What is the coefficient of x in the simplified form of the expression

3(x + 4)(x - 5)^2 - 6(x + 2)^3?

The radical expression √2 -3√2 + 5√2 when simplified has its value to be 3√2

To combine √2, -3√2, and 5√2 into a single simplified radical, we need to first group the terms with the same radicand (the number inside the square root).

In this case, all three terms have a radicand of 2.

Adding -3√2 and 5√2, we get 2√2.

Then, combining this with √2, we have 3√2 as the simplified radical form of the expression.

Thus, the simplified radical form of √2 -3√2 + 5√2 is 3√2.

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An exponential expression with base 25 and a single, simplified exponent is [tex](25)^{-28}[/tex]

In Mathematics, an exponent simply refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

Generally speaking, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the law of indices for powers of the same base number, we have the following:

[tex](25^7)^{-4}=(25)^{7 \times -4}\\(25)^{7 \times -4}=(25)^{-28}[/tex]

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The value of k for this line is equal to -6.

In Mathematics and Geometry, the gradient of any straight line is also referred to as slope and it can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

2 = (-14 - k)/(k + 2)

-14 - k = 2(k + 2)

-14 - k = 2k + 4

-14 - 4= 2k + k

3k = -18

k= -18/3

k = -6

In this context, we can reasonably infer and logically deduce that the value of k is equal to -6.

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Complete Question:

The gradient of the line joining the points (-2,k) and (k, -14) is 2 . Calculate the value of k.

The area of the shaded region under the standard normal curve with z = 0.49 is 1.

The area of the shaded region under the standard normal curve with z = 0.49 is 1.

What is curve?

In mathematics, a curve is a continuous and smooth (i.e., differentiable) mathematical object that represents a path or a trajectory. Curves can be defined in different ways, depending on the context in which they are used.

What is area of curve?

The area of a curve refers to the amount of space enclosed by a curve on a two-dimensional plane. Finding the area of a curve can be a challenging problem, especially when the curve is not a standard geometric shape such as a circle or rectangle.

To find the area of the shaded region under the standard normal curve with z = 0.49, we need to use a standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table, we find that the area to the left of z = 0.49 is 0.6864. This means that the area to the right of z = 0.49 is 1 - 0.6864 = 0.3136.

Since the normal curve is symmetric about the mean (z = 0), the area to the left of z = -0.49 is also 0.6864. Therefore, the area between z = -0.49 and z = 0.49 is:

0.6864 (area to the left of z = 0.49) + 0.3136 (area to the right of z = 0.49) = 1

So the area of the shaded region under the standard normal curve with z = 0.49 is 1.

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Answer:

Spinning Swings

10 more riders

Step-by-step explanation:

To find which ride will have more riders each hour, we need to first convert an hour into minutes.

[tex]\text{1 hour = 60 minutes}[/tex]

Now we let's first find how many riders there will be in the race cars.

So there are 25 riders every 30 minutes.

in 60 minutes there will be:

[tex]25 \times 2 = 50 \ \text{Riders}[/tex]

Now for the spinning swings there are 20 riders every 20 minutes.

In 60 minutes there will be:

[tex]20 \times 3 = 60 \ \text{Riders}[/tex]

Therefore, the spinning swings will have more riders as [tex]60 > 50[/tex].

Now to find how many more riders there will be in the spinning swings.

We simply subtract the total number of riders of each ride from each other.

[tex]\text{Race Cars = 50}[/tex]

[tex]\text{Spinning Swings = 60}[/tex]

[tex]60 - 50 = 10[/tex]

There will be 10 more riders in the spinning cups than the race cars.

The correct answers are: To determine the consumer's eligibility for credit and  To set pricing for credit lines.

what is pricing?

"Pricing" refers to the process of determining the value or cost of a product or service and setting a specific price for it. Pricing decisions involve taking into account various factors such as production costs, market demand, competition, and profit margins, among others. Pricing can also involve setting

In the given question,

Based on section 1.3.2, Credit scores, on page 22 of the report, the two purposes for which credit card issuers use credit scores are:

To determine the consumer's eligibility for credit.

To set pricing for credit lines.

Therefore, the correct answers are:

To determine the consumer's eligibility for credit

To set pricing for credit lines

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now, if we take a looksie at the denominators on all sides, hmmm 2 and 3, so we can get an LCD of 6, so let's multiply both sides by 6 to do away with the denominators.

