11. Find the mean and median of the following data,
2. 5, 7, 1, 9, 13, 10, 8,7

The correct matches are:

If AB = CD, then CD = AB. - Symmetric Property

If MN = XY, and XY = AB, then MN = AB. - Transitive Property

Segment CD is congruent to segment CD. - Reflexive Property

The matching of statements to the properties is as follows:

If AB = CD, then CD = AB. - Symmetric Property

The symmetric property states that if two objects are equal, then the order of their equality can be reversed. In this case, the statement shows that if AB is equal to CD, then CD is also equal to AB. This reflects the symmetric property.

If MN = XY, and XY = AB, then MN = AB. - Transitive Property

The transitive property states that if two objects are equal to the same third object, then they are equal to each other. In this case, the statement shows that if MN is equal to XY, and XY is equal to AB, then MN is also equal to AB. This demonstrates the transitive property.

Segment CD is congruent to segment CD. - Reflexive Property

The reflexive property states that any object is congruent (or equal) to itself. In this case, the statement shows that segment CD is congruent to itself, which aligns with the reflexive property.

So, the correct matches are:

If AB = CD, then CD = AB. - Symmetric Property

If MN = XY, and XY = AB, then MN = AB. - Transitive Property

Segment CD is congruent to segment CD. - Reflexive Property

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Answer:

beesechuurger

Step-by-step explanation:

Answer:

7*-6x-1.5

Step-by-step explanation:

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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Answer:

approx 15%

Step-by-step explanation:

Allison puts $250 down and following that she makes 12 monthly payments of $124.49.  The sum of her payments (total cost) is thus $250 + (124.49/month)(12 months) = $1743.88

The total interest she pays is $1743.88 - ($124.49/month)(12 months), or

$250

We use the simple interest formula:  i = prt, where t is the number of years, and r is the interest rate as a decimal fraction:

$250 = $1599.99*r*1.

                                                                     $250

Solving this for r by division, we get r = --------------- = 0.1463, or approx 15%

                                                                  $1599.99

Answer:

1:27

Step-by-step explanation:

I will use solve in terms of pi

Know that Original volume * scale factor cubed = new volume.

The scale factor is 3 and 3^3 is 27,

Therefore the ratio is 1:27

Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. The correct option is D.

Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

\(L = k \times M\)

where 'k' will be called a scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k²

to get each other corresponding quantities from their similar figures' quantities.

So the area of the first figure = k² × the area of the second figure

Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or

The volume of the first figure = k³ × volume of the second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

Given that the diameter of sphere A is 2 units, it is dilated by a scale factor of 3 to create sphere B. Therefore, the diameter of sphere B is,

Diameter of sphere B = 3 × Diameter of sphere A

                                    = 3 × 2 units

                                    = 6 units

Now, the ratio of diameters of the sphere and the volume of the sphere can be written as,

\((\dfrac{\text{Diameter of sphere A}}{\text{Diameter of sphere B}})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} \\\\\\(\dfrac{2}{6})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}}\\\\\\\dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} = \dfrac{1}{27}\)

Hence, the correct option is D.

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Based on the information given, Brody is older than Nathan, then;

Brody's age is 15 years.

Algebraic expressions are expressions comprising of variables, terms, factors, constants, and coefficients.

They are also made up of mathematical operations like addition, subtraction, multiplication, parenthesis, bracket, division, etc

From the information given, we have that

It is represented thus;

5x + x + 2 = 80

collect like terms

6x = 80 - 2

Subtract like terms

6x = 78

Make 'x' the subject of formula

Divide both sides by 6

x = 78/6

x = 13

But we have that;

Brody's age  = x + 2

Substitute the value of x

Brody's age = 13 + 2

Brody's age = 15 years

Thus, Brody's age is 15 years.

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We are given the equation;

Firstly, let's expand the brackets.

During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?

The weighted least squares algorithm was used on the Community Crime dataset to calculate the average testing error (RMSE) for high and low crime rate groups, along with the average number of training instances in each group.

Here's a general outline of the steps you can follow to implement the solution in python.

1) Load the Community Crime dataset.

