what is a rational number and can you give me a example of them

The variance for the sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores is 5.

The formula for the variance of a sample is:

\(s^2\) = SS / (n - 1)

where SS is the sum of squared deviation scores, n is the sample size, and \(s^2\) is the variance.

In this case, SS = 20 and n = 5, so we can substitute these values into the formula:

\(s^2\) = 20 / (5 - 1)

\(s^2\) = 5

Therefore, the variance for this sample is 5.

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The car will need 6 gallons of gasoline to travel 102 miles

Given that the car travels 442 miles on 26 gallons of gasoline.

Because the more the distance, the more the volume of gasoline used, this is a direct proportion.

So, we have:

It will need 6 gallons.

If his beard  was 8 millimeter long and each passing week it grew 2 additional millimeters, the graph that represents the relationship between the length of his beard in millimeter and time in week has been plotted

The initial length of the beard = 8 millimeter

The length of beard grow in each week = 2 millimeter

Consider the number of week as x

Therefore the linear relationship will be

The length of the beard y = 2x + 8

Plot the graph using the equation

Hence, If his beard  was 8 millimeter long and each passing week it grew 2 additional millimeters, the graph that represents the relationship between the length of his beard in millimeter and time in week has been plotted

The complete question is

Rip van Winkle fell asleep for a very long time. When he fell asleep, his beard was 8 millimeters long, and each passing week it grew 2additional millimeters.

Graph the relationship between the length of Rip van Winkle's beard (in millimeters) and time (in weeks).

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1) The point is on the unit circle.

2) The point is not on the unit circle

3) cos(Θ) = 0.866

We know that all the points on the unit circle have a magnitude of 1, then we can write:

√[ (-0.5)² + (sin(4π/3)²) = 1

This means that the point is on the unit circle.

b) Now the point is (-0.5, sin(5π/6))

We need to do the same thing, this time we will get:

√[ (-0.5)² + (sin(5π/6)²) = 0.71

So this point is not on the number line.

c) Here we know that sin(Θ) = -0.5 and the angle is in the quadrant 4.

Then Θ = Asin(-0.5) = -30°

Remember that -30° is on the fourth quadrant, so this is correct, now the cosine of that is:

cos(-30°) = 0.866

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The scale factor of the dilation of the given object is 4.

The scale factor of dilation:

The scale factor of the dilation of an object is determined by taking the ratio of image length to the corresponding object length.

Dilation is the process of resizing or transforming an object. The transformation that makes the objects smaller or larger with the help of the given scale factor.

The basic formula to find the scale factor of a dilated is:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

\(SD=\frac{32cm^2}{4cm^2}\)

SD=4

Thus, the scale factor of the dilation of the given object is 4.

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Answer

3.7 or approximately 4 gallons

Step-by-step explanation:

7x2=14 total liters.

3.78 liters=1 gallon

14/3.78= 3.7 gallons

Angle CBD or k is equal to 70 degrees.

Angles are formed when two rays, known as the sides of the angle, share a common endpoint, called the vertex of the angle. The size of an angle is measured in degrees or radians. In a geometric plane, angles are usually denoted by a symbol that indicates the vertex, with the vertex being the middle letter, and the two rays are represented as line segments originating from the vertex.

Angles can be classified in different ways, including by their size or magnitude, by their position or direction, and by their relationships with other angles. Some common types of angles include acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (greater than 90 degrees but less than 180 degrees), straight angles (exactly 180 degrees), and reflex angles (greater than 180 degrees). Angles can also be complementary (adding up to 90 degrees), supplementary (adding up to 180 degrees), or congruent (having the same size).

We know that the sum of the angles in a triangle is 180 degrees. Let's use that fact to solve for k.

Angle ABD + angle CBD + angle ABC = 180 degrees

Substituting the given values, we get:

30 + k + 80 = 180

Combining like terms, we get:

k + 110 = 180

Subtracting 110 from both sides, we get:

k = 70

Therefore, angle CBD or k is equal to 70 degrees.

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The 71st percentile of the data set (27, 34, 15, 20, 25, 30, 28, 25) is 30.

To find the 71st percentile in the given data set (27, 34, 15, 20, 25, 30, 28, 25), we first need to arrange the data in ascending order: 15, 20, 25, 25, 27, 28, 30, 34.

