what can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data?

The proof of similar triangles are;

1)  Triangles ABC and EFG are not similar triangles.

2) Both triangles are similar triangles by AA Similarity Postulate

Similar triangles are defined as triangles that have the same shape, but then their sizes may vary. Now, all equilateral triangles, squares of any side lengths are examples of similar objects. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.

1) Triangles ABC and EFG are not similar because none of the corresponding angles nor corresponding sides are congruent to themselves.

2) Looking at both triangles formed, we can say that;

∠JLK ≅ ∠JMN by alternate angles postulate

∠JNM ≅ ∠JKL by alternate angles postulate

Similarly ∠J is congruent to itself by Reflexive property and as such both triangles are similar by AA Similarity postulate.

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An equation of the line that passes through (1, 2) and is parallel to the given line is y=-5x+7.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, the coordinate point is (1, 2) and the line is y=-5x+4.

Here, slope of given equation is m₁= -5

We know that, the slope of parallel lines is equal. That is m₁=m₂.

Now, slope m₂=-5

Substitute, m=-5 and (x, y)=(1, 2) in y=mx+c, we get

2=-5(1)+c

c=7

Substitute, m=-5 and c=7 in y=mx+c, we get

y=-5x+7

Therefore, an equation of the line that passes through (1, 2) and is parallel to the given line is y=-5x+7.

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As per unitary method the recipe makes 20.5 servings of lemonade.

The unitary method is a method used to find the number of servings in a recipe by dividing the total amount of ingredients by the serving size.

Let's say a serving size of lemonade is 1 cup. To find the number of servings, we need to divide the total amount of lemonade by the serving size.

In this case, the total amount of lemonade is

=> 2 cups of lemon juice + 16 cups of water + 2.5 cups of agave nectar

=> 20.5 cups.

So, the number of servings can be found by dividing 20.5 cups by 1 cup per serving, which equals 20.5.

In conclusion, the unitary method is a simple way to find the number of servings in a recipe by dividing the total amount of ingredients by the serving size

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Answer:

Step-by-step explanation:

boody boody

A random variable cannot be negative.

This statement is false.

A random variable can be either positive, negative, or zero.

A random variable is a mathematical representation of a number or object that is affected by random occurrences. It is a function or mapping between probable outcomes in a sample space to a measurable space, frequently to real values.

A random variable is a rule that assigns a number value to each outcome in a sample space, or it may be defined as an unknown variable or a function that assigns numerical values to each outcome of an experiment.

Random variables are classed as discrete or continuous. The key distinction between the two groups is the range of potential values for each variable.

The range of a random variable depends on the underlying probability distribution and the specific scenario being modelled.

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Answer:

#9       (x, y) = (6, 32)

#10      The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same and is $32

Step-by-step explanation:

The graph legend is missing so by looking at the graph alone we are unable to determine which color line corresponds to which kind of kite(Kites-R-Fun or Windy Kites)

However the associated table will help us determine this

The linear equation for a line is expressed as

y = mx + c

where m = slope of the line and b = y-intercept which is the y-value for the point where the line crosses the y-axis(at x = 0)

Slope m = rise/run = Δy/Δx = (y2 - y1)/(x2 - x1) for any two points (x1, y1) and (x2, y2) on the line

Let's take the two  x values as x1=0 and x2=1 and use the table

For Kites-R Fun

x1 = 0 ==> y1 = 8. This is also the y-intercept, b

We see that the red line corresponds to x = 0, y = 8

x2 = 1 ==> y2 = 12

y2 - y1 = rise = Δy =12 - 8 = 4

x2 -   x1 = Δx = 1 - 0 =1

Slope m = 4/1 = 4

Equation of Kites-R Fun is 4x + 8

For Windy Kites

x1 = 0 ==> y1 = 20

y-intercept = 20 or b = 20

x2 = 1 ==> y2 = 22

Rise = Δy =22 - 20 = 2

Run = Δx = 1 - 0 = 1

Slope = m, b = 20

Equation of blue line is

y = 2x + 20

The two equations are:

y = 4x + 8

y = 2x + 20

Equating right sides:

4x + 8 = 2x + 20

Move 2x to the left side and 8 to the right side:

4x + 2x + 8 - 8 = 2x - 2x + 20 -8

2x = 12

x = 6

For x = 6 the costs are the same

Plugging x = 6into equation y = 4x + 8:

y = 4(6) + 8 = 24 + 8 = 32

So the solution set is

(6, 32)

Looking at the graph we see the two lines intersect at this point

(Heck, we could have avoided all this work and just looked at the graph but I don't expect that was what they intended. You can add this as a side note)

On the second part

For Kites-R-US, each kite costs $4

The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same.

Answer:

One person represents 360 degrees / (204 + 84 + 36 + 204 + 12) = 360 degrees / 540 = 4/6 = 2/3 degrees.

Answer:

2d=90

d=45

Explanation: Complementary angles add up to 90 degrees. If the two angles are congruent, it means that both angles have the same measurements.

