Cone A and cone B are mathematically similar. The ratio of the surface area of cone A to the surface area of cone B is 25:4 The volume of cone A is 6000 cm³ Work out the volume of cone B. Optional working​

The limits of the function as x approaches infinity and negative infinity are 0 and negative infinity, respectively, and the horizontal asymptote is y = 0.

A function is a mathematical rule that assigns a unique output for each input.

For the function

=> f(x) = 3x²+2/x³√4x⁶+1,

we will evaluate the limits as x approaches infinity and negative infinity. We will also determine the horizontal asymptote of the function.

When x approaches infinity, the denominator

=> x³√4x⁶+1

becomes very large, so the value of the function becomes very small. Thus, the limit of the function as x approaches infinity is 0.

To determine the horizontal asymptote, we need to look at the degree of the numerator and denominator.

The numerator has a degree of 2 and the denominator has a degree of 3. Since the denominator has a higher degree, the horizontal asymptote is y = 0.

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The component that is missing from the biologist's process is:

c) The biologist did not randomly assign each of the bats to the treatment groups.

When carrying out a research study where you have groups created that you want to study, differences between and within groups can be satisfactory ensuring that they are not systematic when subjects are randomly assigned to groups.

Given, A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area.

a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2).

Thus, it gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently ascribed to experimental treatments.

Therefore, the component that is missing from the biologist's process is: c. The biologist did not randomly assign each of the bats to the treatment groups.

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According to a report from the Neilson company,

a) The probability that exactly 20 of them used Search Engine is 0.068

b)  the probability that 15 or fewer used Search Engines is 0.0560

c) The probability that more than 20 of them used a Search Engine is 0.2484

d) Yes, it would be unusual if fewer than 12 used Search Engine.

a. The probability that exactly 20 of 25 searches used the Search Engine can be calculated using the binomial distribution formula:

b. The probability that 15 or fewer of 25 searches used the Search Engine can be calculated as the sum of the probabilities of 0 to 15 searches using the Search Engine:

c. The probability that more than 20 of 25 searches used the Search Engine can be calculated as the complement of the probability of 20 or fewer searches using the Search Engine:

d. The probability of fewer than 12 of 25 searches using the Search Engine can be calculated as the sum of the probabilities of 0 to 11 searches using the Search Engine:

So Yes, It would be unusual if fewer than 12 of 25 searches used the Search Engine if the probability is less than a certain threshold, such as 0.05, which is often used to determine statistical significance.

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Complete Question:

According to a report of the Nielsen company,76% of internet searches used the  search engine. Assume that a sample of 25 searches is studied.

a. What is the probability that exactly 20 of them used Search Engine?

b.What is the probability that 15 or fewer used Search Engine?

c.What is the probability that more than 20 of them used Search Engine?

d.Would it be unusual if fewer than 12 used Search Engine?

The exponential function calculator available online at BYJU speeds up the calculation and displays the value of the variable quickly.

The e key must be pressed first on the majority of graphing calculators, followed by the exponent key and the exponent input keys, in order to raise e to a power.

Using the free online tool known as the exponential function calculator, you can see the exponent's fluctuating value. The calculation is accelerated by the use of BYJU's online exponential function calculator, which also shows the variable's value in a little amount of time.

Directly below the display area, there is a row of sophisticated operators and features. The Down arrow to the right can be used to access more complex operators and functions. pi (π), superscript for exponents (^), cosine (cos), tangent (tan), logarithm (ln, log), and square root (√) are some of the buttons you'll encounter.

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Answer:

12.7  

Using the Pythagorean theorem, you can easily calculate the length of BC.

So:

BC = sqrt(12^2 - 6^2) = sqrt(144 - 36) = sqrt(108) = 10.39230485  

Now consider triangle BCD. You know all three angles and one side. Using the law of sines you know that ratio of the sine of each angle over the opposite side is constant. So:

BC/sin(55) = CD/sin(90)

BC/sin(55) = CD/sin(90)

sin(90)BC/sin(55) = CD

1*BC/sin(55) = CD

BC/sin(55) = CD

10.39230485/0.819152044 = CD

12.68666167 = CD

12.7 = CD

Step-by-step explanation:

By definite integrals, we find that the area of the region bounded by the functions f(x) and g(x) described in the statement is equal to 4.5 units.

In this problem we must determine the area between two functions, a quadratic equation f(x) and a linear equation g(x).