[tex]4-\cfrac{x-2}{2}=x+\cfrac{1-2x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( 4-\cfrac{x-2}{2} \right)~~ = ~~6\left( x+\cfrac{1-2x}{3} \right)} \\\\\\ 24-3(x-2)~~ = ~~6x+2(1-2x)\implies 24-3x+6~~ = ~~6x+2-4x \\\\\\ 30-3x=2x+2\implies 30=5x+2\implies 28=5x\implies \cfrac{28}{5}=x\implies 5\frac{3}{5}=x[/tex]

Answer:

a

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n[/tex]  a₁ + (n - 1)d

here a₁ = [tex]\frac{3}{5}[/tex] and d = - [tex]\frac{1}{3}[/tex] , then

a₂₁ = [tex]\frac{3}{5}[/tex] + (20 × - [tex]\frac{1}{3}[/tex] )

    = [tex]\frac{3}{5}[/tex] - [tex]\frac{20}{3}[/tex]

    = 0.6 - 6.67

   = - 6.07 ( to 2 decimal places )

The type of sampling used in each case are:

Statement A → Stratified random sampling.

Statement B → Cluster sampling

Statement C → Simple random sampling

Statement D → systematic sampling

There are different ways that samples are classified such as:

1) Convenience sampling: This is where samples are drawn from a conveniently available pool.

2) Random Sampling: This is when we put all the options into a particular hat and drawn some of them.

3) Systematic Sampling: This is when every nth element is taken. For example, we want to survey something in the school, and then we interview every 10th person.

4) Cluster Sampling: This usually divides a population into groups, referred to as clusters, and each element in that cluster is surveyed.

5) Stratified Sampling: This will divide the population into groups. However, unlike cluster sampling, here, only some elements of the group are surveyed.

From the given problem:

Statement A is Stratified random sampling.

Statement B is Cluster sampling

Statement C is Simple random sampling

Statement D is systematic sampling

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Step-by-step explanation:

[tex]2 {}^{a} = 16[/tex]

Since our variable is in the exponent, we take the logarithm of both sides in order to solve for a.

The log base is 2 In order to cancel out base 2,

[tex]a = log_{2}(16) [/tex]

[tex]a = 4[/tex]

The interest earned during the third month of the 7th year is $3,613.55.

What is interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

Let PMT be the monthly payment, r be the monthly interest rate, and n be the total number of payments. Then:

FV = PMT × [(1 + r)n - 1]/r

In this case, we want to find PMT, given that FV = $900,000, r = 0.038/12, and n = 10 × 12 = 120:

[tex]$900,000 = PMT * {[(1 + 0.038/12)}^{120} - 1]/(0.038/12)[/tex]

Solving for PMT, we get:

PMT = $682.48

[tex]FV = $682.48 * [(1 + 0.038/12)^87 - 1]/(0.038/12)\\\\ = $89,324.47\\\\PV = $682.48 * [(1 + 0.038/12)^83 - 1]/(0.038/12) \\\\= $85,710.92[/tex]

The interest earned during the third month of the 7th year is:

$89,324.47 - $85,710.92 = $3,613.55

Therefore, the interest earned during the third month of the 7th year is $3,613.55.

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Answer:

2×2×7=28

Step-by-step explanation:

28÷2=14

14÷2=7

Prime numbers 2, 2, and 7 make 28

If yοu invest $150 a mοnth fοr 8 years, then leave the mοney in the accοunt, withοut making additiοnal payments, fοr anοther 12 years.

a) Yοu will have  yοu will have apprοximately $59,073.95 at the end οf 20 years.$59,073.95 at the end οf 20 years.

b) Earned apprοximately $26,673.95 in interest οver the 20-year periοd.

The wοrth οf a series οf recurrent payments at a specific future date, assuming a specific rate οf return, οr discοunt rate, is the future value οf annuity.

Let's first calculate the tοtal number οf mοnths in 20 years:

20 years x 12 mοnths/year = 240 mοnths

a. we can use the fοrmula fοr the future value οf an annuity:

[tex]FV = PMT x (((1 + r/n)^(n*t) - 1) / (r/n))[/tex]

where:

PMT = the mοnthly payment ($150)

r = the annual interest rate (2.4% οr 0.024)

n = the number οf times the interest is cοmpοunded per year (12)

t = the tοtal number οf years (20)

FV = 150 x (((1 + 0.024/12)^(12*20) - 1) / (0.024/12))

FV ≈ $59,073.95

Therefοre, yοu will have apprοximately $59,073.95 at the end οf 20 years.

b. Tο calculate the amοunt οf interest yοu earned, we can subtract the tοtal amοunt οf mοney yοu invested frοm the future value:

Interest = FV - Tοtal amοunt invested

Interest = $59,073.95 - ($150 x 12 x 8 x 12)

Interest ≈ $26,673.95

Therefοre, yοu earned apprοximately $26,673.95 in interest οver the 20-year periοd.

