, one solution, or multiple solutions (including infinitely many solutions). To find the exact number of solutions, you would need to solve the system of equations.

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Answer:

They celebrated it on March 14 at 1:59 because...

The first few digits of pi are --- 3.14159

The date of March 14 is 3/14. Then you add the 1:59 it makes the first few digits of pi.

Step-by-step explanation:

The tradition to celebrate Pi Day on 14th March started in the late 80's, when the physicist Larry Shaw organized the first Pi Day celebration at the San Francisco Exploratorium. Since then, Pi Day has become a popular way for mathematicians, educators, and students to celebrate and share their interests in mathematics. Many schools, universities, and math clubs around the world host events, such as pi recitation contests, pi-themed games, and pie-eating contests, to celebrate this day.

Eating pie is also a way to join the celebration, as the word "pi" sounds like "pie". People often eat different types of pie on Pi Day, such as pizza pie, sweet pies, and savory pies to celebrate the mathematical constant pi and its connection to the word “pie”.

Answer:

124.29ft (approximately 125ft)

Step-by-step explanation:

Refer to the Image

The probability that you win first prize and your friend wins second

prize is option D: 13/2730.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Total number of prizes awarded = 3

Number of people entering the drawing competition = 15

Number of ways to award the prize = 2730

Out of the 3 prizes the first and the second is needed.

So, the prize for the first and the second positions are fixed and there is no need to consider the remaining 13 people to win the prize.

Hence the remaining number of people who can win the 3rd prize  = 13

The number of ways one of them wins the 3rd prize = 13

The total number of ways = 2730

Therefore, the probability of the first 2 prizes fixed and the remaining 3rd awarded to the rest of the 13 people is 13/2730.

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Answer:

-28

Step-by-step explanation:

f(-4) = 5(-4) - 2³ = -20 - 8 = -28

Different properties, significance of those properties and their applications in mathematics.

Associative property : Associative law states that the order of grouping the numbers does not matter. This law holds for addition and multiplication but it doesn’t hold for subtraction and division. This can be observed from the following examples.

Addition:

a+ (b+c) = (a+b) + c

Subtraction:

a-(b-c) ≠ (a-b) – c.

Multiplication:

a x (b x c) = (axb) x c

Division:

a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

Distributive property : This property is used to eliminate the brackets in an expression. The distributive property states that each term inside the bracket should be multiplied with the term outside. This property is very useful while simplifying the expressions and solving the complicated equations.

Addition:

a(b+c) = ab + ac

Subtraction :

a(b-c) = ab – ac

Commutative property : This property states that there is no change in result though the numbers in an expression are interchanged. Commutative property holds for addition and multiplication but not for subtraction and division.

Addition:

a+b = b+a.

Subtraction:

a-b ≠ b-a.

Multiplication:

a x b = b x a

Division:

a ÷ b ≠ b ÷ a.

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The equation Y = -2x + 3 is a linear equation in slope-intercept form.

This equation represents a straight line with a slope of -2 and a y-intercept of 3.

The slope -2 tells us that for every unit increase in x, the value of y will decrease by 2. The y-intercept 3 tells us that the line passes through the point (0,3) on the coordinate plane.

It's a line that goes down as the slope is negative and the line can be represented by a graph, that can be easily plotted using the slope and the y-intercept. This equation can be used to model real-world situations like linear regression and many other fields.

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The length of BC is 5.7 cm

A dot is used to symbolise a point, which is a place in any space (.). It does not have any size, shape, length, or height. A line segment has a beginning and an end, but a line is stretched in both directions towards infinity.

It is given that the length of AB is 8.6 cm and length of AD is 20 cm.

Also, BC=CD

As there are 4 points (A, B, C, D) on the line and the length of the lone is 20 cm, we     can say

AB+BC+CD= 20 --------------- (1)

Let us consider that BC=CD= x (say)

Substituting the values in equation (1),

8.6+ x+ x=20

Or, 2x =11.4

Or, x=11.4/2

Or, x=5.7 cm

Therefore, we can say that the length of BC is 5.7 cm.

