The results of an awesome survey question are shown below.
If there were a popsicle stick for each selection, what is the probability of selecting one that says books without pictures, replacing it, and then selecting one that says audio books?
Round your answer to the nearest hundredth.

The statement that "as the sample size gets larger, the standard deviation of the sampling distribution will get smaller" is actually true, so none of the statements in the group of answer choices is false.

This phenomenon is known as the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the population distribution.

The standard deviation of the sampling distribution is proportional to the standard deviation of the population divided by the square root of the sample size.

Therefore, as the sample size gets larger, the denominator in this equation gets bigger, causing the standard deviation of the sampling distribution to become smaller.
In conclusion, all the statements in the group of answer choices are true, including the statement about the relationship between sample size and standard deviation of the sampling distribution.

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The likelihood you draw at least one blue card out of the three draws if you're drawing with a replacement is 0.784.

Given that You are randomly drawing 3 cards from a deck that holds 12 red cards and 8 blue cards.

Further, the probability of getting all three red cards is,

Probability = [ (Number of red cards)/(Total number of cards) ] ³

                  = (12/20)³

                  = (0.6)³

                  = 0.216

Since you need the probability of getting at least one blue card, therefore, the probability of getting at least one blue card can be found by deducting the probability of getting no card blue from the total probability.

Thus, the likelihood you draw at least one blue card if you're drawing with a replacement is,

P(X≥1) = 1 - P(x=0)

          = 1 - 0.216

          = 0.784

Hence, the probability is 0.784.

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The random variables y1 and y2 with joint density function f(y1, y2) = e^(-y1y2), y1>0, y2>0, 0 elsewhere were considered in exercise 5.7. The question is whether y1 and y2 are independent.

The answer is yes, y1 and y2 are independent. This is because their joint density function can be factored into a product of their marginal density functions, f(y1) = e^(-y1y2), and f(y2) = e^(-y1y2).

The fact that the joint density function can be expressed as the product of the marginal density functions indicates that y1 and y2 are independent, and that the value of one variable does not affect the value of the other variable.

Therefore, if we know the value of y1, it does not provide any information about the value of y2, and vice versa.

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If Russell runs at a constant speed, then we can use the formula. If we know his speed and the time he runs for, we can calculate the distance he travels.

distance = speed x time

If we know his speed and the time he runs for, we can calculate the distance he travels.

However, since you did not provide any information about Russell's speed, we cannot give a specific answer to the question.

If you provide the speed, we can use the formula above to calculate the distance he travels in 2.8 seconds. Alternatively, if you provide any additional information about the problem, such as the distance he has already traveled or the acceleration he experiences, we may be able to use that information to calculate the distance he travels in 2.8 seconds.

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The volume of the cone is approximately 84.78 cubic inches.To find the volume of a cone with a diameter of 6 inches and a slant height of 9 inches, we need to first find the radius of the cone. The diameter is 6 inches, so the radius is half of that, which is 3 inches.

Next, we can use the Pythagorean theorem to find the height of the cone. The slant height is 9 inches, which is the hypotenuse of a right triangle with legs equal to the radius and the height of the cone. We can write the following equation:

r^2 + h^2 = l^2

where r is the radius, h is the height, and l is the slant height. Substituting the given values, we get:

3^2 + h^2 = 9^2

9 + h^2 = 81

h^2 = 72

h = sqrt(72)

h ≈ 8.485 inches

Now that we have the radius and height, we can use the formula for the volume of a cone:

V = (1/3)πr^2h

Substituting the values we found, we get:

V = (1/3)π(3^2)(8.485)V ≈ 84.78 cubic inches.

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The required,
A. Expression by factoring out the greatest common factor is 3xy(2x - 1 - 8y + 4y),
B.  The completely factored form of the expression 6x²y - 3xy - 24xy²+ 12y² is (2x - 1)(3xy - 12y²).