Next, we calculate the rank of the 71st percentile using the formula:

Rank = (P/100) * (N + 1)

where P is the desired percentile (71) and N is the total number of data points (8).

Substituting the values, we have:

Rank = (71/100) * (8 + 1)

= 0.71 * 9

= 6.39

Since the rank is not an integer, we round it up to the nearest whole number. The 71st percentile corresponds to the value at the 7th position in the ordered data set.

The 7th value in the ordered data set (15, 20, 25, 25, 27, 28, 30, 34) is 30.

Therefore, the 71st percentile of the given data set is 30.

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The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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Each member of the club needs to pay £ 4.895 to cover the cost of hiring the buses.

A youth club's 143 members and eight leaders ride a bus to a bowling alley.

The buses for hire by the beezer bus company hold 32 passengers each.

The cost of each bus to hire is £140.

There are eight leaders and 143 members.

Therefore, there are a total of 143 + 8 = 151 passengers.

So, the number of buses required will be:

= 151 / 32 =  4.7 ≈ 5 buses

Therefore, the cost of hiring 5 buses will be:

= 5 × £140 = £ 700

As the eight leaders will not ay.

Therefore, the amount each member needs to pay is:

= £ 700 / 143

= £ 4.895

Each member of the club needs to pay £ 4.895 to cover the cost of the buses.

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Answer:

si papi

Step-by-step explanation:

Number of ways to select 8 countries from the United Nations is 48,054,722,400

To solve this problem, we need to use the combination method, which states that if there are m ways to perform one task and n ways to perform another task after the first task is completed, then there are m x n ways to perform both tasks in sequence.

Using this principle, we can break down the selection of 8 countries into three separate tasks

Selecting 3 countries from a block of 52: There are 52C3 ways to do this, where 52C3 is the binomial coefficient "52 choose 3," which can be calculated as follows

52C3 = (52 x 51 x 50) / (3 x 2 x 1) = 22,100

Selecting 2 countries from a block of 64: There are 64C2 ways to do this, where 64C2 is the binomial coefficient "64 choose 2," which can be calculated as follows

64C2 = (64 x 63) / (2 x 1) = 2,016

Selecting 3 countries from a block of 73: There are 73C3 ways to do this, where 73C3 is the binomial coefficient "73 choose 3," which can be calculated as follows

73C3 = (73 x 72 x 71) / (3 x 2 x 1) = 1,082,790

To find the total number of ways to select 8 countries, we simply multiply these three quantities together

22,100 x 2,016 x 1,082,790 = 48,054,722,400

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Answer:

113

Step-by-step explanation:

c/b(cheeseburger)-2x

h/b(hamburgers)-x

2x+x=339

3x=339(divide both sides by 3)

x=113

a) 2y = 3x + 8 This equation represents the line passing through the midpoints of BC and AD.

b) the length of the line segment joining the midpoints is indeed half the sum of the lengths of the parallel sides.

a) To show that the line segment joining the midpoints of BC and AD is parallel to both AB and DC, we need to demonstrate that the slopes of the lines are equal.

Let's first find the coordinates of the midpoints of BC and AD:

Midpoint of BC: ( (−2+−4)/2 , (1−2)/2 ) = (−3,-1/2)

Midpoint of AD: ( (1+2)/2 , (2+0)/2 ) = (3/2, 1)

Now, let's calculate the slopes:

Slope of AB: (1-2)/(-2-1) = -1/3

Slope of DC: (-2-0)/(-4-2) = -1/3

Since both slopes are equal, AB is parallel to DC.

Next, let's find the equation of the line passing through the midpoints of BC and AD. We'll use the point-slope form.

Slope of the line passing through the midpoints:

(1-(-1/2))/(3/2-(-3)) = 3/2

Using the midpoint (−3,-1/2), we can write the equation of the line as:

y - (-1/2) = (3/2)(x - (-3))

y + 1/2 = (3/2)(x + 3)

2y + 1 = 3x + 9

2y = 3x + 8

This equation represents the line passing through the midpoints of BC and AD.

b) To show that the length of this line segment is half the sum of the lengths of the parallel sides, we need to calculate the lengths of AB, DC, and the line segment joining the midpoints.

