Melanie pumps 4 in. of water every 4 hours

Melanie pumps 8 in. of water every 4 hours

Melanie pumps 0.5 in. of water every hour

Melanie pumps 14 in. of water every 7 hours

The value of the hypotenuse y = 9, and the value of the opposite side of the right angle triangle x = 4.5

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle 30° in the right angle triangle, the hypotenuse is y, the opposite side is x and the adjacent side is 9√3

cos 30° = √3 = adjacent/hypotenuse

sin 30° = 1/2 = opposite/hypotenuse

√3 = 9√3/y {cross multiply}

y = 9√3/√3 {cancel out √3}

y = 9

1/2 = x/9 {cross multiply}

x = 9/2

x = 4.5

Therefore, by proper application of trigonometric ratios for the right angle triangle, the hypotenuse y is equal to 9 and the opposite side x is equal to 4.5.

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Answer:2

Step-by-step explanation:

Answer:

s>1/6

Step-by-step explanation:

6s+5>6

6-5=1

6s=1

s>1/6

I graphed it on desmos just to be sure and the original inequality and the solution is the same.

hope this helps :)

Answer:

X =56

Step-by-step explanation:

Total angles of a triangle = 180

Since it's the total, we add these three angles

[tex](x - 31) + (x) + (x + 43) = 180[/tex]

Next, we combine like terms

[tex]3x + 12 = 180[/tex]

Next, you can subtract 12 from both sides to get numbers on one side

[tex]3x = 168[/tex]

Last step is to divide by 3 to get the X alone

[tex]x = 56[/tex]

Answer:  

x = 56

F = 25

R = 99

O = 56

Step-by-step explanation:

all triangles equal 180 degrees

that means that when you add angle F, O, + R, you will get 180

create the formula based on this info:

F + R + O = 180

x - 31  + x + 43 + x = 180

solve:

-31+43+x+x+x = 180

12 + 3x = 180

3x = 168

x = 56

now plug in x and find each angle

F = x - 31

F = 56 - 31

F = 25

R = x + 43

R = 56 + 43

R = 99

O = x

O = 56

someone who orders a product through a catalog is responding to Direct marketing.

The act of presenting an offer directly to a target client and providing them with a way to respond immediately is known as direct marketing. It is sometimes referred to as direct response marketing among practitioners. Advertising, in contrast, is a form of mass messaging.

Any form of marketing that communicates or distributes to consumers directly, as opposed to through a third party, is considered direct marketing.

Businesses employ the catalog marketing strategy to combine a variety of products in a single printed piece or online store in the hopes that the recipient would purchase at least one item. Using the information in the catalog, customers make direct purchases from the catalog sender through phone, return mail, or online.

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The snapshot graph of the wave at t=0s is a graph of the displacement of the wave along the x-axis at time t=0s.

It is a graph of the wave's initial position, which is usually a sinusoidal graph with a maximum value at the center and decreasing values as x increases. This is because the wave is traveling from left to right and its amplitude decreases as it moves further from its source. To explain in more detail, a sinusoidal wave is a wave that oscillates up and down in a regular pattern.

The snapshot graph at t=0s will show the wave at its highest point, which is the amplitude of the wave. As the wave moves along the x-axis, its amplitude will decrease as it moves further from its source. The graph will also show the wave's wavelength, which is the distance between two successive crests or troughs.

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Simplifying rational and polynomial expressions are similar in that they both involve combining like terms and reducing the expression to its simplest form.

A rational expression is a fraction in which the numerator and denominator are both polynomials. A polynomial is an expression made up of variables and constants, where the variables are raised to a non-negative integer power.

Here's an example of simplifying a rational expression:

Example: Simplify the rational expression (x^2 + 2x + 1) / (x + 1)

To simplify this rational expression, we can use the technique of factoring the numerator and denominator, then cancelling out any common factors.

First, we factor the numerator: x^2 + 2x + 1 = (x + 1)^2

Then we factor the denominator: x + 1 = (x + 1)

Since the numerator and denominator have a common factor of (x + 1), we can cancel it out: (x + 1)^2 / (x + 1) = x + 1

So the simplified form of the original rational expression is x + 1

In summary, the main similarity between simplifying rational and polynomial expressions is that both involve combining like terms and reducing the expression to its simplest form. The main difference is that a rational expression is a fraction in which the numerator and denominator are both polynomials while a polynomial is an expression made up of variables and constants, where the variables are raised to a non-negative integer power.