Part A: To factor out the greatest common factor (GCF) from the expression 6x²y - 3xy - 24xy² + 12y², we need to find the common factors of all the terms.

The common factors are 3, x, y.

Taking out the GCF, we have:

GCF: 3xy

Rewritten expression: 3xy(2x - 1 - 8y + 4y)

Part B: Now let's factor the entire expression completely.

Given expression: 6x²y - 3xy - 24xy² + 12y²

Group the terms:

(6x²y - 3xy) + (-24xy² + 12y²)

Factor out the GCF from each group:

3xy(2x - 1) - 12y²(2x - 1)

Notice that we now have a common binomial factor, (2x - 1).

Factor out the common binomial factor:

(2x - 1)(3xy - 12y²)

Therefore, the completely factored form of the expression 6x²y - 3xy - 24xy²+ 12y² is (2x - 1)(3xy - 12y²).

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Therefore, the volume of the solid generated by revolving the region bounded by y= x2, y = 0, and x = 2 about the x-axis is 16.

To find the volume of the solid generated by revolving the region bounded by y=x^2, y=0, and x=2 about the x-axis, we will use the method of cylindrical shells.
First, let'sgraph the region to better visualize it.
graph{y=x^2 [-10, 10, -5, 5]}

The region is bounded by the x-axis, the line x=2, and the curve y=x^2. When we revolve this region about the x-axis, we will generate a solid with a cylindrical shape. To find the volume of this solid, we will slice it into thin cylindrical shells and add up the volumes of each shell.
Let's consider a thin slice of the region at x. The height of this slice will be given by the curve y=x^2, and the thickness of the slice will be dx. When we revolve this slice about the x-axis, it will generate a cylindrical shell with radius x and height x^2. The volume of this shell can be calculated using the formula for the volume of a cylinder:

V = 2πrxh

where r is the radius of the cylinder, h is its height, and π is the constant pi. In this case, we have r = x and h = x^2, so
V = 2πx(x^2)
V = 2πx^3
To find the total volume of the solid, we need to add up the volumes of all these cylindrical shells from x=0 to x=2:
V = ∫(0 to 2) 2πx^3 dx
V = πx^4 |(0 to 2)
V = π(2^4 - 0^4)
V = 16π
Therefore, the volume of the solid generated by revolving the region bounded by y=x^2, y=0, and x=2 about the x-axis is 16π.

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The true statement is that SJF Incorporated conducts business in multiple states and a foreign country. This means that the company is subject to different laws, regulations, and taxes in each jurisdiction, and must comply with the requirements of each. This can create complex legal and financial challenges for the company, as it must navigate the different legal systems and business environments of each region.

In particular, SJF Incorporated must be aware of the laws and regulations governing its operations in each jurisdiction. This includes corporate governance requirements, tax laws, labor laws, and environmental regulations, among others. Failure to comply with these requirements can result in legal liabilities, fines, and reputational damage for the company. Therefore, it is important for SJF Incorporated to maintain a strong compliance program that takes into account the differences between the jurisdictions in which it operates.

In addition, SJF Incorporated must also consider the cultural differences and business practices in each region. This includes understanding the local customs, language, and business etiquette, as well as building relationships with local stakeholders and partners. By adapting to the unique characteristics of each region, SJF Incorporated can build a successful and sustainable business across multiple jurisdictions.

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Answer: Your answer is B.

Step-by-step explanation:

The roots of the quadratic equation is x = imaginary

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

A = 9x² + 18x + 79 = 0

On simplifying , we get

The quadratic formula in the form ax² + bx + c = 0, the solutions for x is

x = (-b ± √(b² - 4ac)) / (2a)

In the given equation, a = 9, b = 18, and c = 79.

x = (-18 ± √(18² - 4979)) / (2*9)

x = (-18 ± √(324 - 2844)) / 18

x = (-18 ± √(-2520)) / 18

Since the discriminant (b² - 4ac) is negative (-2520), the quadratic equation does not have any real roots.

