in the previous simulation, when we were building a sampling distribution, what does each dot represent in the graph?

The value of a for which the solution of the inequality is all real numbers is a = 5.

We have to first simplify the inequality:

A(x + 3) < 5x + 15 - x

Ax + 3A < 4x + 15

Ax - 4x < 15 - 3A

Simplifying further:

x(A - 4) < 15 - 3A

Now, we need the inequality to hold for all real values of x. This means that the coefficient of x, (A - 4), must have a fixed sign, and that the right-hand side, 15 - 3A, must be unbounded.

For the coefficient of x to have a fixed sign, we need either A - 4 < 0 or A - 4 > 0. This means that A must be less than 4 or greater than 4.

For the right-hand side to be unbounded, we need 15 - 3A to be equal to positive or negative infinity. Since 15 - 3A is a linear function of A, this only occurs when A = 5.

So, the solution to the inequality for all real numbers is:

if A < 4, then the solution is x < (15 - 3A) / (4 - A)

if A > 5, then the solution is x > (15 - 3A) / (4 - A)

if A = 5, then the solution is all real numbers.

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Minimum value is 50, maximum value is 66, median is 59, Q1 is 53.5 and Q3 is 65. Box-and-whisker plot:

A box plot, often referred to as a whisker plot, shows the distribution of a continuous variable along with details like the median, quartiles, and outliers. A set of data's variety is shown graphically in this way. The plot, often known as a five-number summary, presents five bits of information. The fundamental benefit of box whisker plots is that the overlap between the distributions of various qualities may be calculated by comparing them side by side.

You must determine the minimum value, maximum value, median, and quartiles in order to create a box-and-whisker plot of the provided data.

The base number is fifty.

The highest number is 66.

You must sort the data from smallest to largest in order to determine the median. The listed data are:

50, 51, 51, 52, 53, 53, 54, 55, 58, 58, 58, 60, 61, 62, 63, 65, 65, 66, 66

The middle value of the ordered data is the median. Finding the average of the two middle values is necessary since the data set (18 values) contains an even number of values:

(58 + 60) ÷ 2 = 59

Divide the ordered data into four equal sections before calculating the quartiles. The median of the lower half of the data set is the first quartile (Q1). The median of the data set's upper half represents the third quartile (Q3).

The data set's lower half consists of:

50, 51, 51, 52, 53, 53, 54, 55

The data set's upper half is as follows:

58, 58, 58, **60**, **61**, **62**, **63**, **65**, **65**, **66**, **66**

First quartile (Q1):

(53 + 54) ÷ 2 = **53.5**

Third quartile (Q3) comprises:

(65 + 65) ÷ 2 = **65**

With all of this knowledge at hand, you can now develop a box-and-whisker plan.

Given below:

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For all given Quadrilaterals none has enough information provided in the problem to definitively say - if they are a parallelogram.Hence, option E is correct for all.

If a quadrilateral is a parallelogram, it satisfies the following properties:

It is important to note that in order to definitively conclude that a quadrilateral is a parallelogram, all four properties must be satisfied. If only one or some of the properties are met, it does not necessarily guarantee that the quadrilateral is a parallelogram.

Figure 1-: Adjacent angles are 105 and 75 degrees, which satify the condition of opposite angles being equal but except this no other information is provided, Hence, we don't have enough information to say figure 1 is a parallelogram.

Figure 2-: Diagonals bisect each other and make angle 65 degree with each other. Given that Diagonal 1 bisects Diagonal 2 and the opposite sides of the quadrilateral are equal, by using SAS criterion, the congruency of triangles formed by the diagonals can be derived to say that the opposite angles of the quadrilateral are also equal . However, we still need more information about parallelism of sides to definitively say given quadrilateral is a parallelogram.

Figure 3-: One pair of opposite side is equal in length ,while other pair of line is parallel to each other.This information is insufficient to determine if given quadrilateral is a parallelogram.

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The value of function k(f(x)) is 12x³ + 32x - 8.

Function composition is a way to combine two or more functions to form a new function. In this case, we are given two functions f(x) and k(x), and we need to find the value of k(f(x)), which means we need to apply the function k(x) to the output of the function f(x).

Here we have

Functions f(x)= 3x³ +8x -2 and k(x) = 4x

To find k(f(x)), we need to substitute the expression for f(x) into k(x) wherever we see x. So, we have:

k(f(x)) = 4(f(x)) = 4(3x³ + 8x - 2)

We can simplify this expression by distributing the 4:

k(f(x)) = 12x³ + 32x - 8

Therefore,

The value of function k(f(x)) is 12x³ + 32x - 8.

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The statement is true. The DecimalFormat class is part of the Java API, specifically within java.text package, so it is automatically available to your programs. You can use it to format numbers in various ways, such as for displaying currency or percentages.

