What is f(-x)?
f(x) = -cos x+ 4x
O f(x) = -cos x- 4x
Of(z)= -cos x+ 4x
Of(1) = cos x-4x
Of(x) = cos x + 4x
-

The log 8(1) = 0Let x = log4(x) Evaluate (1024)We know that the logarithm of a number in a given base is the power to which the base must be raised to get the number.

For example, if the base is 2, then log2(8) = 3 because 23 = 8.

Using this definition, we can justify the statement log8(1) = 0 as follows:log8(1) = 0 because 80 = 1. This means that the power to which 8 must be raised to get 1 is 0.

Therefore, log8(1) = 0.Next, we have:x = log4(x) This means that 4 to the power of x equals x. We can solve for x as follows:4x = x4x - x = 0x(4 - 1) = 0x = 0 or x = 1Plugging in x = 1, we get:log4(1) = 1

This is true because 41 = 1. Finally, we can evaluate (1024) as follows:(1024) = (210)10 = 210·10 = 210+1 = 211This is true because 210 is the base-2 logarithm of 1024. Therefore, (1024) = 211.

Now, we need to write a mathematical equation to justify the statement ln(17) ≈ 2.832. To do this, we need to know the definition of the natural logarithm function, denoted as ln(x).

The natural logarithm of a positive number x is the logarithm of x in the base e, where e is a mathematical constant approximately equal to 2.71828. Therefore, we have ln(17) ≈ 2.832 because e2.832 ≈ 17.

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Answer:

6

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

the formula for sum of arithmatic progression=n/2(2a+(n-1)d)

=9/2 (4+8*3)

=9/2*(28)

=9* 14=126

The convolution integral is a mathematical technique used to find the inverse Laplace transform of a function. In this case, we have a function f(s) that we want to find the inverse Laplace transform of. Let's call the inverse Laplace transform of f(s) F(t).

To use the convolution integral, we first need to express f(s) as a product of two Laplace transforms. Let's call these Laplace transforms F1(s) and F2(s):

f(s) = F1(s) * F2(s)

where * denotes the convolution operation.

Next, we use the convolution theorem to find F(t):

F(t) = (1/2πi) ∫[c-i∞,c+i∞] F1(s)F2(s)e^(st)ds

where c is any constant such that the line Re(s)=c lies to the right of all singularities of F1(s) and F2(s).

In our case, we need to find the inverse Laplace transform of a specific function. Let's call this function F(s):

F(s) = 1/(s^2 + 4s + 13)

To use the convolution integral, we need to express F(s) as a product of two Laplace transforms. One way to do this is to use partial fraction decomposition:

F(s) = (1/10) * [1/(s+2+i3) - 1/(s+2-i3)]

Now we can use the convolution theorem to find the inverse Laplace transform of F(s):

f(t) = (1/2πi) ∫[c-i∞,c+i∞] F1(s)F2(s)e^(st)ds

where F1(s) = 1/(s+2+i3) and F2(s) = 1/(10)

Plugging in these values, we get:

f(t) = (1/2πi) ∫[c-i∞,c+i∞] (1/(s+2+i3))(1/(10)) e^(st)ds

Now we can simplify this integral and evaluate it using complex analysis techniques. The final answer will depend on the value of c that we choose.

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Use the convolution theorem to find the inverse Laplace transform of each of the following functions. a. F(S) = S/((S + 2)(S^2 + 1)) b. F(S) = 1/(S^2 + 64)^2 c. F(S) = (1 - 3s)/(S^2 + 8s + 25) Use the Laplace Transform to solve each of the following integral equations. a. f(t) + integral^infinity_0 (t - tau)f(tau)d tau =t b. f(t) + f(t) + sin (t) = integral^infinity_0 sin(tau)f(t - tau)d tau: f(0) = 0 Find the Inverse Laplace of the following functions. a. F(t) = 3t^ze^2t b. f(t) = sin(t - 5) u(t - 5) c. f(t) = delta(t) - 4t^3 + (t - 1)u(t - 1)

Answer:

169/16

Step-by-step explanation:

13/4

what is a square at first

a square is the result of multiplying a number by itself

so the square of 13 will be 169

and the square of 4 will be 16

so easy...bingo

Euclid receives 20 shares of common stock as a nontaxable stock dividend.The basis of the common stock remains the same as in scenario a, which is $96.15 per share.

To calculate the per share basis, we divide the original purchase cost by the total number of shares (including the dividend shares).  In scenario b, Euclid receives a nontaxable preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock, on which the preferred is distributed, has a fair market value of $75,000.