First, we need to determine the limits of the interval of x-values with the help of a graphing tool, represented by the points of intersection of the two functions.

The points of intersection of the two functions are (x₁, y₁) = (- 5, 4) and (x₂, y₂) = (- 2, 1), respectively. Then, the area is defined by the following definite integral:

[tex]I=\int_{-5}^{-2}[g(x)-f(x)]dx\\\\I=\int_{-5}^{-2}(-x-1)-(x+3)^2]dx\\\\I=4.5 unit^2[/tex]

The area of the region represented by the definite integral introduced above is equal to 4.5 units.

The complete question is -

Find the area of the region that is bounded above by the curve f(x) = (x + 3)² and the line g(x) = - x - 1 and bound above the x-axis.

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Answer:

Below

Step-by-step explanation:

If you lose 5 %, you basically have 95 % remaining which is .95 in decimal

y = 1000 * (.95)^x       where x is the number of months  ( x = 9 in this case)

There were 70 Republicans and 84 Democrats in the state senate.

Let x be the number of Republicans in the state senate.

Then the number of Democrats is x + 14.

We know the ratio of Democrats to Republicans is 6 to 5.

According to the given conditions, we can write the equation as follows -

x / (x + 14) = 5 / 6

Cross multiplying, we get,

6x = 5x + 70

Subtracting 5x from both sides of the equation, we get,

x = 70

Therefore, we get that there were 70 Republicans and 84 Democrats in the state senate.

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When it is simpler to describe an angle as the sum or difference of distinct angles (0°, 30°, 45°, 60°, 90°, and 180°), the sum and difference formulae in trigonometry are used to determine the value of the trigonometric functions at those particular angles.

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The five-number summary for the given data set is as follows: Minimum: -6.00, Q1: -2.47, Median: 1.00, Q3: 4.30, Maximum: 7.85.

Minimum: -6.00

Q1: -2.47

Median: 1.00

Q3: 4.30

Maximum: 7.85

To construct the five-number summary for the given set of data, we need to calculate the five parameters: minimum, first quartile (Q1), median, third quartile (Q3) and maximum.

Minimum: The minimum value in the set of data is -6.

Q1: The first quartile is calculated by finding the median of the lower half of the data set. In this case, the lower half consists of the values -6, -4, -2, -1 and 0. The median of this set is -2.47.

Median: The median of the set of data is calculated by finding the middle value of the data set. In this case, the middle value is 1.

Q3: The third quartile is calculated by finding the median of the upper half of the data set. In this case, the upper half consists of the values 1, 3, 4, 6, and 7. The median of this set is 4.30.

Maximum: The maximum value in the set of data is 7.85.

The five-number summary for the given data set is as follows: Minimum: -6.00, Q1: -2.47, Median: 1.00, Q3: 4.30, Maximum: 7.85.

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Answer:

ang. PQR

Step-by-step explanation:

The diameter which subtends an angle to the circumference of the circle is equal to 90 degrees. Hence, either ang. PQR and ang. PSR are both right angles.

Answer:

$69.

Step-by-step explanation:

he store marked up the silver coat rack for $48 * 25/100 = $12.

So the silver coat rack was sold for $48 + $12 = $60.

The sales tax is $60 * 15/100 = $9.

Thus, Prithia paid a total of $60 + $9 = $69.

The intervals can be written as (-∞, 4) and (4, ∞) for increasing, and [4, 4] for decreasing.

The function h(x) = (x - 4)² - 3x + 7 is a parabolic function that opens upwards.

The function has a critical point at x = 4, where it changes direction from decreasing to increasing.

To determine the intervals on which the function is increasing or decreasing, we need to look at the sign of the first derivative of the function, which will tell us if the function is increasing or decreasing at any given x value.

In this case, the derivative of

=> h(x) = 2(x - 4) - 3.

Setting this equal to zero and solving for x, we find that x = 4 is the only critical point.

The second derivative of h(x) is 2, which is positive.

This tells us that the first derivative is increasing, which means the original function is increasing.

Therefore, the intervals on which the function is increasing are all x values greater than 4 or all x values less than 4. The intervals on which the function is decreasing are all x values between 4 and 4.

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I am sorry but I cannot answer your question with the contained elements.

As the y variable tends to increase when the x variable increases, we say the variables have a positive correlation. When the y variable tends to decrease as the x variable rises, we say there is a negative correlation between the variables.