Length of AB:

√((-2-1)^2 + (1-2)^2) = √(9 + 1) = √10

Length of DC:

√((-4-2)^2 + (-2-0)^2) = √(36 + 4) = √40 = 2√10

Length of the line segment joining the midpoints:

√((3/2-(-3))^2 + (1-(-1/2))^2) = √((9/2)^2 + (3/2)^2) = √((81/4) + (9/4)) = √(90/4) = √(9/4 * 10) = (3/2)√10

The sum of the lengths of AB and DC is:

√10 + 2√10 = 3√10

The length of the line segment joining the midpoints is:

(3/2)√10

We can see that the length of the line segment is indeed half the sum of the lengths of AB and DC:

(3/2)√10 = (1/2) * 3√10 = (1/2) * (√10 + 2√10) = 3/2√10 = 3/2√10

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1.746 is the critical t value that corresponds to 90% confidence.

To find the critical t-value that corresponds to 90% confidence with 16 degrees of freedom, follow these steps:
1. Determine the desired confidence level: 90%
2. Calculate the corresponding significance level (alpha) by subtracting the confidence level from 100%: 100% - 90% = 10%
3. Divide the significance level by 2 to get the value for a two-tailed test: 10% / 2 = 5%
4. Look up the critical t-value in a t-distribution table using the degrees of freedom (16) and the 5% value.

From the t-distribution table, the critical t-value for 16 degrees of freedom and 90% confidence is approximately 1.746.

So, the CRITICAL T VALUE that corresponds to a 90% CONFIDENCE level with 16 DEGREES FREEDOM is 1.746, rounded to three decimal places.

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The area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9) is approximately 51.61 square units.

To find the area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9), we can follow these steps:

1. Calculate the vectors PQ and PR by subtracting the coordinates of P from Q and R, respectively.

2. Find the cross product of PQ and PR.

3. Calculate the magnitude of the cross product.

4. Divide the magnitude by 2 to find the area of the triangle.

Step 1: Calculate PQ and PR

PQ = Q - P = (-4 - 1, -3 - 1, -6 - 1) = (-5, -4, -7)

PR = R - P = (6 - 1, 10 - 1, -9 - 1) = (5, 9, -10)

Step 2: Find the cross product of PQ and PR

PQ x PR = ( (-4 * -10) - (-7 * 9), (-7 * 5) - (-10 * -5), (-5 * 9) - (-4 * 5) ) = ( 36 + 63, 35 - 50, -45 + 20 ) = (99, -15, -25)

Step 3: Calculate the magnitude of the cross product

|PQ x PR| = √( (99)² + (-15)² + (-25)² ) = √( 9801 + 225 + 625 ) = √(10651)

Step 4: Divide the magnitude by 2 to find the area of the triangle

Area = 0.5 * |PQ x PR| = 0.5 * √(10651) ≈ 51.61

So, the area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9) is approximately 51.61 square units.

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Complete question is below

Find the area of the triangle determined by the points p(1, 1, 1), q(-4, -3, -6), and r(6, 10, -9)

The AB = -4.

(a) To find AB, we need to multiply matrix A with matrix B. Since A is a 1x4 matrix and B is a 4x1 matrix, we can perform the multiplication as follows:

AB = [2 1 5 1] [1]

[-2]

[-2]

[6]

AB = [(2)(1) + (1)(-2) + (5)(-2) + (1)(6)] = -12

Therefore, AB = -12.

(b) To find BA, we need to multiply matrix B with matrix A. Since B is a 1x4 matrix and A is a 4x1 matrix, we cannot perform the multiplication, as the number of columns in the first matrix (B) does not match the number of rows in the second matrix (A). Therefore, BA is impossible to calculate, and we write:

BA = IMPOSSIBLE.

(a) To find AB, we need to multiply matrix A with matrix B. Since A is a 1x9 matrix and B is a 9x1 matrix, we can perform the multiplication as follows:

AB = [3 5 -2 3 2 2 2 1 -1] [-4]

[1]

[1]

[0]

[3]

[-4]

[-1]

[2]

[-2]

AB = [(3)(-4) + (5)(1) + (-2)(1) + (3)(0) + (2)(3) + (2)(-4) + (2)(-1) + (1)(2) + (-1)(-2)]

= -4

Therefore, AB = -4.