DecimalFormat is a concrete subclass of NumberFormat that formats decimal numbers. It has a variety of features designed to make it possible to parse and format numbers in any locale, including support for Western, Arabic, and Indic digits. It also supports different kinds of numbers, including integers (123), fixed-point numbers (123.4), scientific notation (1.23E4), percentages (12%), and currency amounts ($123). All of these can be localized.

To obtain a NumberFormat for a specific locale, including the default locale, call one of NumberFormat's factory methods, such as getInstance(). In general, do not call the DecimalFormat constructors directly, since the NumberFormat factory methods may return subclasses other than DecimalFormat. If you need to customize the format object, do something like this:

NumberFormat f = NumberFormat.getInstance(loc);

if (f instanceof DecimalFormat) {

    ((DecimalFormat) f).setDecimalSeparatorAlwaysShown(true);

}

A DecimalFormat comprises a pattern and a set of symbols. The pattern may be set directly using applyPattern(), or indirectly using the API methods. The symbols are stored in a DecimalFormatSymbols object. When using the NumberFormat factory methods, the pattern and symbols are read from localized ResourceBundles

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True. The Decimal Format class is a part of the Java API and is included in the java.text package.

It is automatically available to Java programs without the need for any additional installations or imports.

The Decimal Format class is part of the Java API, and it is automatically available to your programs.

The Java API is a collection of pre-written classes, methods, and interfaces that are part of the Java Development Kit (JDK).

These classes and methods provide a wide range of functionalities that can be utilized by Java developers to build robust applications.
The Decimal Format class, specifically, is a subclass of the Number Format class and is used to format decimal numbers according to a specific pattern.

The class provides methods to format and parse decimal numbers and can be used to specify the number of digits after the decimal point, the use of a thousand separator, and the currency symbol.
The Decimal Format class in your Java program, you simply need to import the class using the import statement, and then create an instance of the class.

For example:
import java. text. Decimal Format.
public class MyClass

{
public static void main (String [] args) {
Decimal Format df = new Decimal Format("#.00");
double num = 1234.5678
System.out.println(df.format(num));
}
}
The Decimal Format class using the import statement, and then create an instance of the class called df.

We then use the format method of the class to format the decimal number 1234.5678 with two decimal places.
The Decimal Format class is an essential part of the Java API and is automatically available to your programs.

Its inclusion in the Java API makes it easier for Java developers to format decimal numbers in their applications.

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The required sample size of the given estimate is 1090.9809

The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,

For the 90% confidence the value of the z = 1.645

Now the sample size is given as,

n = [z × σ/2.5]²

Substitute values in the above equation,

n = [1.645×50.2/2.5]²

n = 1090.9809

Thus, the required sample size of the given estimate is 1090.9809.

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The correct answer is (c) 1.9

To calculate the test statistic in this example, we can use the formula for a z-test for proportions:

[tex]z = (p - P) / \sqrt{[P(1-P) / n][/tex]

where:

p is the sample proportion of vegetarians (140/1000 = 0.14)

P is the hypothesized population proportion of vegetarians (0.12)

n is the sample size (1000)

Substituting these values into the formula, we get:

[tex]z = (0.14 - 0.12) / \sqrt{[0.12(1-0.12) / 1000][/tex]

z = 0.02 / 0.0110

z = 1.818 (rounded to three decimal places)

Therefore, the test statistic in this example will be approximately equal to 1.818. The answer closest to this value is (c) 1.9

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Answer: A. 5,220,000 songs were downloaded in the year 2020.

Step-by-step explanation: The interpretation of s(2020) = 5,220,000 is that in the year 2020, 5,220,000 songs were downloaded. The function s(d) represents the number of songs downloaded in a year d, so plugging in 2020 for d gives us the specific number of songs downloaded in that year.

Step-by-step explanation:

18-2x<3(2x-1)-3

21-2x<6x-3

24<8x

3<x

Interval notation

(3, ∞)

The area swept clean by the rear window wiper blade is approximately 91.37 square inches.

We'll calculate the area swept clean by the rear window wiper blade using the given information.
Convert the angle from degrees to radians:

115 degrees * (π radians / 180 degrees) = (23π/36) radians.
Find the length of the arc that the wiper blade traces out:

Arc length = (radius * angle) = (10 inches * (23π/36) radians) ≈ 20.08 inches.
Calculate the area of the sector formed by the arc and the pivot point:

Sector area = (1/2) * (radius² * angle) = (1/2) * (10 inches² * (23π/36) radians) ≈ 100.42 square inches.
Find the length of the arc that the mounting point of the blade traces out:

Arc length = (radius * angle) = (3 inches * (23π/36) radians) ≈ 6.02 inches.
Calculate the area of the sector formed by this arc and the pivot point:

Sector area = (1/2) * (radius² * angle) = (1/2) * (3 inches² * (23π/36) radians) ≈ 9.05 square inches.
Subtract the smaller sector area from the larger one to get the area swept clean by the wiper blade:

Area swept clean = 100.42 square inches - 9.05 square inches ≈ 91.37 square inches.