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The points on a graph are typically used to depict the relationships between two or more things.

Making a diagram that shows the link between two or more objects is known as developing a graph.

Scatterplots frequently reveal relationships or trends.

We say there is a positive correlation between the variables when the y variable tends to rise when the x variable rises.

We say there is a negative correlation between the variables when the y variable tends to decline as the x variable rises.

Therefore, a y variable tends to increase when the x variable increases, we say the variables have a positive correlation. When the y variable tends to decrease as the x variable rises, we say there is a negative correlation between the variables.

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According to the information, the options that correspond to the possible scale copies of the original rectangle would be 4.5 in. by 1.5 in. yes, 13.5 in. by 4.5in. Yes, and 90 in. by 30in. Yeah.

To calculate the possible scales we must carry out the following procedure: First we must make a division between the two lengths of the sides of the rectangle:

9 / 3 = 3

So, the relationship between these two lengths would be 3. Now we just have to check which options follow this proportional relationship. According to this procedure they would be the following:

4.5in. by 1.5in

13.5in. by 4.5in

90 in. by 30in

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For the first question, the percentage of the usual price that Elena's mom paid is 60%, and for the second question, the price that Elena's dad paid is $187.50.

For the first question, to find the percentage of the usual price Elena's mom paid, you can divide the actual price by the usual price and multiply by 100:

$150 ÷ $250 × 100 = 60%

So, Elena's mom paid 60% of the usual price for the cell phone.

For the second question, you can use the percentage of the usual price to find the actual price:

$250 × 75/100 = $187.50

So, Elena's dad paid $187.50 for the other type of cell phone, which is 75% of the usual price.

To summarize, Elena's mom paid 60% of the usual price of $250 and paid $150, while Elena's dad paid $187.50, which is 75% of the usual price.

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Answer:

700

Step-by-step explanation:

A=hxw

A square has all equal sides

700×700=4900

The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.

The general solution to the differential equation d(r)/dt = 5tln(t) can be found using the method of integrating factors.

First, we find the integrating factor:

I = e^∫5ln(t)dt = e^(5t - 5)

Next, we multiply both sides of the equation by the integrating factor:

I * d(r)/dt = I * 5tln(t)

Now, we can integrate both sides of the equation:

∫I * d(r)/dt = ∫I * 5tln(t)dt

Using the substitution u = r and du/dt = d(r)/dt, we can simplify the left side of the equation:

du/dt = I * d(r)/dt

And on the right side, we use integration by parts:

∫I * 5tln(t)dt = (5/2)t^2ln(t) - 5te^5 + C

Finally, we can solve for r:

r = (5/2)t^2ln(t) - 5te^5 + C

The general solution to the differential equation d(r)/dt = 5tln(t) is:

r = (5/2)t^2ln(t) - 5te^5 + C.

Note that C is an arbitrary constant and represents the freedom in choosing the initial conditions for the solution.

Therefore, The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.

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Answer: The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line.

Step-by-step explanation:

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot.

The normal probability plot is a graphical method for determining whether or not a data set is roughly normally distributed . The points in the data are displayed against a hypothetical normal distribution such that they should roughly form a straight line.

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot. It is applied to ascertain if a tiny amount of data is representative of a normal distribution.

A graphical method for locating significant deviations from normalcy is the normal probability plot. Outliers, skewness, kurtosis, the requirement for transformations, and mixes are some examples of this. The raw data, residuals from model fits, and estimated parameter values are used to create normal probability charts.

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2084 is the total number of integers between 4000 and 4999 with at least one repeated digit.

An integer is a whole number, which can be positive, negative, or zero. A repeated digit refers to a digit that appears more than once in the number.

First, let's count the number of integers between 4000 and 4999 that have no repeated digits. We have 4 choices for the thousands place, as it must be 4. For each of the remaining three places, we have 9 choices for digits (0 to 9, except for 4 in the thousands place). So, the total number of integers between 4000 and 4999 with no repeated digits is 4 * 9 * 9 * 9 = 2916.

Next, we need to count the number of integers with one repeated digit. For this, we need to consider two cases:

When the repeated digit is in the thousands place. In this case, there are only 9 choices for the other three digits, as they cannot be 4. The total number of integers in this case is 9 * 9 * 9 = 729.

When the repeated digit is not in the thousands place. In this case, there are 9 choices for the repeated digit and 8 choices for the other two digits. So, the total number of integers in this case is 9 * 9 * 8 = 648.