2) Split the dataset into training and testing sets using a 75-25 ratio. Repeat this process 10 times to perform 10-fold cross-validation.

3) Define the weights \(w_h\) and \(w_l\) for the high crime rate group and low crime rate group, respectively.

4) Implement the weighted least squares algorithm:

  a) Preprocess the data by adding a column of ones to the feature matrix X.

  b) Calculate the weight matrix W based on the weights assigned to each instance.

  c) Calculate the solution \(\hat{\beta}\) using the formula \(\hat{\beta}\) = \((X'WX)^{-1}X'Wy\).

5) Calculate the testing error (RMSE) for each fold and average them to obtain the average testing error.

6) Calculate the average number of training instances in the high crime rate group and low crime rate group.

7) Report the average testing error (RMSE) for the weighted least squares algorithm on different groups (high crime rate and low crime rate) in a table, along with the average number of training instances in each group.

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Complete Question:

Task 1: Define w=[[ \(w_1\) 0 : 0] [ 0: : 0] [0 : \(w_{n-1}\) 0] [ 0 : 0 \(w_n\)]], so it is diagonal matrix with weights sitting on the diagonal.

Then, we can write: J(β)=(y−Xβ) W(y−Xβ) = \(\sum [i=1\ to\ n] w_i(x_i' \beta - y_i)^2\)

Task 2 :  

∂J(β)/∂β =−2X'W(y−Xβ)=0 (this is the differentiation rule from matrix calculus)

Setting:  ∂J(β)/∂β = 0 ⇒ \(\hat{\beta} =(X'WX)^{-1} X' Wy\)

Find:

Task 3. Implement your solution in Python from scratch. Test your implementation on the given Community Crime data set and report experimental results. Use the following experiment design.

- Randomly select 75% data for training and use the rest 25% data for testing. Repeat the random trial for 10 times and report the average testing error (RMSE).

-Let us define two groups in the community: (i) high crime rate group contains community instances whose labels are bigger than 0.8; (ii) low crime rate group contains community instances whose labels are no bigger than 0.8. After experimenting weighted least square, let us report its testing errors on different groups in Table 1. (We will use \(w_h\) to denote weight for instances in the high crime rate group and \(w_l\) to denote weight for instances in the low crime rate group.)

- Report the average number of training instances in the two groups.

Answer:

D

Step-by-step explanation:

Is just 9/11 x 2

ajnansjs

Answer:

Option D is correct

Step-by-step explanation:

9/11=x/22

(9/11)×22=x

18=x

or. x=18

Answer:

A. no solution

Step-by-step explanation:

x+1=x-1-1

x+1=x+(-2)

x-x = 0

1=(-2)

x = no solution

Answer: 40

Hope this helps

The main difference between bar charts and histograms lies in the type of data they represent. Bar charts are used for categorical data, where each bar represents a distinct category. On the other hand, histograms are used for continuous or numerical data, where the bars represent intervals or ranges of values.

Bar charts are graphical representations that use rectangular bars to compare different categories. Each bar represents a separate category, and the height of the bar indicates the frequency, count, or proportion associated with that category. Bar charts are commonly used to display categorical data, such as comparing sales figures for different products or survey responses across different options.

Histograms, on the other hand, are graphical representations that display the distribution of numerical data. Instead of representing distinct categories, histograms group the data into intervals or bins along the x-axis. The height of each bar in a histogram represents the frequency or count of data points falling within that particular interval. Histograms are useful for visualizing the shape, central tendency, and spread of continuous data, such as exam scores, temperatures, or ages.

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Step-by-step explanation:

1525 yards + 1775 yards = 3,300 miles.

3300 yards = 1.875 miles (exactly)

3 miles subtract 1.875 miles = 1.125 miles.

Therefore Chance needs to run 1.125 miles or 1,980 yards more.

Answer:

-a^2*(a^2+21a+22)

best I can do

Answer:

C. 2A/b

Step-by-step explanation:

multiply both sides by 2

2A = bh

divide both sides by b

2A/b = h

To convert the masses of copper and chlorine to moles, Avogadro's unit relationships can be utilized.

