the coefficient of determination measures the variation in the dependent variable that is explained by the regression model.T/F

To solve the system of equations:

5x + 2y = 24

2x + 5y = 24

We can use either elimination or substitution method.

Using elimination method:

Multiplying the first equation by 5 and the second equation by -2, we get:

25x + 10y = 120

-4x - 10y = -48

Adding the two equations together eliminates y:

21x = 72

Solving for x:

x = 72/21 = 8/3

Substituting x back into one of the original equations and solving for y:

5(8/3) + 2y = 24

2y = 24 - 40/3

2y = 12/3

y = 6/2 = 3

Therefore, the solution to the system of equations is:

x = 8/3

y = 3

Answer:a

Step-by-step explanation:

Answer:

[tex]-7^\circ C[/tex]

Step-by-step explanation:

Let

x -----> the height in meters

y ----> the temperature in Celsius degree

we know that

The linear equation in slope intercept form is equal to

[tex]y+mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

The slope or unit rate is equal to

[tex]m=-\dfrac{1}{100} \dfrac{^\circ C}{m}[/tex] ---> is negative because is a decreasing function

The y-intercept or initial value is equal to

[tex]b=4^\circ C[/tex] ----> value of y when the value of x is equal to zero (sea level)

substitute

[tex]y=-\dfrac{1}{100} x+4[/tex]

For x=1,100 m

substitute in the linear equation and solve for y

[tex]y=-\dfrac{1}{100} (1,100)+4[/tex]

[tex]x=-7^\circ C[/tex]

The vector space that has exactly one basis is the trivial vector space, which is the vector space containing only the zero vector.

A basis for a vector space is a set of linearly independent vectors that span the entire space. In a non-trivial vector space (a space that contains more than just the zero vector), there are infinitely many possible bases. This is because any set of linearly independent vectors that span the space can be used as a basis.

However, in the trivial vector space, there is only one vector (the zero vector), and it is linearly independent of itself. Therefore, the trivial vector space has exactly one basis, which is the set containing only the zero vector. Any other set of vectors in the trivial vector space is linearly dependent, and therefore cannot be used as a basis.

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From the information provided the measure of the angles are given as,

m ∠EFH = 71; and m ∠EFG = 142°.

Angles are measured in degrees, which is why they are called "degrees". A complete circle equals 360 degrees, so it is divided into 360 parts. Each part of the revolution is a degree. Any angle, whether acute, obtuse, reflected or right, can be measured with a protractor. Although based on right angles, we are able to distinguish acute, obtuse or reflex angles. But if we have two acute angles to measure, we cannot determine the greater angle between the two. Therefore, we need to use a protractor to measure angles accurately.

According to the Question:

It is to be noted that

m ∠GFH = m ∠EFH

⇒ m ∠EFH = 71°

⇒ m ∠EFG = m ∠GFH + m EFH

Hence,

m ∠EFG = 71 + 71

              = 142°

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The transformation rule is to: rotate triangle ABC by 90 degrees around the origin

As we are given the coordinates of Triangle ABC as:

Coordinate of point A = (1, 1)

Coordinate of point B = (3, 1)

Coordinate of point C = (1, 4)

The coordinates of the transformed image A'B'C' are:

A' (-1, 1) ,

B'(-1, 3)

C' (-4, 1)

The transformation rule would be to rotate triangle ABC by 90 degrees around the origin

The rule for this transformation is:  (x,y) => (-y ,x)

A(1,1) => A' (-1,1) ,

B(3,1) => B'(-1 , 3)

C(1,4)  => C' (-4,1)

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Answer: X= 15

Step-by-step explanation:

The equation for the function is f(x) = 3 * cos (16x + [tex]\frac{16\pi }{3}[/tex] ) + 5.

What is an equation?

A assertion that two expressions with variables and/or numbers are equal is referred to as an equation. The fundamental driving forces behind the evolution of mathematics have been attempts to logically solve equations, which are really questions.

We know that f(x) = a cos (bx + c) + d.

We are given

a = 3 which is the amplitude

Period = 8π

b = 16

Phase shift = [tex]\frac{c}{b}[/tex]

⇒[tex]\frac{\pi }{3}[/tex] = [tex]\frac{c}{16}[/tex]

⇒ c = [tex]\frac{16\pi }{3}[/tex]

d = 5 as there is upward translation

So, from this we get the equation as

⇒f(x) = 3 * cos (16x + [tex]\frac{16\pi }{3}[/tex] ) + 5

Hence, the equation for the function is f(x) = 3 * cos (16x + [tex]\frac{16\pi }{3}[/tex] ) + 5.