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The value of x is 13 / 2 which satisfies the equation "-3 (4x - 5 ) = 2( 1 - 5x)".

In order to determine the value of x that satisfies the equation, we need to solve the equation and find the value of x,

Now solving

the given equation,

-3 (4x - 5 ) = 2( 1 - 5x)

(- 12 x + 15 ) = ( 2  - 10 x)

Shifting the constant terms to one side of the equation and terms having the variable x are kept to another side of the equation.

So,

- 12 x + 10 x =  - 15 + 2

 - 2 x =  -  13

  x = - 13/ - 2

  x = 13 / 2

The value of x is 13 / 2 which satisfies the given equation.

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If you're given a false equation and you multiply both sides by the same non-zero number, the resulting equation will also be a false equation.

If you're given a false equation and you multiply both sides by the same non-zero number, the resulting equation will also be a false equation.

This is because the equation was already unbalanced, and multiplying both sides by the same non-zero number does not change that.

For example, consider the equation 2 + 3 = 6. This is a false equation. If we multiply both sides by 2, we get:

(2 + 3) × 2 = 6 × 2

4 + 6 = 12

The resulting equation 4 + 6 = 12 is also a false equation.

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The mass of mercury II oxide must decompose to form 3.00L of oxygen at 30°c and 0.890atm is 0.010 mole.

A body's mass is an inherent quality. Before the discovery of the atom and particle, it was widely considered to be tied to the amount of matter in a physical body.

A thing's mass is how much matter it has. Something will weigh more the more matter it contains. For instance, an elephant weighs more than a mouse because it contains more stuff.

By an ideal gas equation,

PV = nRT

0.890 × 3 = n × 8.314 × 30

n = 0.890 × 3 ÷ 8.314 × 30

n = 2.67 ÷ 249.42

n = 0.010 M

Thus, The mass of mercury II oxide must decompose to form 3.00L of oxygen at 30°c and 0.890atm is 0.010 mole.

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Using leaner equation we find that After 12 years from now will Jerry's age be (2/3) of the combined ages of his brother and sister at that time.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Let Jerry's brother present age be X years,

Then Jerry's present age will be 2x

And his sister's present age will be 2X - 6

And let y be  the  number of years from now when Jerry's age = (2/3) of combined age of his brother and sister.

So we have that,

(2X + y)  = (2/3) [(X + y) + (2X - 6 + x)]

simplify the above equation

2X + y = (2/3) [3X + 2y - 6]

multiply through by 3/2

3X + (3/2)y = 3X + 2y - 6

subtract  3X from both sides

(3/2)y = 2y - 6

subtract 2y from both sides

-1/2y = -6

divide both sides by -1/2

y = 12 years

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The analyst appears to have done a thorough and careful job developing a predictive model.

Predictive modeling is the process of creating, processing, and validating a model that can be used to estimate future outcomes using known results.

It seems that the analyst has done a thorough and careful job in developing a predictive model.

By using a large data set and randomly dividing it into training and validation subsets, the analyst has ensured that the model is well-calibrated and does not overfit to the training data.

Additionally, by trying multiple models and evaluating their performance on the validation data, the analyst has been able to identify the model that performs the best on unseen data.

Overall, these are good practices for developing a predictive model and improving its accuracy.

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The function is expanding to the right of x = 3.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

Given graph of a quadratic function,

to find where function is increasing,

The maximum value or minimum value of a quadratic function are located at its vertex, which is shaped like a U. The quadratic function's axis of symmetry crosses the function (a parabola) at its vertex.

here vertex  is at x = 3,

the increasing and decreasing of graph is shown by vertex,

the shape of curve is parabola so,

In parabolas, the rate of increase (the slope or rate of change) isn't consistent. If the parabola opens up, it will increase as you move towards the right; if the parabola opens down, it will decrease.

The function is increasing to the right side of 3

The parabola's apex can be found at (3, 2) Therefore, all real numbers make up the domain, and the range is y ≥  2. As can be seen in the figure, the function is expanding to the right of x = 3 and contracting to the left of x = 3

Hence the function is increasing to right at x = 3.

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To find the area of the region enclosed by the graphs of f(x) = x - 2x^2 and g(x) = -5x, we need to find the points where the two graphs intersect and then use those points to find the area of the region between the two graphs.