Hence , the roots would involve complex numbers or imaginary

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Yes, the construction demonstrates how to copy a segment correctly by hand.

The specific construction steps that show this are:

The construction is correct because it follows the steps for copying a segment correctly by hand. The compass is used to measure the length of the original segment, and then the compass is used to draw an arc with the same length.

The line segment CD is drawn through the intersection of the arc and the original segment, and this line segment is congruent to the original segment.

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(a) a = {6, {6}, (6)2}, b = {6, {6}, {{6}}} .  Neither a nor b is a proper subset of the other because they both have elements that are not in the other set.


we need to compare the elements of set a and set b.
First, is a ⊆ b?
Yes, a is a subset of b because all the elements in set a are also in set b.
Second, is b ⊆ a?
No, b is not a subset of a because b has an extra element {{6}} that is not in set a.
Finally, is either a or b a proper subset of the other?
No, neither set is a proper subset of the other because they have the same number of elements and only differ in the way the elements are arranged.

a = {6, {6}, (6)²}, b = {6, {6}, {{6}}}
1. Is a ⊆ b?
No, because (6)² = 36 is an element in a but not in b.
2. Is b ⊆ a?
No, because {{6}} is an element in b but not in a.
3. Is either a or b a proper subset of the other?

Remember to analyze the elements of the sets and compare them to determine if one is a subset or proper subset of the other.

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By creating equation, we can solve for x to get the following values:

8. x = 9;      9. x = 9

In order to solve for x in each problem, note that the segments are equal to each other, therefore, we would create an equation that will enable us solve for x.

8. 2x + 12 = 5x - 15

Combine like terms

2x - 5x = -12 - 15

-3x = -27

Divide both sides by -3:

-3x/-3 = -27/-3

x = 9

9. 8x - 63 = 4x - 27

8x - 4x = 63 - 27

4x = 36

4x/4 = 36/4 [division property]

x = 9

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The statement that if we reject the null hypothesis [tex]H_0: μ=50[/tex], at the 0.05 significance level, then the 95% confidence interval for μ will contain the value 50 is false statement.

The null hypothesis states that there is no relationship between the two variables which are studied. It is denoted by H₀. If the null hypothesis is rejected in hypothesis testing the alternative hypothesis is true.

We have, null hypothesis defined as [tex]H_0: μ= 50[/tex]

then alternative hypothesis is defined as [tex]H_a: μ ≠ 50[/tex].

Level of significance = 0.05

Now, from above discussion, if we reject the null hypothesis of mean is 50 then we can conclude that the population mean value is other than 50. That is the 95% confidence interval for μ does not contain the value 50. Hence, it is a false statement.

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Complete question:

True/ false : if we reject the null hypothesis [tex]H_0: μ=50[/tex] at the 0.05 significance level, then the 95onfidence interval for μ will contain the value 50.

Answer: 28

Step-by-step explanation: Add all together and add 5 to make the 28

The approximate mass of air in a typical room with dimensions 5.7m × 3.9m × 3.0m is about 80.14 kg.

To calculate the approximate mass of air in a typical room with dimensions 5.7m × 3.9m × 3.0m, we need to find the volume of the room first. The volume of the room is given by:

Volume = length x width x height = 5.7m x 3.9m x 3.0m = 66.78 cubic meters

Assuming that the air in the room has a density of approximately 1.2 [tex]kg/m^3[/tex], we can use the formula:

Mass = Density x Volume

where density is in kg/m^3 and volume is in cubic meters.

Substituting the values, we get:

Mass = [tex]1.2 kg/m^3 x 66.78[/tex] cubic meters

Mass ≈ 80.14 kg

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To find the inverse Laplace transform of the function h(s) = as * b * (s - α)^2 / β^2, you can use the inverse Laplace transform formula and properties. Here's the result:
Inverse Laplace Transform{ h(s) } = L^(-1){ as * b * (s - α)^2 / β^2 }

The inverse Laplace transform of this function is a time-domain function represented as h(t). Keep in mind that the inverse Laplace transform is a unique process that transforms a function from the frequency (s) domain back to the time (t) domain. Unfortunately, without more information about the specific values of a, b, α, and β, I cannot provide a more precise answer.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of 6000}}{\left( \cfrac{4}{100} \right)6000}\implies 240[/tex]

The first three nonzero terms of the Taylor series are:

f(x) = 6(x-5π) + 0(x-5π)² + ... = 6x - 30π

What is the Taylor series?

A Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The series provides a way to approximate the function in the neighborhood of that point.

We start by finding the nth derivative of f(x) at x = 5π for any positive integer n:

f(x) = 6 tan x

f'(x) = 6 sec² x

f''(x) = 12 sec² x tan x

f'''(x) = 12 sec⁴x + 24 sec² x tan² x

We can see a pattern emerging in the derivatives, so we can guess that the nth derivative is:

f^(n)(x) = P(n) secⁿx + Q(n) sec⁽ⁿ⁻²⁾x tan² x

where P(n) and Q(n) are polynomials in n.

Now, we can use the definition of the Taylor series:

f(x) = Σ0,∞(x-c)ⁿ

to find the first three nonzero terms of the Taylor series for f(x) centered at c = 5π.

Plugging in the nth derivative at x = 5π:

fⁿ(5π) = P(n) secⁿ 5π + Q(n) sec⁽ⁿ⁻²⁾ 5π tan² 5π

We can simplify this using the fact that sec(5π) = -1 and tan(5π) = 0:

fⁿ(5π) = (-1)ⁿ P(n) + Q(n) (-1)⁽ⁿ⁻¹⁾

Now, we can write out the first few terms of the Taylor series:

f(x) = f(5π) + f'(5π)(x-5π) + (f''(5π)/2!)(x-5π)² + ...

f(5π) = 6 tan(5π) = 0

f'(5π) = 6 sec²(5π) = 6

f''(5π) = 12 sec²(5π) tan(5π) = 0

hence, the first three nonzero terms of the Taylor series are:

f(x) = 6(x-5π) + 0(x-5π)² + ... = 6x - 30π

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Width of door = 3ft

width of window = 9 ft

length of bench = 12 ft

Given that,

1 unit = 3 feet

Now from figure,

Width of door = 1 unit

We know that,

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

In feet Width of door  = 3 feet

Width of window = 3 units

Therefore,

In feet width of window  = 3x3 = 9 feet

length of bench = 4 units

Therefore,

In feet length of bench  = 3x4 = 12 feet

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The complete question is:

in Arvins scale drawing of his garden shed, 1 unit = 3 feet. find the actual measurements in ft:

Width of door

width of window

length of bench

The exact formula for the probability of a node with degree k being attached from the new node is given by the following expression:

pk = (k ⋅ m) / Σj(j ⋅ m)

where m is the average degree of the network and Σj(j ⋅ m) is the sum of the product of the degree and the number of nodes with that degree.

To show that if pk = 1, then Pr{a node with degree k being attached from a new node} = mpk, we can use the definition of conditional probability:

Pr{a node with degree k being attached from a new node} = Pr{new node attaches to a node with degree k} × Pr{a node with degree k is selected}

From the definition of the probability pk, we know that Pr{a node with degree k is selected} = pk. We also know that the probability that a new node attaches to a node with degree k is proportional to the number of nodes with degree k. Let nk be the number of nodes with degree k, then the probability of a new node attaching to a node with degree k is nk / n, where n is the total number of nodes in the network.

Since the network is assumed to be large, we can assume that the number of nodes with degree k is proportional to pk. That is, nk = mpk. Then, the probability of a new node attaching to a node with degree k is:

Pr{new node attaches to a node with degree k} = nk / n = mpk / n

Substituting these values in the expression for Pr{a node with degree k being attached from a new node}, we get:

Pr{a node with degree k being attached from a new node} = (mpk / n) × pk = mpk

Therefore, if pk = 1, then Pr{a node with degree k being attached from a new node} = mpk.