The tax consequences involve determining the new basis of the preferred stock and the common stock after the dividend. a. To find the per share basis of Euclid's common stock after receiving the stock dividend, we divide the original purchase cost by the total number of shares. The original purchase cost was $50,000 for 500 shares, which means the per share basis was $50,000/500 = $100. After receiving 20 additional shares as a dividend, the total number of shares becomes 500 + 20 = 520.

Therefore, the new per share basis is $50,000/520 = $96.15. b. In this scenario, Euclid receives a preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock has a fair market value of $75,000. To determine the new basis of the preferred stock, we consider its fair market value.

Since the preferred stock dividend is nontaxable, its basis is equal to the fair market value, which is $5,000.

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Answer:

top one

Step-by-step explanation:

You are not including -2 (else it would be a greater or equal sign) so the dot has to be empty. You can rule out the middle options.

At this point you either remember that "greater than" means "to the right of" or you pick a convenient number, ie, 0. see that your inequality is true (zero is greater than -2) and you pick the graph where the solid line includes 0.

The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).

Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The radius of gyration Rg is defined as follows.

Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.

R(mean) is the mean position vector of all monomers.

Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).

Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).

The ratio R²/Rg² is given by R²/Rg² = L^(D-2).

When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.

This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.

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Example of a relation R on S:

a. {(1,2), (2,3), (3,4)}

b. {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1)}

c. {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (1,3), (3,1), (2,4), (4,2)}

d. {(1,2), (2,3), (3,4), (1,3), (1,4)}

e. {(1,2), (2,3), (3,1)}

The question asks to provide examples of relations on the set S={1,2,3,4} that satisfy certain properties. A relation R on a set S is a subset of the Cartesian product S×S, where (a,b) is in R if and only if a is related to b by R.

(a) An example of a relation R on S that is antisymmetric but neither reflexive nor transitive is R = {(1,2), (2,1), (3,4)}. This relation is antisymmetric because if (a,b) and (b,a) are both in R, then a=b. However, it is not reflexive because (1,1), (2,2), (3,3), and (4,4) are not in R, and it is not transitive because (1,2) and (2,1) are in R, but (1,1) is not.

(b) An example of a relation R on S that is reflexive and transitive but not antisymmetric is the equality relation R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1)}. This relation is reflexive because (a,a) is in R for all a in S, and it is transitive because if (a,b) and (b,c) are in R, then (a,c) is also in R. However, it is not antisymmetric because (1,2) and (2,1) are both in R, but 1 is not equal to 2.

(c) An example of a relation R on S that is reflexive and antisymmetric but not transitive is the divisibility relation R = {(1,1), (2,2), (3,3), (4,4), (1,2), (1,3), (1,4)}. This relation is reflexive because every number divides itself, and it is antisymmetric because if a divides b and b divides a, then a=b. However, it is not transitive because although 1 divides 2 and 2 divides 4, 1 does not divide 4.

(d) An example of a relation R on S that is antisymmetric and transitive but not reflexive is R = {(1,2), (2,3), (1,3)}. This relation is antisymmetric because if (a,b) and (b,a) are both in R, then a=b. It is also transitive because if (a,b) and (b,c) are in R, then (a,c) is also in R. However, it is not reflexive because (2,2) and (3,3) are not in R.

(e) An example of a relation on S that has none of the properties of reflexive, antisymmetric, and transitive is R = {(1,2), (2,3)}. This relation is not reflexive because (1,1), (2,2), (3,3), and (4,4) are not in R. It is not antisymmetric because (1,2) and (2,1) are both in R. Finally, it is not transitive because (1,2) and (2,3) are in R, but (1,3) is not.

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Answer:

18:18

Step-by-step explanation:

You first do 36-18 and then add your answer with the 18 to check it and correct it.

Based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

To determine the amount of capital this year based on the given information, we can use the investment and depreciation rates.

Let's denote the amount of capital this year as K1.

According to the information provided:

People invest 55% of income, but we don't have any information about income. Therefore, we cannot determine the exact investment amount.

10% of capital depreciates. Based on this, the capital at the beginning of this year (K1) can be calculated as follows:

K1 = K - 0.1K

= 0.9K

Since we know that the capital last year was equal to 25, we substitute K = 25 into the equation above:

K1 = 0.9 * 25

= 22.5

Therefore, based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.

Two important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.

The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.

Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.

Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}

On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.

Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.

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Answer: 0.8333

Step-by-step explanation:

We conclude: that the parents will get a fairly accurate estimate of his height at age 21 years because the data are clearly correlated.

The correct option is:  such a prediction could be misleading, since it involves extrapolation.

We find the regression equation has positive slope and for a new born child height is intercept

H = 0.3739A + 20.4595

is the relation between height and age.

When we find 252 months this is very far from the age we have considered and hence:

A = 252

H = 0.3739(252) + 20.4595

H = 114.6823

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The given question is incomplete, complete question is:

John's parents recorded his height at various ages up to 66 months. Below is a record of

the results.

Age (months) 36 48 54 60 66

Height(months) 35 38 41 43 45

John's parents decide to use the least-squares regression line of John's height on age

based on the data in the previous problem to predict his height at age 21 years (252

months). We conclude

A) John's height, in inches, should be about half his age, in months.

B) The parents will get a fairly accurate estimate of his height at age 21 years, since

the data are clearly correlated.

C) such a prediction could be misleading, since it involves extrapolation.

D) all of the above.

The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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Complete question:

Jason has two bags with 6 tiles each. The tiles in each bag are shown below:

1 2 3 4 5 6

Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing the tile numbered 2 from the first bag and the tile numbered three from the second bag?

Answer: 1/36

Step-by-step explanation:

Number of tiles in each bag = 6

Probability of drawing tile numbered 2 from the first bag and the tile numbered 3 from the second

Probability of drawing number 2 from first bag :

P(numbered 2) = (required outcome / possible outcome)

P(numbered 2) = 1/6

Probability of drawing number 2 from first bag :

P(numbered 3) = 1/6

Since they are independent events :

P(drawing 2 from bag one and 3 from bag 2) :

1/6 × 1/6 = 1/36

The decimal value of the given postfix (RPN) expression "4 7 2 - * 6 4 / 7 *" is 14.0 when rounded to one decimal place.

To evaluate the postfix expression, we follow the Reverse Polish Notation (RPN) method. We start by scanning the expression from left to right.

1. The first number encountered is 4, which we push onto the stack.

2. The next number is 7, which is also pushed onto the stack.

3. Then we encounter 2. Since the next operation is subtraction (-), we pop 2 and 7 from the stack and calculate 7 - 2 = 5. The result 5 is pushed back onto the stack.

4. The multiplication (*) operation is encountered. We pop 5 and 4 from the stack and calculate 5 * 4 = 20. The result 20 is pushed onto the stack.

5. The number 6 is pushed onto the stack.

6. Next, we encounter 4. As the next operation is division (/), we pop 4 and 6 from the stack and calculate 6 / 4 = 1.5. The result 1.5 is pushed back onto the stack.

7. Finally, the multiplication (*) operation is encountered again. We pop 1.5 and 20 from the stack and calculate 1.5 * 20 = 30. The result 30 is pushed onto the stack.

At this point, the stack contains only the final result, 30.0. Therefore, the decimal value of the given postfix expression is 30.0, which, when rounded to one decimal place, becomes 14.0.

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The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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Volume of the solid obtained by rotating the region is 67π/6 .

Given,

Curves:

y=x², y=0, x=1, and x=2 .

The arc of the parabola runs from (1,1) to (2,4) with vertical lines from those points to the x-axis. Rotated around x=4 gives a solid with a missing circular center.

The height of the rectangle is determined by the function, which is x² . The base of the rectangle is the circumference of the circular object that it was wrapped around.

Circumference = 2πr

At first, the distance is from x=1 to x=4, so r=3.

It will diminish until x=2, when r=2.

For any given value of x from 1 to 2, the radius will be 4-x

The circumference at any given value of x,

= 2 * π * (4-x)

The area of the rectangular region is base x height,

= \(\int _1^22\pi \left(4-x\right)x^2dx\)

= \(2\pi \cdot \int _1^2\left(4-x\right)x^2dx\)

= \(2\pi \left(\int _1^24x^2dx-\int _1^2x^3dx\right)\)

= \(2\pi \left(\frac{28}{3}-\frac{15}{4}\right)\)

Therefore volume of the solid is,

= 67π/6

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Answer:it’s 15

Step-by-step explanation:because think about it if it was 12 it wouldn’t be 60% it would be 70%

Answer:

a group of 4 people can be selected in 35 ways

Answer:

x= 72

Step-by-step explanation:

- move 9 to the right.

- when a number moves to the other side, their sign changes.

- in this case, 9 multiplies by 8.

- thus 9 x 8 equals to 72.

Answer:

x=0

Step-by-step explanation:

1.Subtract 8x from both sides

2.Simplify the expression

3.Divide both sides by the same factor

4.Cancel terms that are in both the numerator and denominator

Answer: x=0

Step-by-step explanation:

z = 32°

then

53 + 32 + y = 180 °   ( a straight line )

y = 95°

The corner points of the Graph of the inequality -x + y ≥ 2 are (-2, 0), (0, 2)

What is Linear Inequality?

Linear inequalities are mathematical expressions that compare two expressions using the inequality symbol. The expression might be either algebraic or numerical, or a mix of the two. A linear function is any function with a straight line as its graph.

Solution:

We need to plot the graph of the given inquality -x + y ≥ 2

Please refer to the graph attached below

The corner points of the Graph are (-2, 0), (0, 2)

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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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A statement which best describes the reflection include the following: C. a reflection over the line x = 3.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

Based on the graph of triangle ABC and triangle ΔA’B’C’, we can logically deduce the following coordinates after a reflection over the line x = 3:

A = (-2, 2)   → A' = (8,2)

B = (0, 4)    → B' = (6, 4)

C = (2,2)     → C' = (4, 2)

Therefore, the two triangles are identical (similar) because they are reflections of each other. Also, the distance between the point C and point C' is 2 units, therefore, with a line that is parallel to the y-axis and lies at point x = 3, as shown in the image attached below.

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Complete Question:

ΔA’B’C’ is a reflection of ΔABC. Which best describes the reflection?

A coordinate plane showing triangles A B C and A prime B prime C prime. The coordinates of the first figure are A negative 2 comma 2, B zero comma 4, and C 2 comma 2. The coordinates of the second figure are A prime 8 comma 2, B prime 6 comma 4, and C prime 4 comma 2.

a.)A reflection over the line x = 2

b.)A reflection over the line y = 3

c.)A reflection over the line x = 3

d.)A reflection over the y-axis

Answer:

The correct answer is:

You can map ABC to A'B'C' by translating it 6 units left and reflecting it across the x-axis, which is a series of rigid motions.

Explanation:

In ABC, the coordinates are:

A(1, -3)

B(5, 3)

C(4, -1).

In A'B'C', the coordinates are:

A'(-5, 3)

B'(-1, -3)

C'(-2, 1)

Each point is mapped to its image:

A(1, -3)→A'(-5, 3)

B(5, 3)→B'(-1, -3)

C(4, -1)→C'(-2, 1

Comparing the x-coordinates in the pre-image and image, we notice that the image has an x-coordinate that is 6 less than that of the pre-image:

1-6 = -5

5-6 = -1

4-6 = -2

This means that the figure must be translated 6 units left; that is the only way to have this change on the pre-image to form the image.

Comparing the y-coordinates of the pre-image with those of the image, we notice that they are negated:

-(-3) = 3

-(3) = -3

-(-1) = 1

This means the pre-image was reflected across the x-axis; this is the only way to negate the y-coordinate and not change the x-coordinate.

These are rigid motions because they do not change the shape or size, they simply move it and change its orientation.

Step-by-step explanation:

Hope this will help u

Answer:

27/100 because if u write the decimal out in word form it's 27 hundredths and its the same thing if u write 27/100 in word form

Fallacies of relevance are types of logical fallacies that occur when an argument is presented without a relevant connection to the subject matter.

Rather than addressing the topic, these fallacies are aimed at the listener's feelings, emotions, or biases.There are many different types of fallacies of relevance, but some of the most common are ad hominem, straw man, appeal to authority, and red herring. Ad hominem, for example, is a type of fallacy that attacks the speaker rather than addressing the argument they are presenting.. It can undermine the quality of your argument and make you seem less credible.

However, if you want to describe a time when you used these fallacies, you might think back to a situation where you were arguing with someone and felt like you were losing the argument. In this case, you might have resorted to a fallacy of relevance to try to regain control of the conversation. In conclusion, it is important to avoid using fallacies of relevance in your arguments. Instead, focus on addressing the topic at hand and presenting logical, evidence-based arguments.

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Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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Answer:

y = 2/3x

Step-by-step explanation:

Slope-intercept formula: y = mx + b

m = 2/3 because the slope is 2/3.

b = 0 because the y value of the origin is 0, as the point is at (0, 0).

That makes y = 2/3x + 0, but adding zero does nothing so you take it out to get y = 2/3x.

Answer:

2x - 3y = 0

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

here m = \(\frac{2}{3}\) , then

y = \(\frac{2}{3}\) x ( multiply through by 3 to clear the fraction )

3y = 2x

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearranging the above equation into this form

2x = 3y ( subtract 3y from both sides )

2x - 3y = 0 ← in standard form