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Answer:

Step-by-step explanation:

angle 4 is congruent to angle 4 because they are alternate interior angles.

angle 5 is congruent to angle 3 because they are alternate interior angles.

angle 1+angle 2+angle 3 is equal to (=) angle 1+angle 2+angle 3

angle 1+angle 2+angle 3=180 degree(being sum of interior angles of a trianngle)

Answer:

what grade is this for

Step-by-step explanation:

The correct answer is D) parameter. A parameter is a measurable quantity that is inherent in the problem and is usually set by external factors. A measurable quantity that is inherent in the problem is called a D) parameter.

A parameter is a measurable and fixed value that characterizes a particular aspect of a problem, while a variable can change during the course of the problem-solving process. Decision variables are the unknowns that you need to find in order to optimize a problem, and uncontrollable variables are factors that cannot be controlled during an experiment or problem-solving process. An algorithm is a step-by-step procedure to solve a problem, and an enumeration variable is not a relevant term in this context. Parameters are used to define the boundaries of a problem and are often used in mathematical models to represent real-world situations. They differ from variables, which can change and are often used to represent unknowns in a problem, and from uncontrollable variables, which cannot be directly controlled or manipulated by the decision-maker.

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Answer:

30c + 10(0.2) = 40(0.32)

Step-by-step explanation: i hope this answer your question if this is wrong or correct please let me know

Step-by-step explanation:

Para hacer las porciones para 32 personas, multiplique cada cantidad de ingrediente por 4 ya que la receta proporciona 8 porciones y 8 * 4 = 32

Papa seca = \(\frac{1}{2} *4\)

                     = 2 papas secas

Cerdo = \(\frac{1}{2} *4\)

       = 2 kg de carne de cerdo

Cebollas = 1 * 4

            = 4 cebollas grandes

Aji panca = 3 * 4

               = 12 cucharadas de aji panca

Ajo molido = \(1\frac{1}{2} *4\)

                       = \(\frac{3}{2} *4\)

                       = 6 cucharadas de ajo molido

Sal = 1 * 4

      = 4 cucharadas de sal

Answer:

False.

Step-by-step explanation:

Using the property of distribution, (a + b)² will be a² + b², never a² + b.

No, for any two integers a and b, (a + b)² ≠ a² + b is a false statement.

For the given two integers a and b,

The given expression

(a + b)² = a² + b (false statement)

The correct statement is-

(a + b)² = (a + b)(a + b)

(a + b)² = a² + b² +  2ab

Thus, no, for any two integers a and b, (a + b)² ≠ a² + b.

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Answer:

x=150

Step-by-step explanation:

x/30-x/40=5/4

or, (4x-3x)/120=5/4

or, x/120=5/4

or, x=600/4

or, x=150

The distance of 40 lb will be 5ft, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

The fulcrum be located from the 40 lb.

The weight of bar is 9ft long.

Now, we will calculate the distance,

40x = 50(x-1)

40x = 50x - 50

40x - 50x = -50

-10x = -50

x = 5

Therefore, the required answer is 5ft.

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Answer:

A. (3, 8) and \(2\sqrt{2}\)

B. (2, 4) and \(2\sqrt{10}\)

Step-by-step explanation:

Midpoint formula: \((\frac{x1+x2}{2} ,\frac{y1+y2}{2})\)

Distance formula: \(\sqrt{(x_{2}-x_{1}) ^2+(y_{2}-y_{1}) ^2 }\)

A. plug in the points in the formulas

(4, 7) and (2, 9)

Midpoint:

\((\frac{4 + 2}{2} , \frac{7+9}{2} )=6/2, 16/2 = (3,8)\)

Length:

\(\sqrt{(2-4)^2+(9-7)^2}=\sqrt{4+4} =\sqrt{8} =2\sqrt{2}\)

B.

(5, 5) and (-1, 3)

Midpoint:

\((\frac{5-1}{2} , \frac{5+3}{2} )=4/2,8/2=(2,4)\)

Length:

\(\sqrt{(-1-5)^2+(3-5)^2} =\sqrt{-6^2+-2^2} =\sqrt{36+4} =\sqrt{40} = 2\sqrt{10}\)

Can you consider marking my answers as brainliest lol it would mean a lot. Hope this helped.

Answer:

3+(-5)-7+6=3-5-7+6=-3

Answer:

0 because there is no image....