An explanation graph is what?

A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.

We can find the points of intersection by setting the two functions equal to each other and solving for x:

x - 2x^2 = -5x

2x^2 + 5x - x = 0

2x(x+5) -1(x+5) = 0

(2x-1)(x+5) = 0

x = 1/2 or x = -5

The solution x = -5 is extraneous as it does not give a valid value for the x-coordinate of the point of intersection.

So, x = 1/2 is the valid solution.

So the two graphs intersect at (1/2, 1/4)

Now, we can find the area of the region enclosed by the two graphs by finding the definite integral of the function f(x) - g(x) with respect to x, where the definite integral is taken between the points of intersection x= -5 and x=1/2

So, the definite integral of (x-2x^2)-(-5x) with respect to x, between x = -5 and x =1/2 is:

∫[(x-2x^2)-(-5x)]dx = ∫(x-2x^2+5x)dx = ∫(3x-2x^2)dx between -5 and 1/2

= [x^2-2/3x^3] between -5 and 1/2

= (1/2)^2 - 2/3(1/2)^3 - (-5)^2 + 2/3(-5)^3

= 1/4 - 2/24 - 25 + 2/3*125/27

= 1/4 - 1/12 + 5/3

= (12-3+40)/12 = 49/12

So the area of the region enclosed by the graphs is 49/12 square units.

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Answer:

(-2.25, -0.5)

or (-2 1/4, -1/2)

or (-9/4, -1/2)

Step-by-step explanation:

The difference in x coordinate between point a and point b is 9 and y coordinate is 2.

Point a is lower and point b is higher, which means we need to multiply the difference between the coordinate x and y by 1/4 plus the coordinate of point a because pointt p is on the 1/4 segment a to b.

9 * 1/4 = 9/4 = 2.25

2 * 1/4 = 2/4 = 0.5

point a has the coordinate of ( -5, -1 )

-5 + 2.25 = -2.25

-1 + 0.5 = -0.5

the new coordinate should be (-2.25, -0.5)

or (-2 1/4, -1/2)

or (-9/4, -1/2)

Answer:

Option C. - (negative eleven-fourths, negative one-half)

Step-by-step explanation: edg 2023

Answer:

You have to first convert them to improper fractions, by multiplying the whole with the denominator (bottom number). And then you add the answer with the numerator (top number). This answer is then the numerator of the improper fraction, and the denominator remains the same. Then you add the two improper fractions. If the denominators are different, you find the lowest common multiple (LCM) of the denominators and multiply both the numerator and denominator so that the new denominator is the lowest common multiple. Then you add the numerators and keep the denominator the same

Example:

5[tex]\frac{3}{6}[/tex] + 3[tex]\frac{3}{4}[/tex]

5[tex]\frac{3}{6}[/tex]

= 5 x 6 = 30

= 30 + 3 = 33

= [tex]\frac{33}{6}[/tex]

3[tex]\frac{3}{4}[/tex]

= 3 x 4 = 12

= 12 + 3 = 15

= [tex]\frac{15}{4}[/tex]

[tex]\frac{33}{6}[/tex] +    [tex]\frac{15}{4}[/tex]

LCM of 6 and 4 is 12

[tex]\frac{33}{6}[/tex]

= 33 x 2 and 6 x 2

= 66 and 12

= [tex]\frac{66}{12}[/tex]

     [tex]\frac{15}{4}[/tex]

= 15 x 3 and 4 x 3

= 45 and 12

= [tex]\frac{45}{12}[/tex]

[tex]\frac{66}{12}[/tex] +  [tex]\frac{45}{12}[/tex] = [tex]\frac{111}{12}[/tex]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 1/3 and that it passes through (-6 , 8)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -8= \cfrac{1}{3} (x +6) \\\\\\ y-8=\cfrac{1}{3}x+2\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+10 \end{array}}[/tex]

The constant of proportionality between 'y' and 'x' in the graph is 0.20

The constant of proportionality of a proportional relationship between two variables, x and y, can be defined as the ratio of y to x, which is expressed as, k = y/x, where x and y are the coordinates of one point one the line that represents the proportional relationship.

When two quantities are directly proportional, then a percentage increase in one of the quantities that will result in an equal percentage increase in the other quantity, and the two quantities are therefore, increasing at the same rate to each other.