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The radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.

Radius is a line segment that extends from the center of a circle or sphere to its circumference. It is the distance from the center to the edge of the circle or sphere. It is also used to measure the length of an arc of a circle. Radius is a necessary measure when calculating the area of a circle or sphere, as well as the volume of a sphere.

The arc length of a semicircle is given by the formula s = πr,
where r is the radius of the semicircle. In this case,
we are given the radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.

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The arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.

What is an arc?

An arc is part of a circle's circumference. It is a segment of a curved line that is formed when a straight line intersects a circle or a curved shape. Arcs can be measured in length, angle, or radius, depending on the context.

To find the arc length of a semicircle, we need to know the radius of the circle and the angle subtended by the arc at the center of the circle.

Let's assume the radius of the semicircle is 'r'. Since it is a semicircle, the angle subtended by the arc at the center of the circle is 180 degrees or π radians.

The formula for arc length is given by:

arc length = radius x angle in radians

In this case, the angle is π radians and the radius is 'r'. Therefore, the arc length of the semicircle is:

arc length = r x π

We can leave the answer in terms of π or substitute the value of π to get a numerical answer. For example, if the radius of the semicircle is 4 units, the arc length will be:

arc length = 4 x π

arc length ≈ 12.57 units (using π ≈ 3.14)

Therefore, the arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.

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Answer:

Approx. 4.47

Step-by-step explanation:

To calculate the standard deviation for the data, we need to follow these steps:

1. Calculate the mean (average) of the data:

mean = (13 + 17 + 9 + 21) / 4 = 15

2. Calculate the difference between each data point and the mean:

13 - 15 = -2

17 - 15 = 2

9 - 15 = -6

21 - 15 = 6

3. Square each difference:

(-2)^2 = 4

2^2 = 4

(-6)^2 = 36

6^2 = 36

4. Calculate the variance by taking the average of the squared differences:

variance = (4 + 4 + 36 + 36) / 4 = 20

5. Calculate the standard deviation by taking the square root of the variance:

standard deviation = sqrt(variance) = sqrt(20) ≈ 4.47

Therefore, the standard deviation for the data is approximately 4.47.

The surface area (A) of a cylinder is given by the formula A = 2πr² + 2πrh, where r is the radius of the cylinder and h is its height.

In this case, the radius of the cylinder is 3x - 2 cm, and its height is x + 3 cm. Substituting these values into the formula, we get:

A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)

Simplifying this expression, we get:

A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)

A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π

A = 24πx² - 10πx - 12π

So the surface area of the cylinder is 24πx² - 10πx - 12π.

he is literally hitting the gritty

Step-by-step explanation:

the length of the diagonal is calculated out of the length and width by using Pythagoras (after all, one length, one width and the diagonal are creating a right-angled triangle).

25² = length² + width²

length = 2×width + 10

we are using the second in the first equation :

25² = (2×width + 10)² + width²

625 = 4×width² + 40×width + 100 + width²

525 = 5×width² + 40×width

105 = width² + 8×width

width² + 8×width - 105 = 0

a quadratic equation

ax² + bx + c = 0

has the general solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 1

b = 8

c = -105

width = (-8 ± sqrt(8² - 4×1×-105))/(2×1) =

= (-8 ± sqrt(64 + 420))/2 =

= (-8 ± sqrt(484))/2 =

= (-8 ± 22)/2 = -4 ± 11

width1 = -4 + 11 = 7

width2 = -4 - 11 = -15

a negative size of the length of a side of a shadow does not make any sense, so, our valid solution is

width = 7 in.

and then

length = 2×width + 10 = 2×7 + 10 = 14 + 10 = 24 in.

The simplest form of the fraction in this problem is given as follows:

t^6.

The fraction in the context of this problem is defined as follows:

2(t^4)³/2t^6.

The numeric constant of both the numerator and the denominator is of two, hence it can be simplified, as follows:

(t^4)³/t^6.

