Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change.

Answer:

R200

Step-by-step explanation:

R200

Answer:

1.   752/47=16

2.  375/25=15

3.  576/24=24

hope this helps!!:)

Step-by-step explanation:

1.

1. Find the Greatest Common Factor (GCF) of 752 which is 47 .

2. Divide both the numerator and the denominator by the GCF.

752/47

47/47

3. simplify

16

hope this helps!!:)

Answer:

24.95-6.95= 18

18 divided by 8 = 2.25

So each tube of paint cost 2.25 dollars

Step-by-step explanation:

for the first equation we are subtracting the cost of the canvas from the total cost to find the cost of 8 tubes of paint and we get that 8 tubes of paint cost 18 dollars. Next we divide 18 by 8 to get the cost of a single tube of paint and we get 2.25.

Answer: 360

Step-by-step explanation:

If you double 18 and then multiply by 10 will be 360.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 x 20

The product of the numbers 18 and 20 will be 360.

If you double 18 and multiply the number by 10 will be

2(18) x 10 = 36 x 10 = 360

If you double 18 and then multiply by 10 will be 360.

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Answer:

what are the given values?

Answer:

Step-by-step explanation:

B

true,A hypothesis is a proposed explanation or statement that is offered to be true or false based on scientific research.

Hypotheses are tested in various fields such as science, economics, social science, or marketing research to determine the outcomes.A null hypothesis is a statement that reflects no statistical significance between the two variables being tested. It is a hypothesis where a researcher is attempting to prove that there is no significant difference between two variables.

The null hypothesis is represented as H0, and it is the opposite of the alternate hypothesis.The null hypothesis always contains an equality sign, whereas the alternative hypothesis may or may not contain an equality sign. The equality sign in the null hypothesis means that the researcher is trying to establish that there is no relationship between the variables. If the researcher finds no difference between the two variables, the null hypothesis is accepted.

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Answer:

Step-by-step explanation:

Answer:

4y4 the 1st one

may this help you

The matrix A, representing the linear mapping that projects vectors onto a unit vector a, is A = (a * a^T), where a * represents the outer product of a. The determinant of A is 0, and the rank is 1. A is not invertible, and its eigenvalues are 0 and 1, with eigenvectors parallel to a.

To determine the matrix A representing the linear mapping that projects vectors onto the unit vector a, we can use the outer product of a. The matrix A is given by A = (a * a^T), where a * represents the outer product.

The determinant of A can be calculated as det(A) = det(a * a^T) = det(a) * det(a^T) = det(a) * det(a) = |a|^2 = 1^2 = 1.

The rank of A is the number of linearly independent rows or columns. Since A is formed from the outer product of a, its rank is 1.

Since the determinant is non-zero, A is invertible. However, in this case, the determinant is 1, so A is not invertible.

Geometrically, the projection matrix A maps any vector x onto the vector a. Hence, the eigenvectors of A are the vectors parallel to a, and the eigenvalues are the factors by which the vectors are scaled. In this case, the eigenvalues are 0 and 1, with eigenvectors parallel to a.

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Answer:

You need to be specific on which is the length, height and width. Making the most basic assumption I would have to assume the answer is 228

Step-by-step explanation:

Formula for the surface area of a rectangular prism is A=2(wl+hl+hw)

A = 2 x (9 x 6 + 4 x 6 + 4 x 9)

A = 2 x (54 + 24 + 36)

A = 2 (114)

A = 228

The statement about both functions that is true is: B. The y-intercept of f(x) is greater than the y-intercept of g(x).

The y-intercept of a function is the output value (y) of the function when the input value (x) is zero. On a graph, it would be the value of y-coordinate of the point where the line cut across the y-axis.

From the table given for function g, the value of y when x is zero is 3. The y-intercept for g(x) is 3.

From the graph given for function f, the value of the point at which the line intercepts the y-axis is 6. Therefore, the y-intercept for f(x) is 6.

Therefore, the statement about both functions that is true is: B. The y-intercept of f(x) is greater than the y-intercept of g(x).

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(a) The probability that the other person is shorter than x is = 1/2

(b) The probability that the first person chosen is shorter than x is 1/2.

(a) If we know that at least one person is taller than x, then there are two cases to consider:

The first person chosen is taller than x:

In this case, the probability of the second person being shorter than x is 1/2.

The second person chosen is taller than x:

In this case, the probability of the first person being taller than x is 1/2.

The total probability that at least one person is taller than x and the other person is shorter than x is the sum of these two cases:

P = (1/2) * (1/2) + (1/2) * (1/2)

= 1/2

(b) If we know that the person chosen second is taller than x, then the only possibility is that the first person chosen is shorter than x.

The probability of this happening is 1/2.

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Answer:

Step-by-step explanation:

B

x is approximately equal to 6.

The ratios of the sides of a right triangle are called trigonometric ratios.

Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

sin = Perpendicular/ Hypotenuse

Cos = Base / Hypotenuse

tan = Perpendicular/Base

In the figure attached with the answer we can see that in Triangle ABC ,

tan 50.1 = x / 5

5(tan 50.1) = x

Therefore x is approximately equal to 6.