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175 texts would need to be sent for the charges of the two companies to be equal.

Let's represent the number of texts as 'x'.

For the first company, the total charge would be $13 + $0.12x (since they charge 12 cents per text).

For the second company, the total charge would be $20 + $0.08x (since they charge 8 cents per text).

To find the number of texts needed for the charges to be equal, we can set up the equation:

$13 + $0.12x = $20 + $0.08x

$0.12x - $0.08x = $20 - $13

$0.04x = $7

x = $7 / $0.04

x = 175

Therefore, 175 texts would need to be sent for the charges of the two companies to be equal.

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Answer:

r - 1  + (-1) / (r+5)

Step-by-step explanation:

1) divide r² by r to get r.  write this on top.

2) multiply this r by r + 5 to get r² + 5r

3) subtract ( r² + 5r) from  r² + 4r. this gives answer of -r

4) bring down the -6 from dividend

5) divide -r by r to get -1

6) multiply -1 by r + 5. this gives answer -r - 5

7) subtract (-r - 5) from -r - 6. this gives answer of -1

8) now we cannot divide -1 by r. that means -1 is our remainder.

9) you can confirm this by multiplying out (r + 5) (r - 1) = r² + 4r - 5.

this is 1 more than our original divisor (that was -6)

We can see here that according to the partial W-2 form, the money that was paid in FICA taxes is: B. $1789.87.

Governments impose taxes as obligatory financial charges or levies on citizens, businesses, and other organizations to pay for public expenses and fund government operations.

FICA taxes are comprised of Social Security and Medicare taxes.

The Social Security tax rate is 6.2% and the Medicare tax rate is 1.45%. The total FICA tax rate is 7.65%.

The breakdown of the FICA taxes paid:

Social Security tax: $1430.20

Medicare tax: $359.67

Total FICA taxes: $1789.87

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There are 360 ways for a four-letter words that can be formed using the letters of the word finite. So, correct option is B.

To find the number of four-letter words that can be formed using the letters of the word "finite," we can use the permutation formula, which is:

nPr = n! / (n-r)!

where n is the total number of items to choose from, and r is the number of items to choose. In this case, we have 6 letters to choose from (n=6), and we want to choose 4 letters (r=4).

Therefore, the number of four-letter words that can be formed is:

6P₄ = 6! / (6-4)!

= 6! / 2!

= (6 x 5 x 4 x 3 x 2 x 1) / (2 x 1)

= 720 / 2

= 360

Therefore, the answer is 360, which corresponds to option B.

In summary, there are 360 four-letter words that can be formed using the letters of the word "finite," by using the permutation formula to calculate the number of possible arrangements of the 6 letters taken 4 at a time.

So, correct option is B.

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In 2.22 years, there will only be 50,000 African penguins left.

Since the population of African penguins is cut in thirds every year, we can use the exponential decay model to describe its population as follows:

P(t) = P₀(1/3)^t

where P(t) represents the population after t years, and P₀ represents the initial population in 2000, which is 200,000.

So, the formula for the population of African penguins after t years is:

P(t) = 200,000(1/3)^t

To find how many years it will take for the population to be reduced to a certain number, we can plug in that number for P(t) and solve for t.

For example, if we want to find out how many years it will take for the population to be reduced to 50,000, we can write:

50,000 = 200,000(1/3)^t

Divide both sides by 200,000:

1/4 = (1/3)^t

Take the natural logarithm of both sides:

ln(1/4) = ln[(1/3)^t]

ln(1/4) = t ln(1/3)

Solve for t:

t = ln(1/4) / ln(1/3)

Using a calculator, we get t ≈ 2.22 years.

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-412 degrees is equivalent to -0.907571 radians.