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The area swept clean by the rear window wiper blade is approximately 31.53 square inches.

To determine the area swept clean by the rear window wiper blade, we first need to find the length of the arc covered by the blade. We can use the formula:

arc length = radius * angle in radians

To convert the angle from degrees to radians, we multiply by[tex]\pi /180[/tex]:

115 degrees x [tex]\pi /180[/tex] = 2.007 radians

The radius is the length of the wiper arm, which is 13 inches minus the distance from the pivot point to the blade, which is 3 inches. Therefore, the radius is:

13 inches - 3 inches = 10 inches

Now we can calculate the arc length:

arc length = 10 inches x 2.007 radians = 20.07 inches

So the area swept clean by the wiper blade is approximately equal to the area of the sector formed by the arc and the two radii. The formula for the area of a sector is:

area = (angle in radians / [tex]2\pi[/tex]) x [tex]\pi r^2[/tex]

Plugging in values we have:

area = (2.007 / [tex]2\pi[/tex]) x [tex]\pi[/tex][tex](10 inches)^2[/tex] = 31.53 square inches

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The statement " Some irrational numbers do not have an additive inverse" is false because every real number, whether rational or irrational, has an additive inverse.

Every real number, whether rational or irrational, has an additive inverse. The additive inverse of a real number x is the number that, when added to x, gives zero as the result. For any real number x, its additive inverse is -x.

This is a fundamental property of the real numbers and is true regardless of whether a number is rational or irrational. Therefore, any irrational number, such as the square root of 2 or pi, also has an additive inverse. For example, the additive inverse of the irrational number √2 is -√2, since √2 + (-√2) = 0.

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Answer:

$481

Step-by-step explanation:

37×$17=$481

he made $481

Answer:

-6/7

Step-by-step explanation:

From the figures, AB is a tangent to the C because they make a right angles (90⁰)

Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.

We shall be determining the angle at C to see if it gives 90⁰

Using trigonometrical ratios of tangent

TanB = Opposite/Adjacent

Tan B. = 4.8/7.2

Tan B = 0.6667

B = Tan⁻¹0.6667

<B = 33.69⁰

Also in the same manner,

TanS = opp/Adj

Tan S = 7.2/4.8

Tan S = 1.5

S = Tan⁺¹1.5

< S = 56.31⁰

Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰

Therefore AB makes tangent at C

20.  

Tan C = Opp/Adj

Tan C = 15/11.2

Tan C = 1.3393

C = Tan⁺¹1.3393

< C = 53.25

Also, Tan B = 11.2/15

Tan B = 0.7467

B = 36.75

<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰

Therefore AB makes a tangent at C

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If M is the midpoint of the leg CG, then the

a) Area of ABD = 18.75 ft^2

b) Area of MOC = 15 ft^2

To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.

First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write

AB/CD = AD/CO

Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:

AB/CD = BC/CO

We also know that the area of AOD is 15 ft^2

Area of ABD/ Area of COD = AB/CD

We can substitute the ratio AB/CD from the similarity relation above to get

Area of ABD/ Area of COD = BC/CO

Since the bases of the trapezoids are parallel

Area of ABD/ Area of COD = BD/CO

Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write

Area of ABD/ Area of COD = 5/3

Area of ABD = 5/8 × Area of COD

We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore

Area of ABD = 5/8 × 30 = 18.75 ft^2

Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.

Let x be the length of OC, and let y be the length of OG. Then we have

Area of MOC/ Area of MOG = x/y

Also, since M is the midpoint of CG, we have

x = 2y

Substituting this into the first equation, we get

Area of MOC/ Area of MOG = 2

We know that the area of MOG is half the area of AOD, so

Area of MOG = 15/2 ft^2

Therefore, we have

Area of MOC = 2 × Area of MOG = 15 ft^2

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The length of each segment is:

YW = 5 units

WZ = 8 units

The length of each segment can be found by using "bisector of an angle in a triangle theorem".

The theorem states that "the bisector of an angle in a triangle theorem divides the opposite sides in the ratio of the sides containing the angle".

Applying the theorem on the given triangle, we can say:

XY/XZ = YW/WZ

8/12.8 = (t/2)/(t-2)

8(t-2) = 12.8(t/2)

8t - 16 = 6.4t

8t - 6.4t = 16

1.6t = 16

t = 10

YW = t/2

YW = 10/2

YW = 5 units

WZ = t - 2

WZ = 10 - 2

WZ = 8 units

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"It can vary - it really depends on the distribution of the variable."