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Answer:

3/2

Step-by-step explanation:

Xab is anti-symmetric and Yab is symmetric, XaXbYaYb is the product of an anti-symmetric and a symmetric tensor, which is always zero. Therefore, XabYab = 0.

To show that the fact that a covariant second rank tensor is symmetric in one coordinate system is a tensorial property, we need to prove that if Tab = Tba in one coordinate system, then the same is true in any other coordinate system.

Let x'^i be a new set of coordinates related to the old set x^i by a transformation:

x'^i = f^i(x^1, x^2, x^3)

where f^i are differentiable functions. Then, the components of the tensor T in the new coordinates are:

T'ab = ∂x^i/∂x'^a ∂x^j/∂x'^b Tab

where we have used the chain rule for partial derivatives. Using the fact that Tab = Tba in the original coordinate system, we can write:

T'ab = ∂x^i/∂x'^a ∂x^j/∂x'^b Tba

We can also write:

T'ba = ∂x^i/∂x'^b ∂x^j/∂x'^a Tba

Comparing these two expressions, we see that in order for T'ab = T'ba, we need to have:

∂x^i/∂x'^a ∂x^j/∂x'^b Tba = ∂x^i/∂x'^b ∂x^j/∂x'^a Tba

This is true if and only if the partial derivatives commute, which is the case if the functions f^i are sufficiently smooth. Therefore, the fact that Tab = Tba in one coordinate system is a tensorial property, and holds in any other coordinate system.

To prove that XabYab = 0 given that Xab is anti-symmetric and Yab is symmetric, we can use the properties of the tensor product. The tensor product of two tensors X and Y is defined as:

(X ⊗ Y)ab = XaYb

Using this definition, we can write:

XabYab = (X ⊗ Y)(ab)(ab) = (XaYb)(XaYb)

Since Xab is anti-symmetric, we have XaYb = -XbYa. Substituting this into the above expression, we get:

(XabYab) = (-XbYa)(XaYb) = -XbXaYaYb

But Yab is symmetric, so we can write YaYb = YbYa. Substituting this into the above expression, we get:

XabYab = -XbXaYbYa

Since the order of the factors in a product of real numbers can be interchanged, we can write:

XabYab = -XbXaYbYa = -XbYaXaYb

But Xab is anti-symmetric, so we have XaXb = -XbXa. Substituting this into the above expression, we get:

XabYab = (-1)(-1)XaXbYaYb = XaXbYaYb

Since Xab is anti-symmetric and Yab is symmetric, XaXbYaYb is the product of an anti-symmetric and a symmetric tensor, which is always zero. Therefore, XabYab = 0.

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20 terms on the right side of the given equation \(20=20+18+16+...+x\).

The first n terms of the arithmetic sequence are added together to form the sum of the first n terms of AP.

Therefore, we can only evaluate the sum of n terms in a sequence if we are aware of the type of sequence it is. Usually, when calculating the sum of an n-number of terms, we take into account arithmetic progression. The common distinction between each following term and each preceding term remains unchanged throughout this progression. Natural numbers are an illustration of Arithmetic Progression, where the common difference is 1. We must therefore be familiar with the formula in order to calculate the sum of natural numbers.

We can use formula for sum of n terms-

\(S = \frac{n}{2}(2a + (n-1)d)\)

where, S- sum of n terms

n- number of terms

a- first term

d- difference between two consecutive terms

Here, S= 20 , a = 20, d= -2

we have to find n,

\(S = 20 = \frac{n}{2}(2(20) + (n-1)(-2)) \\20 = \frac{n}{2}(40-(2n-2))\\40 = n(40-2n+2)\\40 = 42n-2n^2\\2n^2 -42n +40 = 0\)

solving this quadratic equation-

\(2n^2 -42n +40 = 0\\2n^2 -40n-2n+40=0\\2n(n-20)-2(n-20) = 0\\(2n-2)(n-20)=0\)

when,

\(2n-2 = 0\\n=1\)

When,

\(n-20=0\\ n=20\)

as we can see that there are more than 1 terms present in the series so answer will be 20 terms.

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Answer:1. 2

2. 20

3. 5499999.5 or5500000

Step-by-step explanation:

Answer:

1. 2

2. 20

3. 5,499,999.5 = 5,500,000

At great axial distances x from a current-carrying loop, the magnetic field varies as:

b. x^-3

Here's the step-by-step explanation:

1. The magnetic field B at a point on the axis of a current-carrying loop can be given by the formula: B = (μ₀Ia²) / (2(a² + x²)^(3/2))

2. In this formula, μ₀ is the permeability of free space, I is current, a is the radius of the loop, and x is the axial distance from the loop.

3. When the axial distance x is much greater than the radius a (i.e., x >> a), the term a² in the denominator becomes negligible compared to x².

4. Therefore, the formula simplifies to: B ≈ (μ₀I) / (2x³)

As you can see, the magnetic field B varies as x^-3 at great axial distances from the current-carrying loop.