Adding the total number of integers in both cases, we get 729 + 648 = 1377 integers between 4000 and 4999 with at least one repeated digit.

Finally, subtracting the number of integers with no repeated digits from the total number of integers between 4000 and 4999, we get 5000 - 2916 = 2084. This is the total number of integers between 4000 and 4999 with at least one repeated digit.

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Divide the area value by 640 to get 1 Acre = 0.0016 Square Miles.

It is necessary to calculate how many times 640 is multiplied by the number of acres in order to get how many square miles. Each 640 acres equals 1 square mile. Calculators and hand division are both acceptable methods of division.

The result of multiplying two lengths is a square unit of area, such as a square mile. Given that each length in square miles is expressed in miles, miles2 is obtained by multiplying miles by miles.

The two-acre plot's circumference, if two square acres were placed side by side, would be 1252.26 feet, or almost four and a half times around, or a mile.

1Acre = 0.0015625

          = 0.0016Sq. miles

divide the area value by 640

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The length of the rectangular swimming pool is, 50 m.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

A rectangular swimming pool has a perimeter of 150 m.

And, The length of the pool is twice the width of the pool.

Now, Let the width of the pool = x

Then, The length of the pool = 2x

We know that;

Perimeter of rectangle = 2 (Length + Width)

Substitute all the given values, we get;

⇒ 150 = 2 (2x + x)

⇒ 150 = 2 × 3x

⇒ 150 = 6x

⇒ x = 150 / 6

⇒ x = 25

Thus, The length of the rectangular swimming pool = 2x

                                                                               = 2 × 25

                                                                               = 50 m

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Correct option is D, the population density of Florida is 3.3 × 103 people/mi^2.

The population density, or the number of people divided by the area's size, is determined by the number of people who reside there. Many different creatures' distribution, growth, and migration can all be described using population density.

The average number of people in a population per unit of area or volume is known as population density. For instance, the density of a population of 100 insects living in a 100 square metre area is equal to one bug per square metre.

Three alternative methods are frequently used to determine population density. There are three types of density: agricultural, physiological, and mathematical.

Given,

population of Florida is about 1.8 × 10^ 7 people

land area of Florida is about 5.4 × 10^4 square miles

population density = the number of individuals / size of the area

population density = 1.8 × 10^ 7 / 5.4 × 10^4

= 3.3 × 103 people/mi^2.

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A rhombus has 6 and 8 centimeter diagonals, 24 cm2 is the size of the rhombus.

The product of the lengths of the diagonals divided by two equals the area of a rhombus. The formula Area = (d1 d2)/2 sq. is used to determine the area of a rhombus using diagonals.

The product of the lengths of the diagonals divided by two equals the area of a rhombus.

Knowing that, First diagonal, d1=6 cm. Diagonal 2, d2 = 8 cm Rhombus surface area is given by A=d1d22 =682 =482 =24 cm2. So, the rhombus has a 24 cm2 surface area.

A rhombus has 6 and 8 centimeter diagonals, 24 cm2 is the size of the rhombus.                

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The fourth vertex of the rectangle using the coordinate plane is; (4, 21)

The three coordinates of the rectangle are expressed as;

(21, 21)

(21, 1)

(4, 1)

Now, when we tal about a rectangle, it is pertinent to note that two points must have the same y coordinates while two points must also have the same x -coordinates because the two parallel sides of a rectangle are equal.

Thus, we already have two sides with 21 as x-coordinate but only one with 4 as x-coordinate and as such the fourth point will have 4 as x-coordinate.

Similarly, only one point has 21 as y-coordinate and as such the fourth point will have its' y-coordinate as 21.

(4, 21)

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The acceleration of the bug at any given time t is a.

The theory used in this question is the equation of motion.

This equation states that the position of an object is equal to the product of the acceleration and the time plus a constant.

Given:

The equation x(t)=at + b,

where a and b are both nonzero, describes the position of an insect travelling along the x axis.

The equation x(t)=at + b can be rewritten as x(t)=a(t) + b.

This equation states that the position of the bug is equal to the product of the acceleration (a) and the time (t) plus a constant (b).

Therefore, the acceleration of the bug at any given time t is a.

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The value of 'x' in x² - 50 = 0 is either - 7.07 or + 7.07.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, A quadratic equation x² - 50 = 0, where x belongs to R.

x² = 50.

x = ± √50.

x = ± 7.07.