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The price of the TV is £208.

given the initial price of the TV as  £260

now the  Percentage rebate on TV is 20%

so the rebate is given by

=> 20 /100 * 260

=> 2 *26

=> 52

so total off on the TV is  £52

Actual price of the TV is  £260 -  £52 = £208

An initial product or service price reduction that is expressed as a percentage of the original price is known as a percentage rebate. It is a technique for providing a discount or incentive to clients, and it is typically provided for a brief period of time or on particular goods or services. For instance, a 10% rebate on a product would entitle the buyer to a 10% discount off the list price.

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The angle of incline, of the target θ = 14.036.

The angle of elevation or depression can be calculated using the following formula: t a n = O A, where A is the horizontal distance between the observer and the point and O is the length of the side opposite the angle of elevation or depression, or the object's perpendicular distance from the horizontal line.

To calculate the slope percentage, multiply the result by 100 after dividing the height difference between two points by their separation. The rise is the height difference between two locations. The distance between the locations is known as the run. The result is that (rise / run) x 100 is equal to the percent slope.

Given,

the height of triangle = 12in

base of triangle = 48 in

tan θ = perpendicular / base

tanθ = 12/48

θ = tan ⁻¹( 12/48)

θ = 14.036

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Complete question -

To find out how many pages Van fills with his new baseball cards, we need to divide the total number of cards by the number of cards that fit on each page.

He has 45 baseball cards and each page holds 9 cards.

So, we can divide 45 by 9.

45 / 9 = 5

Therefore, Van fills 5 pages with his new baseball cards.

It's worth noting that this method gives the number of full pages that are filled and if there are any remaining cards, we have to add one more page for the remaining cards.

equation of a line : y=mx+b

Answer : y= -1x+2

Answer:

Step-by-step explanation:

-2(x-3)=-6(x+4)     [Original Equation]

-2x+6=-6x-24      [remove the parentheses]

?   -2x+6x+6 =-24   [add 6x to both sides]

   4x + 6 = -24      [combine like terms]

    -2x+6x+6=-6x-24+6x  [Add 6x to both sides]

    4x+6x+6=-6x-24+6x

    -2x+6x+6=-24    [Add 6x and subtract 6 from both sides]

    4x + 6 = -24     [This step is justified by the additive property of equality.]

x=-7.5

Which set of statements shows the equation that is

most likely the missing step and the property that

justifies the missing step?

4x-6=24

This step is justified by the additive property of equality

4x-6=24

This step is justified by the multiplicative property of equality

4x+6=-24

This step is justified by the multiplicative property of equality.

The correct answer is:

4x+6=-24

This step is justified by the additive property of equality.

Answer:

Step-by-step explanation:

180 degrees in total

The required solution to the given inequality is x > - 5.5 which means x is greater than -5.5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The statement is given as "twice x is greater than -11"

This can be in the algebraic form written as :

2x > - 11

Divided both sides of the above inequality, we get

x > - 11/2

x > - 5.5

Thus, the required solution to the given inequality is x > - 5.5.

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The question seems incomplete, the complete question would be as:

What is the solution to the inequality that represents twice x is greater than -11?

Answer:

≈ 0.17

Step-by-step explanation:

1/6 ≈ 0.17

The given equations do not represent a par of coincident lines. As the equations do not satisfy the conditions.

It is given that the pair of equations are,

4x + 3y - 1 = 5 and 12x + 9y = 15

To determine if the equations represent a pair of coincident lines.

Here we get, a₁ = 4, b₁ = 3, c₁ = -1

a₂ = 12, b₂ = 9, c₂ = -15

So, a₁/a₂ = 4/12 = 3

b₁/b₂ = 3/9 = 3

c₁/c₂ = -1/-15 = 1/15

Therefore,

[tex] \frac{a1}{a2} = \frac{b1}{b2}≠ \frac{c1}{c2} [/tex]

Thus, the given equations do not represent a pair of coincident lines

Now, if you put these equations in any graphing software or here I have used Desmos then you will get the graph (attached image), which further shows that the lines do not coincide.

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The cost of the carpet is $526.75

What is the area of any shape?