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Answer: 0,93 meter

Step-by-step explanation:

480mm = 48cm

48 + 45 = 93cm

93cm = 0.93m

The total length of a spinal cord and a femur, in meters, is 0.93.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that the femur, or thigh bone, of an average human, is 480 millimeters long. The spinal cord of an average human is 45 centimeters long.

The total length will be calculated as below:-

The value of 480mm will be 48 centimeters.

48 + 45 = 93cm

93cm = 0.93m

Therefore, the total length of a spinal cord and a femur, in meters, is 0.93.

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Research study measuring relationship suggests that video games may have a detrimental effect on an individual's grades.

This study analyzes the correlation between video game usage and academic performance. Scholastic Aptitude Test (SAT) and grade-point average (GPA) scores were used to gauge academic performance. The amount of time a student spends playing video games has a negative correlation with students' GPA and SAT scores. As video game usage increases, GPA and SAT scores decrease.

A chi-squared analysis found a p value for video game usage and GPA was greater than a 95% confidence level (0.005 < p < 0.01). This finding suggests that dependence exists. SAT score and video game usage also returned a p value that was significant (0.01 < p < 0.05). Chi-squared results were not significant when comparing time spent studying and an individual's SAT score. This research suggests that video games may have a detrimental effect on an individual's GPA and possibly on SAT scores. Although these results show statistical dependence, proving cause and effect remains difficult, since SAT scores represent a single test on a given day. The effects of video games maybe be cumulative; however, drawing a conclusion is difficult because SAT scores represent a measure of general knowledge. GPA versus video games is more reliable because both involve a continuous measurement of engaged activity and performance. The connection remains difficult because of the complex nature of student life and academic performance. Also, video game usage may simply be a function of specific personality types and characteristics.

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The instantaneous rate of change at x = 2 is 0

at x = 3 is negative

0 <= x <= 4 is 0

a function has an instantaneous rate of change of 0 at a maximum or minimum

the instantaneous rate of change at x = 3 being negative means it goes down after the maximum or minimum meaning it is a maximum

the average rate of change on the interval is 0, so the function goes up and then down

these all sound like a parabola

y = -2(x - 2)^2 + 10 is a parabola that fits the requirements

Answer:

125%

Step-by-step explanation

125% of 12 is 15

Answer:

0.8 or 80%

Step-by-step explanation:

12/15=0.8 or 80%

The given statement exists true. A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization).

A matrix can be expressed as the union of two distinct matrices, Q and R, using the QR matrix decomposition. R is a square upper/right triangular matrix and Q is an orthogonal matrix. R is also invertible because it is square and doesn't have zeros in its diagonal entries.

A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization). Finding eigenvalues and solving linear least squares problems both use QR factorization.

A = QR. Be aware that the QR-factorization of a rectangular matrix A is sometimes understood with Q square and R rectangular rather than Q rectangular and R square, as with the MATLAB command qr.

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Answer:

There are 4 possible scenarios where given relation could not be a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Step-by-step explanation:

From Function Theory, we remember that a relation is not a function when at least one element from domain (x-coordinate) is related to one or more elements from range (y-coordinate). Hence, there are four possibilities of making the relation not a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.

Let x = number of seats on the main-floor

y = number of balcony seats

We know that if all the seats are sold, then the total income is $4,200, we can write the equation:

x*8 + y*5 = $4,200

And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:

0.25*x*8 + 0.4*y*5 = $1,200

x*2 + y*2 = $1,200

2(x + y) = $1200

x + y = $600

x = 600 - y

putting the value of x in equation1)

8(600-y) + 5y = 4200

4800 - 8y + 5y = 4200

3y = 600

y = 200

and x = 600 - 200 = 400

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Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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Difference between polygon curves and non-polygon curves is explained with the help of a diagram.

Polygons are classified according to the number of sides (or vertices). Classification is explained with the help of suitable figures in the table listed in section 3.2.1. Students must understand this concept and remember the classifications given.

A diagonal is a line segment connecting two non-consecutive vertices of a polygon.

After that Convex and concave polygon are discussed. Before moving to angle sum property students will learn about regular and irregular polygons.

A regular polygon is both equiangular and equilateral.

A rectangle is equiangular but not equilateral.

A square has sides of equal length and angles of equal measure that's why it is considered as a regular polygon.

Talking about angle sum property; Angle sum property states that the sum of measures of the three angles of a triangle is 180°.

After going through the introductory section students about the above discussed topics need to solve the problems of exercise 3.1.

Sum of the measure of the exterior angles of a polygon is another topic that will be discussed in this chapter.

The sum of the measures of the external angles of any polygon is 360°.

Various kinds of quadrilaterals are explained like trapezium, parallelogram, etc. Point to be noted that kite is also a special type of quadrilateral. Angles of parallelogram and some special parallelograms are also discussed.

The opposite angles of a parallelogram are of equal measure.

A short note about diagonal of parallelogram is given that in general, diagonals of a parallelogram are not of equal length.

Some special parallelograms are listed in this section like rhombus, square and rectangle.

Properties of all quadrilateral are an important part of this chapter. Students must learn all the properties listed.