Using the coordinates of a point on the graph, (5, 1), find the constant of proportionality, k:

Constant of proportionality (k) = y/x = 1/5

Constant of proportionality (k) = 0.20

Therefore, the constant of proportionality that represents the proportional relationship between the variables, x and y, is calculated as, 0.20.

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Answer:

the second one and the last one

The Quadratic Formula is a formula that is used to find the roots of a quadratic equation.

The roots of an equation are the points where the graph of the equation intersects the x-axis. To find a complex root of an equation, you need to find the points where the graph of the equation intersects the x-axis

To find a complex root of an equation, you need to find the points where the graph of the equation intersects the x-axis. To do this, you can use the Quadratic Formula.

The Quadratic Formula is a formula that is used to find the roots of a quadratic equation. A quadratic equation is an equation that has the form ax^2 + bx + c = 0. The Quadratic Formula is:

x = -b +/- sqrt(b^2 - 4ac)/2a

To use the Quadratic Formula, you need to plug in the values of a, b, and c. Once you have plugged in the values, you will need to solve the equation. The roots of the equation are the points where the graph of the equation intersects the x-axis.

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Answer:

The slope is 4.

Step-by-step explanation:

y=mx+b says that m is the slope and b is the y intercept. So this means slope=4 and int = 8.

Answer: 4

Step-by-step explanation:

        This question is given to us in slope-intercept form. This is written as y = mx + b. The slope is the m variable, y = mx + b.

        Using the equation given, the slope is;

                 y = 4x + 8 ➜ m = 4

The acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

We have a table that gives the values of mass, acceleration and force of object A and object B.

We have to find by how many times greater must the acceleration of Object B be than the acceleration of Object A to make the table true.

The formula to calculate the force is -

F = m x a

From the table,

Mass = 40 Kg

Force = 1800 N

By substitution

a =F/m  = 1800/40  = 45 m/s²

The acceleration of Object A is 9m/s² .  On comparing the acceleration of both the objects, we can see that the acceleration of Object B is 5 times the acceleration of Object A.

Hence, the acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

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The value of x is 6, f(x) an absolute minimum is (5, -16, 328.4475).

The derivative of f is  [tex]$& f(x)=e^x\left(-x^3+3 x\right)-3[/tex]

[tex]& f(x)=-e^x x^3+3 x e^x-3\end{aligned}$$[/tex]

Domain for: [tex]$0 \leq x \leq 5$[/tex] is [0,5]

[tex]$& \frac{d}{d x}[f(x)]=\frac{d}{d x}\left[-e^x x^3\right]+\frac{d}{d x}\left[3 x e^x\right]+\frac{d}{d x}[-3] \\$$[/tex]

[tex]\\& f^{\prime}(x)=\left(-e^x\right)\left(3 x^2\right)+\left(x^3\right)\left(-e^x\right) \\& +(3 x)\left(e^x\right)+\left(e^x\right)(3)+0 \\\\[/tex]

[tex]& f^{\prime}(x)=-3 x^2 e^x-x^3 e^x+3 x e^x+3 e^x \\[/tex]

[tex]& f^{\prime}(x)=e^x\left[-x^3-3 x^2+3 x+3\right]\end{aligned}$$[/tex]

Set the first derivative equal to zero and

solve for x to find the critical number.

[tex]$$-x^3-3 x^2+3 x+3=0$$[/tex]

x=-3.601679 (outside of the domain) not valid here

x=-0.6601231 (outside of the domain) not valid here

x=1.2618022 ... TEST this one

Now to find the absolute extremes, test the critical numbers and the endpoints by plugging their x-values back into the f (x) function to find their y - value.

Testing x = 0

x = 1.2618022

x = 5

Finding their y-values:

[tex]& f(0)=e^0\left[-(0)^3+3(0)\right]-3=0-3=-3 \\\\& f(1.2618022)=e^{1.2618022} \cdot\left[-(1.2618022)^3+3(1.2618\right. \\\\& f(1.2618022)=3.273978192[/tex]...Highest y-value.

absolute maximum: (1.2618022,3.273978192)

Where x==1.2618022

[tex]& f(5)=-e^5(5)^3+3(5) e^5-3 \\\\ f(5)=-125 e^5+15 e^5-3 \\\\& f(5)=-110 e^5-3=-16,328.4475 \\[/tex]

absolute minimum: (5, -16, 328.4475)

where x = 5.