Avogadro's number (6.022 x 10^23) represents the number of particles (atoms, molecules, ions) in one mole of a substance. Using this concept, the relationship between mass and moles can be established by utilizing the molar mass of the respective elements.

To convert the mass of copper to moles, the molar mass of copper (Cu) is required. The molar mass of copper is determined by adding up the atomic masses of its constituent atoms, which can be found on the periodic table. By dividing the mass of copper by its molar mass, the number of moles of copper can be obtained. Similarly, to convert the mass of chlorine to moles, the molar mass of chlorine (Cl) is used. By dividing the mass of chlorine by its molar mass, the number of moles of chlorine can be determined.

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Answer:

True an angle is two intercepting line segments that share an point

False The definition of a square is it has to have four congurent angles ,sides and 2 sets of parallel lines.

Step-by-step explanation:

The projection of the point (4,4) onto the line passing through (3,1) is the point on the line that is closest to (4,4). To find this projection, we need to first find the direction vector of the line, which is (3-1, 1-0) = (2,1).

Next, we need to find the vector from the point (3,1) to the point (4,4), which is (4-3, 4-1) = (1,3).

Then, we can use the formula for projecting a vector onto another vector:

proj_v u = ((u · v) / (v · v)) v

where u is the vector we want to project, v is the vector we want to project onto, and · denotes the dot product.

Applying this formula, we get:

proj_v u = ((1,3) · (2,1)) / ((2,1) · (2,1)) (2,1)

= (5/5) (2,1)

= (2,1)

So the projection of (4,4) onto the line passing through (3,1) is the point (3,1) + (2,1) = (5,2).

To find the projection of vector (4, 4) onto vector (3, 1), you can follow these steps:

Step 1: Calculate the dot product of the two vectors.
Dot product = (4 * 3) + (4 * 1) = 12 + 4 = 16

Step 2: Calculate the magnitude squared of the vector you are projecting onto (3, 1).
Magnitude squared = (3 * 3) + (1 * 1) = 9 + 1 = 10

Step 3: Divide the dot product by the magnitude squared.
Scalar = 16 / 10 = 1.6

Step 4: Multiply the scalar by the vector you are projecting onto (3, 1) to find the projection.
Projection = 1.6 * (3, 1) = (4.8, 1.6)

So, the projection of (4, 4) onto (3, 1) is (4.8, 1.6).

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The terms and expressions are matched as follows:

We have that letter w represents the number of words made, while letter t represents the number of tiles not used.

Then the multipliers from the points are given to build the expressions, as follows:

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An ordered pair is a solution of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.

In mathematics, an equation in two variables represents a relationship between two quantities. An ordered pair consists of two values, typically denoted as (x, y), that represent the coordinates of a point in a two-dimensional plane.

When these values are substituted into the equation, if the equation holds true, then the ordered pair is considered a solution or a solution set to the equation. This means that the relationship described by the equation is satisfied by the values of the ordered pair. In other words, the equation is true when evaluated with the values of the ordered pair.

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The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

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Answer: a = -3.25, b = -4, c = 0.5 and d = -4

Step-by-step explanation:

To find the coefficient of a cubic function, we can use the values in the given table to set up a system of equations and then solve for the unknowns.

Here is the system of equations we can set up using the values in the table:

y = ax^3 + bx^2 + c*x + d

0 = 0a + 0b + 0c + d

-4 = 1a - 4b + 1c + d

-26 = 8a - 4b + 2c + d

-48 = 27a - 4b + 3c + d

We can then solve this system of equations using matrix operations or Cramer's rule.

a = -26/8 = -3.25

b = -4

c = -26-8a = -26+26.5 = 0.5

d = -48-27a-4b-3c = -48+91.75-44-30.5 = -4

Therefore, the coefficient a = -3.25, b = -4, c = 0.5 and d = -4 for the cubic function y = ax³ + bx² + cx+d

It's important to note that this method of solving a system of equations is the most common way but not the only way to get the coefficients in this case.