The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.

Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.

Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.

The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.

While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.

In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.

A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.

Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.

There is no established guideline, however 8–10 intervals are typically utilized.

A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.

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The height of the pyramid whose volume is already given would be = 1,440,000 ft

To calculate the height of the pyramid, the formula of the Volume of the pyramid should be used.

Volume = 1/3lwh

where l = base length = 8h-30 ft= 3.75 ft

w = base width= 8h+20 ft = -2.5 ft

h = h ft

The volume of the pyramid = 4,500,000 cubic feet

4,500,000 = 1/3 × (3.75)(-2.5)h

Make h the subject of formula;

h = 4500000×3/3.75×(-2.5)

h = 13500000/9.375

h = 1,440,000 ft.

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The measure of the angle m∠FGH is 83°.

Since the measure of an angle formed by a two tangents drawn from a point outside the circle is one-half the the difference of the intercepted arcs.

Thus, we can say:

m∠FGH = 1/2 * (∠FIH - 97°)

∠FIH = 360 - 97 = 263° (sum of angle in a circle)

m∠FGH = 1/2 * (263 - 97°)

m∠FGH =  1/2 * 166

m∠FGH = 83°

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The correct statement about the graph is,

A graph of two solid lines that intersect at point (4, 0).

Given that;

This system of inequalities models the scenario.

4x + 2y ≤ 16

And, x + y ≥ 4

Now, We can draw the inequalities in graph, we get;

The intersection point of the inequality is, (4, 0)

Thus, The correct statement about the graph is,

A graph of two solid lines that intersect at point (4, 0).

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The measures of center and variability that would be most appropriate to describe the given distribution is D) Median and IQR.

The middle value in a set of data is represented by the median, a measure of central tendency. It is the value that, when a dataset's values are ranked from lowest to highest, distinguishes the lower from the upper half of the dataset.

The middle 50% of a dataset's interquartile range (IQR) is a measure of variability that captures this dispersion. It is the difference between the data's first (Q1) and third (Q3) quartiles. The number that divides the lowest 25% of the data from the remaining data is known as the first quartile, and the value that separates the highest 25% of the data from the remaining data is known as the third quartile.

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The complete question is:

Answer:

The correct answer is:

10√2

Explanation:

In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.

In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.

Let's denote the side length of each square as "s" inches.

According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the hypotenuse is 20 inches, so we have:

20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)

400 = 2s^2

Dividing both sides by 2, we get:

200 = s^2

Taking the square root of both sides, we get:

s = √200

Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:

√200 = √(100 x 2) = 10√2

So, the side length of each quilt piece is 10√

The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.

This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).

[tex]h = \sqrt{p^2 + b^2}[/tex]

Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.

20 = √2p²  (since p and b are equal, b can be taken as p)

On squaring both sides,

400 = 2p²

p² = 400/2

p² = 200

p = √200

p = 10√2 = b

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39 degrees of freedom will be used to find the t-critical statistic value.

We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.

The degrees of freedom (df) for a t-distribution are calculated as given below:

df = n - 1

where n is the sample size of the problem.

In this case, the sample size is 40, so the degrees of freedom would be:

df = 40 - 1 = 39

Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.

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Answer: The function that has real zeros at x = 3 and x = 7 is:

f(x) = (x - 3)(x - 7)

Expanding this function using FOIL (First, Outer, Inner, Last) method:

f(x) = x^2 - 10x + 21

Therefore, the answer is:

f(x) = x^2 - 10x + 21

Step-by-step explanation:

The two statements that completes the above proof are:

ΔABC ~ ΔDEC - Side - Angle - Side Postulate

∠1≅∠2 - Corresponding angles.

The Side-Angle-Side (SAS) postulate states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.

Corresponding angles are equal because of the congruence of the triangles. Two angles are corresponding if they occupy the same relative position in two distinct intersecting lines, such that they are on the same side of the transversal and are in the same position in relation to the intersection. Corresponding angles are equal if the two intersecting lines are parallel.

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The prism has an 8/27 cubic centimetre volume.

The following formula determines a cube's volume:

V = s³

where V is the volume of the cube and s is the length of one of its sides.

In other words, to find the volume of a cube, you simply need to raise the length of one of its sides to the third power (cube it).

The volume of a cube = s³

Given that the prism is composed of cubes with a one-third-centimeter side measurement.

Volume of a cube = (1/3)³ = 1/27

There are 8 cubes in the prism.

Therefore, the volume of the prism is;

=8(1/27)

= 8/27 cubic centimeter.

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The complete question is:

The prism below is made of cubes which measure of a centimeter on one side. What is the volume?

Note: Figure is not drawn to scale.

The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?

Image is attached below.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

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