Answer:

b) 31.25

Step-by-step explanation:

Since it is an isosceles triangle, the two missing angles are equal.

The sum of the angle measures in a triangle is 180 degrees.

Angle D and E are both x

So we set up an equation:

180 = 117.5 + x  + x

180 = 117.5 +2x

62.5 = 2x

x = 31.25

According to the given statements regarding matrix and vectors, we found that statements a, b, and c are true. Others are false.

a. True. Certain elementary row operations on a matrix, such as row swaps, row scalings, and row additions, can affect the linear dependence relationships among the columns of the matrix.

b. True. The columns of an invertible matrix form a linearly independent set, which is also a basis for the vector space of the matrix.

c. True. A basis is a spanning set (a set of vectors that can generate any other vector in the space) that is as large as possible, meaning that it has the minimum number of vectors required to generate all other vectors in the space.

d. False. A single vector by itself is linearly independent, meaning that it cannot be expressed as a linear combination of other vectors.

e. False. If W is a subspace of a vector space V, then a basis for W is a set of vectors that can generate any other vector in W, but not necessarily all vectors in V.

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Complete Question:

Show T/F.

a. in some cases, the linear dependence relations amoung the columns of a matrix can be affected by certain elementary row operations on the matrix.

b. the columns of an invertible matrix form a basis for .

c. a basis is a spanning set that is as large as possible.

d. a single vector by itself is linearly dependent.

e. if , then is a basis for .

Answer: 2x-3=10

(x=the number)

Answer: 25/8 or 3.125 or [tex]3\frac{1}{8}\\ \\[/tex]

Step-by-step explanation: Length times width (L x w)

The  value of x is 94.5.

We are given that a basketball player averages 13.5 points per game.

x=Number of points scored in 7 games

We have to find the value of x

In order to find the points scored in 7 games we will multiply 7 by 13.5.

Number of games=7

Number of point scored in one game=13.5

Number of points scored in 7 games=

Number of points scored in 7 games=94.5

Hence, value of x=94.5

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The length of SR is 3.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

ST is parallel to PQ.

The length of PQ is the same as the length of SR.

PR = 10 and ST = 3

Now,

ST = 3 and ST is parallel to PQ.

This means,

PQ = 3 and the length of PQ is the same as the length of SR.

So,

SR = 3

Thus,

SR is 3.

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Answer: D

Step-by-step explanation:

The lateral surface area of a cube the edge of 8 cm is 384cm^2.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object. Suppose that the cube in consideration has its side of 'a' units length.

Then, the surface area S of that cube is:

=6a^2

Given;

The edge of cube= 8cm

Now, the lateral surface area;

=6a^2

=6*8*8

=6*64

=384

Therefore, the lateral surface area will be 384cm^2.

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Calculating a relationship between college admission scores and freshman gpa requires the  Correlational statistics type of statistics. Correlational statistics are used to measure the strength of the relationship between two variables.

This type of statistic is used when attempting to determine the relationship between college admission scores and freshman GPA. By measuring the correlation between the two variables, it can be determined if there is a correlation between college admission scores and freshman GPA. Correlational statistics can measure the direction, strength, and significance of the relationship between two variables.

This type of statistics can provide information such as the degree to which two variables move together and the extent to which one variable changes as the other variable changes. Correlational statistics can also provide information on how much of the variability in one variable is explained by the other variable. Correlational statistics can be used to determine if there is a correlation between the two variables and, if so, the strength of that correlation.

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The two x-values that the supplied vectors are orthogonal to are 0 and 10 respectively.

A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector.

The term can also refer to a quantity's mathematical or geometrical representation.

Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

A movement from one point to another is described by a vector. A vector quantity has a magnitude and a direction (size).

There is just magnitude for scalar quantities.

An arrow-labeled line segment can serve as a visual representation of a vector.

So, we have:

xi+2xj and xi - 5j

As is common knowledge, when two vectors are orthogonal, their dot product equals zero, which means:

(xi + 2xj)*(xi-5j) = 0

x*x+2x*-5 = 0

x²-10x = 0

x(x-10) = 0

x = 0 or x - 10 = 0

x = 0 or x = 10

Therefore, the two x-values that the supplied vectors are orthogonal to are 0 and 10 respectively.

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Answer:

think its B

Step-by-step explanation:

im doing the test

Answer:

Step-by-step explanation:

its b

Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters, average speed = 74.4 km/h.

It is defined as the distance traveled by an object in a certain amount of time. The unit of speed is usually meters per second (m/s) or kilometers per hour (km/h). Speed is a fundamental concept in physics, as it is a measure of the motion of objects. It is also an important concept in engineering, transportation, and many other fields. The speed of an object can be determined by dividing the distance traveled by the time taken to travel that distance.  The magnitude of speed represents the rate of change of position, and the direction indicates the direction of the change.

To find the amount of fuel used to get to the gate, we need to multiply the distance traveled by the fuel consumption per kilometer.

1. Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters. Rounding to the nearest whole number, the answer is 31 liters.

2. To find the average speed, we need to divide the distance traveled by the time taken.

Average speed = 392 km / (5 hours + 14 minutes/60) = 74.4 km/h.

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The total area of this rectangular deck is equal to: D. 564.5 ft².

Mathematically, the area of a rectangular deck can be calculated by using this mathematical expression:

Area of a rectangular deck, A = LW

Where:

Therefore, the area of the additional dimension can be calculated as follows;

Area of additional dimension, A = 20.25 × 18

Area of additional dimension, A = 364.5 ft².

Now, we can calculate the total area of this deck as follows;

Total area = original area + new area

Total area = 200 ft² + 364.5 ft²

Total area = 564.5 ft²

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Answer:

d

Step-by-step explanation:

The maximum number of edges in a simple undirected disconnected graph of n vertices can be any value that is less than or equal to n(n-1)/2.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

The maximum number of edges in a simple undirected disconnected graph of n vertices can be found using the formula for the maximum number of edges in an undirected graph,
E = n(n-1)/2.

However, for a disconnected graph, this formula only applies to each connected component of the graph separately. Therefore, the maximum number of edges in a simple undirected disconnected graph of n vertices is n(n-1)/2 for each connected component, so the total maximum number of edges is n₁(n₁-1)/2 + n₂(n₂-1)/2 + ... + nₐ(nₐ-1)/2, where n₁, n₂, nₐ are the number of vertices in each connected component.

So, in general, the maximum number of edges in a simple undirected disconnected graph of n vertices can be any value that is less than or equal to n(n-1)/2.

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Answer:

the answer is in the picture

The approximately 99.38% of the data falls between the values 120 and 280.

To find the percentage of data that falls between the values 120 and 280, we need to find the standard scores (z-scores) that correspond to these values and use a standard normal table to find the proportion of data within this range.

First, we'll find the z-score for 120:

z = (120 - 200) / 40 = -2.5

Similarly, the z-score for 280 is:

z = (280 - 200) / 40 = 2.5

Now we can use a standard normal table to find the proportion of data between -2.5 and 2.5 standard deviations from the mean. This proportion is approximately 0.9938 or 99.38%.

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This statement can be represented mathematically as: 2(x - 7) ≤ -29. The solution to the inequality is x ≤ -8 means x is less than or equal to -8.

Here, x is the number we are trying to find and "2(x - 7)" represents "twice the difference of a number and seven."

To solve for x, we can start by expanding the expression inside the parentheses:

2(x - 7) = 2x - 14

Now, we can substitute the expression for 2(x - 7) into the inequality:

2x - 14 ≤ -29

Next, we can isolate x by adding 14 to both sides of the inequality:

2x ≤ -15

Finally, we can divide both sides by 2 to obtain:

x ≤ -8

So, the solution to the inequality is "x is less than or equal to -8". This means that any number that is less than or equal to -8 satisfies the inequality.

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Answer:

Y=2x+2

Step-by-step explanation:

The equation of a line with gradient "m" and passing through the point (x1, y1) can be found using the point-slope form of a line:

y - y1 = m (x - x1)

For a gradient of 2 and a point of (1, 4), we can substitute the values into the equation:

y - 4 = 2 (x - 1)

Expanding the right-hand side, we get:

y - 4 = 2x - 2

Adding 4 to both sides:

y = 2x + 2

So, the equation of the line with a gradient of 2 and passing through the point (1, 4) is y = 2x + 2.

Answer:

y=2x+2

This answer should work on mathswatch

Answer:

angle 1 = 45 degrees, angle 2 = 90 degrees

Step-by-step explanation:

For angle 1:

2 of the properties of a square are that it has 4 right angles (90 degrees) and the diagonals bisect the angles.

Angle BAD = 90 degrees

Ray AC bisects angle BAC. And by definition of bisection, angle 1 = 90/2 = 45 degrees

So angle 1 = 45 degrees

For angle 2:

Angle two is an angle of triangle BAE. Angles BAE and ABE are = 45 degrees because of what is stated above for angle 1.

Since the sum of the measure of the angles in a triangle is 180. We can solve for Angle 2 by doing 180 = 45 +45+ angle 2

180 = 90 + angle 2

angle 2 = 90 degrees

Answer:

W

Step-by-step explanation:

One input can only have one output! So, the x, y, and z diagrams are all wrong. So, the answer is W.

The value of the variable x in the isosceles trapezoid is 14.

An isosceles trapezium is a trapezium with equally sized non-parallel sides. In other words, the legs are equal in length and the bases are parallel.

Calculation of the value of the variable:

Since the measure of one angle should be 38 degrees

And, there is the equation 2x + 10 degrees

So for determining the value of x here we have to equate the equation

Since Angles are equal in an isosceles trapezoid

So,

2x + 10 = 38

2x = 38 - 10

2x = 28

x = 14

Therefore, The value of the variable in the isosceles trapezoid is 14.

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