The area of a shape is a measure of the size of the region occupied by the shape. The formula for finding the area of a shape depends on the specific shape being considered

Based on the information given:

The carpet costs $1.75 per square foot

Get the area of the carpet

Area = 24(7) + 7(15) + 0.5(28) + 0.5(28)

Area of the composite figure = 273 + 28

Area of the composite figure = 301 ft²

Cost of the carpet = 301 * 1.75

Cost of the carpet = $526.75

Hence, the cost of the carpet is $526.75

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Answer:  the Coat is $526.75

Jasmine will make $61000 annually in 2019.

A percent increase refers to how much a percentage has gone up over time.

Given that, Jasmine started a new job in 2010 with an annual salary of $38,000, her salary increases by 5.4% each year,

We know that, percentage of increase =

A = P(1+r)ⁿ

A = Final amount

P = Initial amount

r = rate

n = time

Here, A = ?

P = 38000

Time = 2019 - 2010 = 9

r = 5.4% = 0.054

A = 38000(1+0.054)⁹

A = 38000(1.054)⁹

A = 61002.7053

A ≈ 61000

Hence, Jasmine will make $61000 annually in 2019.

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Answer:

17

Step-by-step explanation:

67 minus 33 leaves 34 red bikes but divided that by half gives you 17

Answer: Area = 28.3cm²

               Circumference =  18.9cm

Step-by-step explanation:

Area = πr²

        = π × 3²

        = 28.27

        = 28.3cm² (estimate to 3s.f always)

Circumference = 2πr

                          = 2 x π x 3

                          = 18.85

                          = 18.9cm (estimate to 3s.f always)

The area and the circumferences of the circle are 28.27 square meters and 18.85 meters.

Given is a circle with radius 3m we need to determine the area and the circumferences of the circle,

To determine the area and circumference of a circle with a radius of 3m, we can use the following formulas:

Area of a circle: A = πr²

Circumference of a circle: C = 2πr

Here, "r" represents the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14159.

Let's calculate the values:

Area:

A = πr²

A = 3.14159 x (3m)²

A = 3.14159 x 9m²

A ≈ 28.27 square meters

Therefore, the area of the circle is approximately 28.27 square meters.

Circumference:

C = 2πr

C = 2 x 3.14159 x 3m

C ≈ 18.85 meters

Therefore, the circumference of the circle is approximately 18.85 meters.

Hence the area and the circumferences of the circle are 28.27 square meters and 18.85 meters.

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A 45 degree angle is called an acute angle

There are 5 types of angles according to their measure:

1) Acute angle: it is the one that measures more than 0° and less than 90°.

2) Right angle: an angle that measures 90°.

3) Obtuse angle: an angle measuring more than 90° and less than 180°.

4) Extended angle: an angle measuring 180°.

5) Complete angle: an angle that measures 360°.

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

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The solution to the system of equations y 3x 2 5x 2y 15 40 19 is ( -19,55)

A solution of the system is any collection of x 1, x 2, x 2,... x n values that simultaneously satisfies the system of linear equations presented above. The equations are referred to as consistent if the system of equations has one or more solutions.

It can be written as-

y= -3x-2

=> 3x+y= -2...................(1)

5x+2y = 15.....................(2)

multiplying Eqn (1) by 2 and

removing from equation (2)

x= -19

replacing x with -19 in equation (1)

3×(-19) +y= -2

y = 55

Consequently, the lines indicated by the

Equations given intersect at (-19, 55).

The resolution of an equation system

= ( -19,55)

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Answer: (5y+6)/2

Step-by-step explanation:

Mariela spends $50 on a used microwave. By 60%, she raises the price. When a 5.8% sales tax is additionally included, the ultimate cost is 20 in 60% and 47.1 in 5.8%.

Cost plus markup % multiplied by cost is the formula used to increase a product's markup percentage. Let's say you're utilising a markup of 60% and the item costs $75. multiplying by 60 percent $75. Now you have $45. For instance, the markup percentage would be 50% if the cost to produce your product was $50 and the selling price was                      $75: ($75 - $50) / $50 =.50 × 100=50%.

0.6 is 60 hundredths of a unit, thus write it as 0.60. 60% is equal to 60 hundredths. The decimal point can alternatively be shifted two places to the right to find the % equivalent. As a result, the markup equation is now: markup = 100 × (revenue - cost) / cost. Last but not least, use revenue = cost + cost × markup / 100 to determine the selling price.

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