So, The value of x can be - 7.07 or it can be + 7.07 squaring both numbers will result to approximately 50.

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The requried solution of the given expression is given as x = 7.07, -7.07.

Zeros of an equation are defined as the value of the independent variable where the equation or function gives zero.

Here,
Given expression,
x² - 50 = 0
x² = 50
x = √50
x = ±7.07

Thus, the requried solution of the given expression is given as x = 7.07, -7.07.

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The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

The area of a square with sides of one inch is equal to one square inch (plural: square inches).

We have that:

Let the dimension of the paper be x and y.

Such that:

Length = [tex]x[/tex]

Width = [tex]y[/tex]

So:

Area = [tex]x*y[/tex]

Substitute 128 for Area

[tex]128=x*y[/tex]

Make x the subject.

[tex]x=\frac{128}{y}[/tex]

When 1 inch margin is at top and bottom

The Length becomes:

[tex]Length =x+1+1[/tex]

[tex]Length = x+2[/tex]

When 2-inch margin is at both sides

The width becomes:

[tex]Width = y+2+2[/tex]

[tex]Width = y+4[/tex]

The New Area (A) is then calculated as:

[tex]A = (x+2)*(y+4)[/tex]

Substitute [tex]\frac{128}{y}[/tex] for x

[tex]A = (\frac{128}{y}+2 )*(y+4)[/tex]

Open Brackets

[tex]A = 128 + \frac{512}{y} + 2y + 8[/tex]

Collect Like Terms

[tex]A = \frac{512}{y} + 2y + 8+128[/tex]

[tex]A = \frac{512}{y} +2y+136[/tex]

[tex]A = 512y^{-1} +2y + 136[/tex]

To calculate the smallest possible value of y, we have to apply calculus.

Differentiate A with respect to y

[tex]A' = -512y^{-2}+2[/tex]

Set

[tex]A' = 0[/tex]

This gives:

[tex]0=-512y^{-2}+2[/tex]

Collect Like Terms

[tex]512y^{-2} = 2[/tex]

Multiply through by [tex]y^{2}[/tex]

[tex]y^{2} *512y^{-2} = 2*y^{2}[/tex]

[tex]512 = 2y^{2}[/tex]

Divide through by 2.

[tex]256 = y^{2}[/tex]

Take square roots of both sides.

[tex]\sqrt{256= y^{2} }[/tex]

[tex]16 =y\\\\y=16[/tex]

Recall that:

[tex]x = \frac{128}{y}[/tex]

[tex]x = \frac{128}{16}[/tex]

[tex]x=8[/tex]

Recall that the new dimensions are:

[tex]Length = x+2[/tex]

[tex]Width = y+4[/tex]

So:

[tex]Length = 8+2[/tex]

[tex]Length = 10[/tex]

To double-check.

Differentiate A'

[tex]A' = -512y^{-2}+2[/tex]

[tex]A'' = -2 * -512y^{-3}[/tex]

[tex]A'' = 1024y^{-3}[/tex]

[tex]A'' = \frac{1024}{y^{3} }[/tex]

The above value is:

[tex]A'' = \frac{1024}{y^{3} } > 0[/tex]

In other words, the estimated numbers are at their lowest.

Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

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The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

The area of a square with sides of one inch is equal to one square inch (plural: square inches).

We have that:

Let the dimension of the paper be x and y.

Such that:

Length = x

Width = y

So:

Area = xy

Substitute 128 for Area

128 = xy

Make x the subject.

x=128/y

When 1 inch margin is at top and bottom

The Length becomes:

length = x+2

When 2-inch margin is at both sides

The width becomes:

width = y+4

The New Area (A) is then calculated as:

A = (x+2)(y+4)

Substitute  for x

A = (128/y +2)(y+4)

Open Brackets

A = 128 +512/y + 2y +8

Collect Like Terms

A = 512/y + 2y +136

To calculate the smallest possible value of y, we have to apply calculus.

Differentiate A with respect to y

A' = -512/y*y  +2

Set

A' = 0

This gives:

y = 16

Recall that:

x = 128/y

x = 8

Recall that the new dimensions are:

Length = x +2

Width = y+4

So:

Length = 10

To double-check.

Differentiate A'

A'' = 1024/y*y*y

The above value is greater than 0

In other words, the estimated numbers are at their lowest.

Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

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