At the numerator, we apply the power of power rule, meaning that when we have a single base elevated to multiple exponents, we can multiply the exponents, hence:

(t^4)³ = t^(4 x 3) = t^12.

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence the simplified expression is given as follow:

t^12/t^6 = t^(12 - 6) = t^6.

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The solution to the expression using laws of exponents is: t⁶

Some of the laws of exponents are:

1) Product of powers rule: This means that we are to add the powers together when multiplying like bases.

2) Quotient of powers rule: This means that we are to subtract powers when dividing like bases.

3) Power of powers rule: This means that we are to multiply powers together when raising a power by another exponent.

4) Power of a product rule: This means that when any base is to be multiplied by an exponent, distribute the exponent to each part of the base.

We are given the expression:

2(t⁴)³/2t⁶

2 is common to both numerator and denominator and they will cancel out to give: (t⁴)³/t⁶

Using power of power rule on the numerator, we have:

t¹²/t⁶

Using quotient of powers rule, we have:

t¹²/t⁶ = t¹²⁻⁶

= t⁶

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As a result, chairs in modern movie theatres are about 21.05% larger than those from theatres built 30 years ago.

By reducing the value through the overall value and multiplying the outcome by 100, the percentage may be calculated. The proportion is calculated using the method (value/total value)100%.

We can use the formula for percentage increase to solve this problem:

% increase = (new value - old value) / old value × 100%

The new value is the current average width of a movie theater seat, which is 23 inches. The old value is the width of a movie theater seat from 30 years ago, which is 19 inches.

% increase = (23 - 19) / 19 × 100% ≈ 21.05%

Therefore, current movie theater seats are approximately 21.05% wider than a theater seat from 30 years ago.

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Answer:

b = 62°

Step-by-step explanation:

We Know

A triangle sum is 180°

We know two angles, one is 68.5° and the other is 49.5°.

Find angle b

We Take

180 - (68.5 + 49.5) = 62°

So, b = 62°

The triangles that translate to triangle X are A and F.

Triangle ABC is translated to triangle A'B'C', 5 square(s) to the right and 4 square(s) down.

Triangles can be translated by moving each of their vertices a certain distance in a certain direction. The distance and direction of the translation can be described using vector notation.

For example, a translation of a triangle by the vector <a, b> would move each vertex of the triangle a units to the right and b units up. The resulting translated triangle would have the same shape and size as the original triangle, but would be located in a different position in the plane.

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Image transcribed:

Select all of the triangles below which are translations of triangle X.

Triangle ABC is translated to triangle A'B'C'.

Fill in the gaps below to describe the translation.

Triangle ABC is translated to triangle A'B'C'.

Fill in the gaps below to describe the translation.

___ square(s) to the left/right and ___ square(s) up/down

A

B

C

A'

B'

C'

The inventory cost under:

a. First-in, first-out (FIFO) - $326.

b. Last-in, first-out (LIFO) - $289.

c. Weighted average cost - $308.

a. Calculation of inventory cost using the First-in, First-out (FIFO) method:

There are 11 units of the item in the physical inventory on December 31. Under FIF7 units will be from items purchased on Nov 30 and 4 units will be from items purchased on Aug 13.

( 7 units * 30) + (4 units *29)

= 210 + 116 = $326

b. Calculation of inventory cost using the Last-in, First-out (LIFO) method:

There are 11 units of the item in the physical inventory on December 31. Under LIFO Method, 10 units will be from items purchased on Jan 1 and 1 unit will be from items purchased on Aug 13.

10 units * 26 + (1 unit * 29)

= $289

c. Calculation of Weighted Average cost per unit:

$644/23 units

=$28 per unit

Calculation of inventory cost using the Weighted Average Cost method:

11 units * 28

= $308

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The sum of the digits of the product p×q is 8

A positive integer bigger than one that can be divided only by itself and by one is referred to as a prime number.

Given that: p³ - pq² = 42024

p (p² - q²) = 42024

Since factors, 42024 = 2³ x 3 x 17 x 103, and p and q are prime numbers, we can see that p must be 3, 17 or 103, We can try each case:

If p = 3 then we have:

3 (9 - q²) = 42024

q² = -13,999

This equation has no real solutions for q, so p cannot be 3.

If p = 17, then we have:

17 (289 - q²) = 42024

q² = -2183

This equation also has no real solutions for q, so p cannot be 17 either.