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Question: Write an equation for a function with the given characteristics. A cosine curve with a period of 8π, an amplitude of 3, a right phase shift of π/3, and a vertical translation up 5 units.

f(x) = ______________

It is not mathematically accurate to say that 2+2=4+4=8.

In arithmetic, 2+2 equals 4 and 4+4 equals 8, so each equation is evaluated separately. The sum of 2+2 and 4+4 is indeed 8, but they are not equal to each other.

Perhaps you meant it as a playful or creative statement, but from a mathematical standpoint, it is not accurate.

What is an arithmetic equation?

An arithmetic equation is a mathematical statement that uses arithmetic operations to relate two or more quantities. It typically involves addition, subtraction, multiplication, and division of numbers.

Arithmetic equations can take many forms, but they generally follow the pattern of a mathematical expression or formula that uses variables or numerical constants to represent quantities. The goal of solving an arithmetic equation is to determine the value of the variable that makes the equation true.

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Complete question is: It is not mathematically accurate to say that 2+2=4+4=8.

The equation of the line shown in the graph, from (–2,2) to (–3,–1) is y = -5/4x – 7/4.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

To solve for the equation of the line, we can use the point-slope formula, y – y1 = m(x – x1), where m is the slope of the line and (x1, y1) is a point on the line. In this case, the point (x1, y1) is (–2,2) and the slope of the line is m = (–1 – 2)/(–3 – (–2)) = –3/–1 = 3. Therefore, the equation of the line is y – 2 = 3(x – (–2)).

Simplifying, we get y = 3x + 2. To put the equation in the slope-intercept form, y = mx + b, we can rewrite the equation as y = 3x + 2 = 3x + 2 – 2 = 3x – 2 + 2 = 3x – 2, which is the equation of the line, y = –5/4x – 7/4.

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The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This line is a horizontal line, which means that all points on the line have the same y-coordinate.

To verify this equation, we can use the two points given on the graph: (-2,-3) and (3,-3). Using the slope-intercept form of a line, we can plug in the points to determine the equation of the line.

The slope-intercept form is y = mx + b, where m is the slope, x is the x-coordinate, and b is the y-intercept. The slope is calculated by finding the change in y over the change in x. In this case, both points have the same y-coordinate, so the slope is 0. Therefore, the equation of the line is y = 0x + b.

Plugging in the coordinates of one of the points, (-2,-3), we get -3 = 0x + b. By solving for b, we get b = -3. Substituting b into the equation, we get y = 0x - 3. This is the equation of the line shown in the graph.

In conclusion, the equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This equation was verified by using the slope-intercept form of a line and plugging in the two points given on the graph.

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Por lo tanto, se pueden plantar 224 árboles en el terreno rectangular de 32m x 28m, considerando que cada árbol necesita 4m² para descollarse.

Para calcular el número de árboles que pueden plantarse en el terreno, primero necesitamos determinar el área total del terreno y luego dividirlo por el espacio requerido por cada árbol.
1. Calcula el área total del terreno rectangular:
Área = largo x ancho
Área = 32 m x 28 m
Área = 896 m²
2. Divide el área total entre el espacio requerido por cada árbol:
Número de árboles = Área total / Espacio por árbol
Número de árboles = 896 m² / 4 m²
Número de árboles = 224

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The volume of the 3-D figure is 385/81 cubic units or approximately 4.753 cubic units (rounded to three decimal places).

To find the volume of the 3-D figure, we need to multiply its three dimensions:

Volume = (3 2/3) x (1 2/3) x (2 1/3)

First, we need to convert the mixed numbers to improper fractions:

3 2/3 = 11/3, 1 2/3 = 5/3, and 2 1/3 = 7/3.

Now, we can multiply:

Volume = (11/3) x (5/3) x (7/3)

Volume = 385/81 cubic units, which is the exact answer.

If we want to approximate the answer, we can use a calculator to get:

Volume ≈ 4.753 cubic units (rounded to three decimal places).

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The area of the rectangle is 136 square units.

What are quadrilateral graph ?

A quadrilateral graph is a graphical representation of a quadrilateral, which is a four-sided polygon. It is a coordinate system that uses a Cartesian plane, where the x and y axes are used to plot the four vertices of the quadrilateral. The four vertices of the quadrilateral are represented by four points on the graph, and the sides of the quadrilateral are represented by the line segments connecting the points. By examining the coordinates of the vertices and the lengths of the sides, we can determine the properties of the quadrilateral, such as whether it is a parallelogram, a rectangle, a square, a trapezoid, or a kite. Quadrilateral graphs are useful tools for visualizing and analyzing quadrilaterals in geometry.

To find the area of a rectangle, we need to know the length of two adjacent sides. Let's use the points Q and R to determine the length of the rectangle.