Answer:

153.6

Step-by-step explanation:

Answer:

153.6

Step-by-step explanation:

32x4=128

128x3=384

384x2=768

768/5=153.6

On solving the provided question, we can say that The attached table shows some iterations using this formula. To 3 dp, the solution of equation  is x ≈ -2.803.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

You want to use the iterative formula x = ∛(5x -8) to find a solution to x³ -5x +8 = 0, starting with x₁ = -3.

Iteration

Your iterator appears to be found by solving for x:

 x³ -5x +8 = 0

 x³ = 5x -8

 x = ∛(5x -8)

The attached table shows some iterations using this formula. To 3 dp, the solution is x ≈ -2.803.

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The appropriate set of hypothesis is:

Null hypothesis (H0): The proportion of residents in the community who play the state lottery is equal to 15%.
Alternate hypothesis (Ha): The proportion of residents in the community who play the state lottery is not equal to 15%.

To test the claim made by the local newspaper, you would need to set up a hypothesis. The appropriate set of hypotheses in this case would be:
Null hypothesis (H0): The proportion of residents in the community who play the state lottery is equal to 15%.
Alternate hypothesis (Ha): The proportion of residents in the community who play the state lottery is not equal to 15%.
By setting up these hypotheses, you can then collect a random sample from the community and analyze the data to determine if there is enough evidence to support the claim made by the newspaper.

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The product of (3 - √5)(7 - √5) simplifies to 26 - 10√5.

To multiply and simplify the expression (3 - √5)(7 - √5), we can use the distributive property of multiplication over addition. Here are the steps:

1. Start by multiplying the first terms in each set of parentheses: 3 * 7 = 21.

2. Then multiply the outer terms: 3 * (-√5) = -3√5.

3. Next, multiply the inner terms: -√5 * 7 = -7√5.

4. Finally, multiply the last terms: -√5 * -√5 = 5.

Now we can combine these terms to simplify the expression:

21 + (-3√5) + (-7√5) + 5

Combine the like terms: 21 + 5 - 3√5 - 7√5

Combine the constants: 21 + 5 = 26.

Combine the radical terms: -3√5 - 7√5 = -10√5.

The final simplified expression is: 26 - 10√5.

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Answer:

What is the question?

Step-by-step explanation:

The global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

To use Lagrange multipliers, we need to define the Lagrangian function as follows:

L(x, y, λ) = f(x, y) - λg(x, y)

where g(x, y) is the constraint function, which in this case is g(x, y) = x^2 + y^2 - 80.

So, we have:

L(x, y, λ) = (x - 1)^2 + (y + 2)^2 - λ(x^2 + y^2 - 80)

Next, we need to find the partial derivatives of L with respect to x, y, and λ, and set them equal to 0:

∂L/∂x = 2(x - 1) - 2λx = 0

∂L/∂y = 2(y + 2) - 2λy = 0

∂L/∂λ = x^2 + y^2 - 80 = 0

Simplifying the first two equations, we get:

x(1 - λ) = 1

y(1 - λ) = -2

Dividing these two equations, we get:

x/y = 1/-2 => x = -y/2

Substituting this into the constraint equation, we get:

(y/2)^2 + y^2 = 80 => 5y^2 = 320 => y = ±4√5

Substituting this back into x = -y/2, we get:

x = ∓2√5

So, the critical points are (2√5, -4√5) and (-2√5, 4√5).

To determine whether these are maximum or minimum values, we need to compute the second partial derivatives of L:

∂^2L/∂x^2 = 2 - 2λ

∂^2L/∂y^2 = 2 - 2λ

∂^2L/∂x∂y = 0

At the critical points, we have λ = 1/5, so:

∂^2L/∂x^2 = -2/5 < 0, so (2√5, -4√5) is a local maximum.

∂^2L/∂y^2 = -2/5 < 0, so (-2√5, 4√5) is a local maximum.

To determine whether these are global maximum or minimum values, we need to compare the values of L at these critical points and at the endpoints of the constraint region:

L(2√5, -4√5) ≈ 15.314

L(-2√5, 4√5) ≈ 15.314

L(4√2, 0) = 18

L(-4√2, 0) = 18

So, the global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

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Answer:

3

Step-by-step explanation:

24 divided would not be an even number. so there will be left overs. you will have 3 left over