To convert -412 degrees to radians, we need to use the formula:

[tex]radians = (\pi/180) \times degrees[/tex]

where pi is the mathematical constant pi (approximately 3.14159) and degrees is the angle in degrees that we want to convert.

First, we need to handle the negative sign.

A negative angle means that we are rotating in the opposite direction, which is equivalent to adding 360 degrees to the angle.

So, we can add 360 to -412 to get:

-412 + 360 = -52

Now, we can use the formula to convert -52 degrees to radians:

[tex]radians = (\pi/180) \times (-52)[/tex]

radians = -0.907571

Therefore, -412 degrees is equivalent to -0.907571 radians.

To understand this conversion in more detail, it is important to understand what degrees and radians are.

Degrees are a unit of measurement for angles, where a full circle is divided into 360 equal parts. Radians are another unit of measurement for angles, where a full circle is divided into [tex]2\pi[/tex] (or approximately 6.28) equal parts.

One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

Converting between degrees and radians is important in many areas of mathematics and physics, particularly when dealing with trigonometric functions such as sine, cosine, and tangent.

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The volume of the solid is (7π/5) cubic units.

We have,

To find the volume of the solid obtained by rotating the region under the curve y = x³ about the line y = -1 over the interval [0,1], we can use the method of cylindrical shells.

Consider an infinitesimally thin vertical strip of width dx at a distance x from the y-axis.

The height of this strip is given by the difference between the curve

y = x³ and the line y = -1.

The height of the strip is (x³ - (-1)) = (x³ + 1).

The circumference of the cylindrical shell is given by 2πx, and the thickness of the shell is dx.

Hence, the volume of the shell is given by dV = 2πx (x³ + 1) dx.

To find the total volume, we integrate this expression over the interval [0,1]:

V = ∫ [0,1] 2πx (x³ + 1) dx.

To find the volume, we evaluate the integral:

V = ∫[0,1] 2πx (x³ + 1) dx

Let's integrate term by term:

V = 2π ∫[0,1] ([tex]x^4[/tex] + x) dx

Integrating each term separately:

V = 2π [(1/5)[tex]x^5[/tex] + (1/2)x²} evaluated from 0 to 1

Plugging in the limits:

V = 2π [(1/5)([tex]1^5[/tex]) + (1/2)(1²)] - [(1/5)([tex]0^5[/tex]) + (1/2)(0²)]

V = 2π [(1/5) + (1/2)] - [0 + 0]

V = 2π (7/10)

V = (14π/10)

Simplifying the fraction:

V = (7π/5)

Therefore,

The volume of the solid is (7π/5) cubic units.

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Let x be the length of the candle before it was lit. The candle burns at a constant rate of 0.9 inches per hour, so after burning for 3.5 hours, the length of the candle remaining is 9.85 - 0.9(3.5) = 6.25 inches. We can set up the equation:

x - 0.9(3.5) = 6.25

Simplifying this equation, we get:

x = 9.95 inches

Therefore, the length of the candle before it was lit was 9.95 inches.

In this problem, we used the fact that the rate at which the candle burns is constant, and we used this information to calculate how much of the candle had burned after 3.5 hours. From there, we were able to set up an equation to find the length of the candle before it was lit. This problem illustrates how to use algebraic equations to solve real-world problems involving rates and quantities.

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The distribution that is the limit of a Hypergeometric Distribution as the population size increases (and other conditions are satisfied) is the Binomial Distribution.

The Hypergeometric Distribution models the probability of drawing a specific number of successes (items of interest) from a finite population without replacement. It is appropriate when sampling without replacement from a small population.

However, as the population size becomes significantly larger, the Hypergeometric Distribution can be approximated by the Binomial Distribution. The Binomial Distribution models the probability of obtaining a certain number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.

The conditions for the approximation to hold are that the population size is much larger than the sample size, and the probability of success in the population remains constant. In such cases, the Hypergeometric Distribution converges to the Binomial Distribution.

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