Length of QR = √((x₂- x₁)² + (y₂ - y₁)²)

= √((-4 - 6)²+ (-3 - 3)²)

= √((-10)²+ (-6)²)

= √(100 + 36)

= √(136)

Similarly, we can find the length of ST:

Length of ST = √((x₂ - x₁)²+ (y₂ - y₁)²)

= √((9 - (-1))² + (-2 - (-8))²)

= √((10)² + (6)²)

= √(100 + 36)

= √(136)

Since QR and ST are opposite sides of the rectangle and have equal length, we know that the rectangle is indeed a rectangle. Therefore, the area of the rectangle is simply the product of the length and width:

Area of rectangle = length * width

= √(136) * √(136)

= 136 square units

Hence, the area of the rectangle is 136 square units.

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In a statistical problem, a population consists of all items of interest in a statistical problem.The correct option in this case is option C - all items of interest in a statistical problem.

Population refers to the complete set of observations or items for which inferences are being made in statistical inference. It's the group that researchers are interested in studying, and it's the group to which they hope to extend their conclusions.

In statistics, the population is the entire collection of individuals, objects, or measurements that researchers are interested in studying. Researchers utilize statistical techniques to make inferences about population parameters based on data obtained from samples.

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Answer:

4x + 8

Step-by-step explanation:

You multiple 4 by x, and then 4 by 2, and add them together

The area of the shaded region in the given shapes is determined as 0.544 in².

The area of the shaded region is calculated by subtracting the area of the inscribed hexagon from the area of the circle.

Let's start by finding the side length of the regular hexagon inscribed in the circle.

The distance from the center of the circle to any vertex of the hexagon is equal to the radius of the circle, which is 1 inch.

In a regular hexagon, all sides are equal in length, so each side of the hexagon is also equal to 1 inch.

The area of the regular hexagon can be found using the formula:

Area of a regular hexagon = (3√3/2) x (side length)²

Substituting the side length of 1 inch, we get:

Area of regular hexagon = (3√3/2) x (1 inch)^2

= (3√3/2) square inches

= 2.598 in²

Now, to find the area of the circle, we can use the formula:

Area of a circle = π x (radius)²

Substituting the radius of 1 inch, we get:

Area of circle = π x (1 inch)²

= π square inches

= 3.142 in²

Area of the shaded region = area of circle - area of hexagon

= 3.142 in² - 2.598 in²

= 0.544 in²

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the answer is

=3x+yx3+zx

=3x + 3y+3z

The rate at which air is being pumped in when the radius of the sphere is 10 cm and increasing at a rate of 2 cm/s is 400π/3 cm³/s.

The volume V of a sphere with radius r is given by V = (4/3)πr³. Taking the derivative of this expression with respect to time t, we get dV/dt = 4πr²(dr/dt). This equation relates the rate of change of volume to the rate of change of the radius. We are given that the radius is increasing at a rate of 2 cm/s, so dr/dt = 2 cm/s.

At the instant when the radius is 10 cm, we can find the rate at which air is being pumped in by substituting r = 10 cm and dr/dt = 2 cm/s into the equation for dV/dt. Thus, we have dV/dt = 4π(10)²(2) = 800π cm³/s.

Therefore, when the radius of the spherical balloon is 10 cm and is increasing at a rate of 2 cm/s, the rate at which air is being pumped in is 400π/3 cubic centimeters per second.

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The best graphical representation for the pediatrician's data would be a histogram. A histogram is a type of graph that shows the distribution of continuous data. In this case, the weights of the 14-year-olds would likely be continuous data. A histogram would allow the pediatrician to visualize the distribution of weights and identify any outliers or unusual patterns.

Answer:histogram

Step-by-step explanation:

Value of angle ∠QUR in the given figure is 139°.

Vertically opposite angles are pairs of angles that are opposite to each other when two straight lines intersect. When two lines intersect, they form four angles, and the vertically opposite angles are the angles that are opposite to each other and share a common vertex.

In the given figure;

∠SUR=41°

∠TUS=90°

∠TUS=∠QUN  ( Vertically opposite angle)

∠TUN is a straight line, angle subtended over it makes 180°

∠TUS makes 90° so, ∠SUN will be 90°

∠SUN=∠SUR+∠RUN

90°=41°+∠RUN

∠RUN=90°-41°

∠RUN=49°

∠QUR=∠QUN+∠RUN

∠QUR=90°+49°

∠QUR=139°

Hence, Value of angle ∠QUR in the given figure is 139°

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Answer:

d

Step-by-step explanation:

95,000÷100 then multiply by $0.83 since it's a wood home in the suburbs.

Answer: 22.3

Step-by-step explanation:

The dummy variable is used to capture the effect of the categorical variable and it has no effect on the quadratic or cubic relationship between the independent and dependent variable.