Therefore, the absolute minimum of F(x) is (5, -16, 328.4475) and x is 5.

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The equation the line is, x+2y=2

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (-6,4) and, (2,0)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y-4)/(x+6)=(0-4)/(2+6)

=>-2y+8=x+6

=>x+2y=2

Hence, the required equation is,  x+2y=2

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Answer: The correct options are:

1. Significantly different from

1. Inconsistent

Sales Data for Midwest:

Midwest region total stores Sales equal to 63.1%. The percentage for a current store is less than the total stores therefore data in the given table is not consistent. The data given is relatively for the first month's sales and is significantly different from the other stores.

Step-by-step explanation:

Answer:

The estimate of ^50 to the nearest tenth is 7.1. The two perfect squares closest to 50, one greater than 50 and less than 50, are 49 and 64. The square roots of 49 and 64 are 7 and 8, respectively.

Answer:

a) 4

b) 8

Step-by-step expla nation:

a) 3.2 ÷ 0.8 = 4

b) 7.5 + 0.5 = 8

The volume of the 95% solution that we need is 390 mL.

We are told that we have in the solution that we have;

We have also been told that we are trying to make a solution that would contain a known volume of 60% alcohol solution

Given the mixture of the solutions that we have, we can write;

(455 * 0.3) + (0.95 * x) = (0.60 * x)

x is the unknown volume that we are looking for

136.5 + 0.95x = 0.6x

x = 390 mL

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Hence proved that  (a − b) − c = (a − c) − (b − c). Intuitively, since   (a − b) − c is what you get by removing elements of  c  from  a-b , you can also remove elements of  c  from  a  and  b  prior to do the set difference.

Sets  are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.

Let  U=a ∪ b ∪ c  and let’s denote by  X′  the complement of  X  with respect to  U  (where  X  is any subset of  U ). In what follows, all sets considered will be subsets of  U .

Then we can write  [tex]X−Y = X∩Y[/tex], and therefore

[tex](a−c)−(b−c)=(a ∩ c′) ∩ (b∩c′)′\\ = (a∩c′) ∩ (b′ ∪ c)\\ = (a∩c′ ∩ b′) ∪ (a ∩ c′ ∩ c)\\ = (a ∩ c′ ∩ b′) ∪ ∅\\ = a ∩ c′ ∩ b′[/tex]

On the other hand,

[tex](a−b)−c= (a∩b′) ∩ c′= a ∩ b′ ∩ c′[/tex]

Therefore we have proved that  (a − b) − c = (a − c) − (b − c).

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Ella can make 6 and a half cakes with 3.25 pound of raspberries, provided she uses 0.5 pound of raspberries per cake.

We can solve this problem using division.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another.This number of times need not be an integer. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples.

The division with remainder of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of the second number can be allocated. For example, if 21 apples are divided between 4 people, everyone receives 5 apples again, and 1 apple remains.

Now, we know that Ella uses 0.5 pound of raspberries in every cake, and she wants to know how many cakes she can make with 3.25 pound of raspberries.

Using division,

No. of cakes = [tex]\frac{3.25}{0.5} = 6.5[/tex]

Therefore, Ella can make 6 and a half cakes with 3.25 pound of raspberries, provided she uses 0.5 pound of raspberries per cake.

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Ella can make 6 and a half cakes with 3.25 pound of raspberries, provided she uses 0.5 pound of raspberries per cake.

Now, According to the question:

What is Ratio and Proportion in Math?

The definition of ratio and proportion is described here in this section. Both concepts are an important part of Mathematics. In real life also, you may find a lot of examples such as the rate of speed (distance/time) or price (rupees/meter) of a material, etc., where the concept of the ratio is highlighted.

Proportion is an equation that defines that the two given ratios are equivalent to each other. For example, the time taken by train to cover 100km per hour is equal to the time taken by it to cover the distance of 500km for 5 hours. Such as 100km/hr = 500km/5hrs.

They are in proportion

0.5lb for 1 cake

how many cakes for 3.25lb?

number of cakes : weight= 1/0.5

Now, we want to find how many for 3.25

x/3.25=1/0.5

times both sides by (0.5)(3.25)

0.5x=3.25

Divide both sides by 0.5 aka times 2 to both sides

x= 6.5

Hence, Ella can make 6 and a half cakes with 3.25 pound of raspberries, provided she uses 0.5 pound of raspberries per cake.

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