If p = 103, then we have:

103 (10609 - q²) = 42024

10609 - q² = 408

q² = 10201

q = 101

This equation also has a solution for q = 101, so p = 103

Product of pq = 103×101 = 10403

So, the sum of the digits of the product pq = 1+0+4+0+3 = 8

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Answer:

385865

Step-by-step explanation:

this is not correct question because I can't see this

The ratio of the shaded area to the unshaded area in the figure is 1 : 5.5 which can be calculated by adding the areas of the two squares and triangle EDH.

Area is the amount of two-dimensional space taken up by a shape or object. It is measured in square units, such as square centimeters, square meters, or square miles.

The ratio of the shaded area to the unshaded area in the figure can be calculated by adding the areas of the two squares and triangle EDH, and then subtracting the shaded area.

First, calculate the total area of the figure:

Area of the two squares = (BC)²

= (CD)²

= (4)²

= 16

Area of triangle EDH = ½ x BC x DH

= ½ x 4 x 5

= 10

Total area = 16 + 10

= 26

Next, calculate the shaded area:

Shaded area of square CDEF = 25% x 16

= 4

Total shaded area = 4

Finally, calculate the ratio of the shaded area to the unshaded area in the figure:

Unshaded area = 26 - 4

= 22

Ratio of the shaded area to the unshaded area = 4 : 22

= 1 : 5.5

Therefore, the ratio of the shaded area to the unshaded area in the figure is 1 : 5.5.

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Question:

A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.

In the figure, the proportion of shaded to unshaded region is 1:5.5.

The area of the shaded region is the difference between the area of the entire polygon as well as the area of the polygon's unshaded part. In polygons, the area of the shaded portion can occur in two ways. The shaded area can be found in the centre of a polygon or on its sides.

As previously stated, the area of the shaded region is determined by subtracting the area of a complete polygon from the area of the unshaded region.

outer shape region – area of the interior unshaded shape = The shaded area

To begin, compute the entire area of the figure:

Area of the two squares [tex]=(BC)^2[/tex]

[tex]=(CD)^2\\\\=(4)^2\\\\=16[/tex]

Area of the EDH triangular [tex]=\frac{1}{2} \times BC\times DH[/tex]

Substitute values in the above equation

[tex]=\frac{1}{2} \times 4\times 5\\\\=10[/tex]

Total area = 16 + 10

                 = 26

The shaded region is then calculated as follows:

CDEF square shaded region = 25% x 16

                                                = 4

Total shaded area = 4

Finally, compute the shaded-to-unshaded area ratio in the figure:

Unshaded area = 26 - 4

= 22

Shaded to unshaded region ratio = 4 : 22

= 1 : 5.5

As a result, the shaded area to unshaded area ratio in the image is 1: 5.5.

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The complete question is,

A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.

Answer:

1048576

Step-by-step explanation:

2^20=1048576

Answer:  y = x + 6

Step-by-step explanation: "y = m x + b" is the format used to find the equation of a line on a graph.

Y and X remain the same in the equation, however you replace "m" with the value of the slope. In this problem, the slope is "1" because the rise is 1 and the run is 1, making it 1/1 or 1. Because the slope is "1", we do not need to include the number "1" in our equation.

Finally, "b" is the y-intercept (in other words, the place where the line crosses the y-axis). In this problem, the line crosses at "6"; therefore, 6 will replace b in the equation completing it.

The complete table that shows the proportional relationship is:

x                                 y

0.8                             4

3.2                             16

12.8                            64

The ratio of the given y-value and x-value is calculated as:

y/x = 4/0.8 = 5

Thus, the ratio of the next terms must all be 5.

The second x coordinate is 3.2. Thus:

y/3.2 = 5

y = 3.2 * 5

y = 16

Difference of the first 2 x-values = 3.2 - 0.8 = 2.4

Thus, the third value of x will be:

3.2 + 2.4 = 5.6

Thus, the third y-coordinate = 5.6 * 5 = 28

Similarly, the fourth value of x will be:

5.6 + 2.4 = 8.0

Thus, the fourth y-coordinate = 8 * 5 = 40

The sixth value of x will be:

8 + 2.4 + 2.4 = 12.8

Sixth value of y = 12.8 * 5 = 64

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Complete question is:

Drag numbers to the table so it shows a proportional relationship between x and y.

Tiles : 8.8 , 12.8 , 5.6 , 64 , 6.4 , 16

X axis Y axis

0.8.      4

3.2       ?

?           ?