When x is a dummy variable, there will be no difference in OLS estimators between quadratic and cubic regression models. This statement is true.OLS stands for Ordinary Least Squares regression. It is a statistical method used to determine the relationship between one or more independent variables (predictors) and a dependent variable. The OLS regression method minimizes the sum of squared residuals (differences between actual and predicted values).Dummy variables are used in regression analysis to represent categorical variables.

These are represented by a variable with a binary value of 1 or 0, depending on whether the observation falls in that category or not. This variable is used to represent a categorical variable in regression analysis so that the model can capture the effect of that variable in the analysis.In regression analysis, the regression model is a function of the independent variable, also called the predictor variable, and the dependent variable. A quadratic regression model is a polynomial regression model of degree 2. It means that the relationship between the dependent and independent variable is a quadratic function.

A cubic regression model is a polynomial regression model of degree 3. It means that the relationship between the dependent and independent variable is a cubic function. When x is a dummy variable, there will be no difference in OLS estimators between quadratic and cubic regression models. The OLS estimators will be the same because the dummy variable will have no effect on the fit of the model. Hence, this statement is true.

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The area of the blue glass needed to fill each dot on the butterfly wing is 144π square inches.

The distance around each dot on the butterfly wing is given as 24π inches. This means that the circumference of each dot is 24π inches. The circumference of a circle is:

Circumference = 2πr

where "r" is the radius of the circle. So, we can write:

2πr = 24π

Simplifying this equation, we get:

r = 12

Therefore, the radius of each dot is 12 inches.

To find the area of the blue glass needed to fill each dot, we can use the formula for the area of a circle:

[tex]Area = \pi r^2[/tex]

Substituting the value of the radius, we get:

[tex]Area = \pi(12)^2[/tex]

Simplifying this equation, we get:

Area = 144π square inches

Therefore, the area of the blue glass needed to fill each dot on the butterfly wing is 144π square inches.

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The complete question is :

An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of metal ring. The distance around each dot is 24π inches. The artist plans to fill the inside of each dot with blue colored glasses. What is the area of the blue glass will be needed to fill each butterfly dot?

the points do not fall on a straight line, but rather curve upward as volume increases. This reflects the fact that the scale factor needed to dilate the basic box increases as the volume of the new box increases.

Volume is a physical quantity that measures the amount of space occupied by an object, substance, or material. It is usually measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or liters (L).

The volume of an object is determined by its three-dimensional dimensions, namely length, width, and height. For example, the volume of a cube is calculated by multiplying its length, width, and height measurements together.

by the question.

To find the scale factor needed to dilate the basic box to a box with a volume of 8 cubic feet, we can use the formula for the volume of a cube: [tex]V=s^{2}[/tex], where V is the volume and s is the length of one side of the cube.

Thus, we can solve for the new length of one side of the cube, which we'll call x:

[tex]8 = x^{3}[/tex]

Taking the cube root of both sides gives:

x = 2

So, the company would need to dilate the basic box by a scale factor of

2 to create a box with a volume of 8 cubic feet.

To find the approximate scale factor needed to dilate the basic box to a box with a volume of 10 cubic feet, we can use the same formula:

[tex]10 = x^{3}[/tex]

Taking the cube root of both sides gives:

x ≈ 2.154

So, the company would need to dilate the basic box by a scale factor of approximately 2.154 to create a box with a volume of 10 cubic feet.

Using the formula. [tex]V=s^{2}[/tex], we can fill in the table as follows:

Volume (cubic feet) Scale Factor

0                                        0

1                                         1

5                                        1.71

8                                        2

10                                     2.15

15                                        2.47

20                                     2.71

We can then plot these points on a graph with volume on the x-axis and scale factor on the y-axis and connect them with a smooth curve to show the relationship between the two variables.

[tex]10 = x^{3}[/tex]

Taking the cube root of both sides gives:

x ≈ 2.154

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The length of the secant AC, obtained using the tangent secant theorem is AC = 25 units

The tangent secant theorem indicates that when a secant ABC and a tangent, CD meets at an external point C  to a circle, the relationship between segments are; AC × BC = CD².

Segment addition postulate indicates that we get;

AC = AB + BC

Where;

AB = 3·x + 1

BC = 9

Therefore;

AC = (3·x + 1) + 9 = 3·x + 10

AC × BC = (3·x + 10) × 9 = 27·x + 90

AC × BC = 27·x + 90

CD = 15

CD² = 15² = 225

AC × BC = CD²

Therefore; 27·x + 90 = 225

27·x = 225 - 90 = 135

x = 135/27 = 5

x = 5

AC = 3·x + 10

Therefore; AC = 3 × 5 + 10 = 25

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Answer:

y = x + 3

Step-by-step explanation: