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The mass of the wire is given by the integral [tex]\int[0, R] k\sqrt{(1 + (-x/\sqrt{(9 - x^2}))^2}[/tex] dx, and the centre of mass is given by [tex]\int[0, R] x(k\sqrt{1 + (-x/\sqrt{9 - x^2})^2}[/tex] dx divided by the mass.

Find the mass and centre of mass of the wire?

To find the mass and center of mass of the wire, we need to integrate the linear density function along the curve of the wire.

The linear density function is given as a constant k, which means the mass per unit length is constant.

To find the mass of the wire, we integrate the linear density function over the length of the wire. The length of the semicircle can be found using the arc length formula:

[tex]s = \int[0, R] \sqrt{(1 + (dy/dx)^2} dx[/tex]

In this case, the equation of the semicircle is x² + y² = 9, so y = √(9 - x²). Taking the derivative with respect to x, we have dy/dx = -x/√(9 - x²).

Substituting this into the arc length formula, we have:

s = ∫[0, R] √(1 + (-x/√(9 - x²))²) dx

To find the centre of mass, we need to find the weighted average of the x-coordinate of the wire. The weight function is the linear density function, which is a constant k.

Therefore, the mass of the wire is given by the integral [tex]\int[0, R] k\sqrt{(1 + (-x/\sqrt{(9 - x^2}))^2}[/tex] dx, and the center of mass is given by [tex]\int[0, R] x(k\sqrt{1 + (-x/\sqrt{9 - x^2})^2}[/tex] dx divided by the mass.

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Answer:

Proportional and h.200=g

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3x-7=8

x=5

Answer:

Distancia restante = 1,3 kilómetroslp

Step-by-step explanation:

Dados los siguientes datos;

Distancia total = 4,5 km

Distancia recorrida = 3200 metros a kilómetros = 3200/1000 = 3,2 km

Para encontrar la distancia restante para cubrir la longitud requerida;

Distancia total = distancia recorrida + distancia a la izquierda

4.5 = 3.2 + distancia a la izquierda

Distancia a la izquierda = 4.5 - 3.2 Distancia restante = 1,3 kilómetros

Answer:

the answer is the cheese soup has a good change of being picked but not as good as the chicken soup there would so 3:2 to 2. so if they picked the cheese soup the first time then there is not a good change of the cheese souo to be picked again i hope that helps if not let me know

Answer:

[tex]\boxed {\boxed {\sf b= \sqrt{192}}}[/tex]

Step-by-step explanation:

Since this is a right triangle, we can use Pythagorean Theorem to find the sides.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse.

In this triangle, 8 and x are the legs because they form the right angle. 16 is the hypotenuse because it is opposite the right angle.

[tex]a=8 \\c=16[/tex]

Substitute the values into the formula.  

[tex]8^2+b^2=16^2[/tex]

Solve the exponents.

[tex]64+b^2=256[/tex]

Subtract 64 from both sides to isolate the variable.

[tex]64-64+b^2= 256-64 \\b^2=192[/tex]

Take the square root of both sides.

[tex]\sqrt {b^2}=\sqrt{192}\\ b=\sqrt{192}[/tex]

The missing side is equal to √192

The proportion of weeks in which the waste disposal facility is overloaded is approximately 0.4920.  No, this is not an acceptable level because it is not unusual for the system to be overloaded.

To solve this problem, we need to find the proportion of weeks in which the waste disposal facility is overloaded, given that the weights of the samples of 4712 households are normally distributed with a mean of 26.97 lb and a standard deviation of 12.29 lb.

Let's denote X as the random variable representing the mean weight of the samples of 4712 households in a week. We want to find P(X > 27.22).

To calculate this probability, we can use the standard normal distribution. First, we need to standardize the random variable X using the z-score formula:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation.

Substituting the given values:

z = (27.22 - 26.97) / 12.29

z ≈ 0.0203

Next, we can use a standard normal distribution table or a calculator to find the proportion of weeks in which the waste disposal facility is overloaded:

P(X > 27.22) = P(Z > 0.0203)

Looking up the z-score 0.0203 in the standard normal distribution table, we find that the corresponding proportion is approximately 0.4920.

Therefore, the proportion of weeks in which the waste disposal facility is overloaded is approximately 0.4920. This means that it is not unusual for the system to be overloaded.

So the correct answer is:

No, this is not an acceptable level because it is not unusual for the system to be overloaded.

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Answer:

Each litters can be represented as; x and y respectively to the 7% and the 28%

x + y =1

7x + 28y =19.6

This a simultaneous equation and can either be solved by using elimination or substitution method

Using the substitution method

eqn1, x=1-y

putting into eqn2

7(1-y)+28y =19.6

7-7y+28y=19.6

21y=12.6

y=3/5

but x=1-y

so

x=1-3/5

x=2/5

The domain and range of the inverse of the function f(x) = 0.5x need to be determined. The domain and range of the inverse function g(x) = 2x are both all real numbers.

To find the domain and range of the inverse of a function, we can swap the roles of x and y in the original function and then solve for y.

The original function is f(x) = 0.5x. Swapping x and y, we get x = 0.5y. Solving this equation for y, we multiply both sides by 2, giving us y = 2x.

The domain of the inverse function, denoted as g(x), is the set of all possible x-values. In this case, the domain of g(x) is the same as the range of the original function f(x). The range of f(x) is all real numbers, so the domain of g(x) is also all real numbers.

Similarly, the range of the inverse function is the set of all possible y-values. In this case, the range of g(x) is the same as the domain of the original function f(x). The domain of f(x) is all real numbers, so the range of g(x) is also all real numbers.

Therefore, the domain and range of the inverse function g(x) = 2x are both all real numbers.

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The rate of change of the function is -1/6

From the question, we have the following parameters that can be used in our computation:

(3,-1) and (-3,0)

The rate of change of the function is calculated as

Rate = Change in y/Change in x

Using the above as a guide, we have the following:

Rate = (0 + 1)/(-3 - 3)

Evaluate

Rate = -1/6

Hence, the rate of change of the function is -1/6

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The correct option is A) 9∕8, evaluating the exponent expression with a = -2 and b = 3, we find that the value is -8.

We are given the expression a^b, where a = -2 and b = 3. Substituting these values into the expression, we have (-2)^3.

To evaluate this expression, we raise -2 to the power of 3. When we raise a negative number to an odd power, the result will be a negative number.

So, (-2)^3 will yield a negative value.

Calculating (-2)^3, we multiply -2 by itself three times: (-2) × (-2) × (-2). This equals -8.

Therefore, the correct option is A) 9∕8 and the value of the exponent expression (-2)^3 is -8.

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Answer:

1=4

5=8

2=5

Step-by-step explanation:

Answer:

1, 5, 2 is the x values.

Step-by-step explanation:

you just subtract 3 from the y's

Answer:

If 100km enables consumption of 6lts

what about 42lts

42/6 multiply by 100km

42/6*100= 700km

The car will consume 42lts in 700 km.

Thank you.

Step-by-step explanation:

The solution of the differential equation is 1 = c₁v₁ + c₂v₂ and 5 = c₁v₁ + c₂v₂

We are given a system of two differential equations:

x₁' = – 5x₁ + 0x₂

x₂' = – 16x₁ + 3x₂

To solve this system, we can use several methods, such as substitution or matrix methods. In this explanation, we will use the substitution method.

We can write the given system of differential equations in matrix form as follows:

X' = AX

where X is the column vector [x₁, x₂], X' is the derivative of X, and A is the coefficient matrix:

A = [–5 0]

[–16 3]

To find the eigenvalues λ and eigenvectors v, we solve the characteristic equation:

|A - λI| = 0

where I is the identity matrix. Solving this equation will give us the eigenvalues and eigenvectors.

A - λI = [–5-λ 0]

[–16 3-λ]

Setting the determinant of A - λI to zero, we get:

(–5-λ)(3-λ) - (0)(–16) = 0

Simplifying, we have:

(λ + 5)(λ - 3) = 0

Solving this equation, we find two eigenvalues:

λ₁ = -5

λ₂ = 3

For each eigenvalue, we need to find its corresponding eigenvector. For λ₁ = -5, we solve the system of equations:

(A - (-5)I)v₁ = 0

Substituting the values of A and λ₁, we have:

[0 0] v₁ = 0

[–16 8]

Simplifying the equation, we get:

0v₁ + 0v₂ = 0

-16v₁ + 8v₂ = 0

From the first equation, we can see that v₁ can take any value. Let's choose v₁ = 1 for simplicity. Substituting this value into the second equation, we get:

-16(1) + 8v₂ = 0

-16 + 8v₂ = 0

8v₂ = 16

v₂ = 2

So, for λ₁ = -5, the corresponding eigenvector is v₁ = [1, 2].

Similarly, for λ₂ = 3, we solve the system of equations:

(A - 3I)v₂ = 0

Substituting the values of A and λ₂, we have:

[-8 0] v₂ = 0

[–16 0]

Simplifying the equation, we get:

-8v₁ + 0v₂ = 0

-16v₁ + 0v₂ = 0

From the first equation, we can see that v₁ can take any value. Let's choose v₁ = 1 for simplicity. Substituting this value into the second equation, we get:

-16(1) + 0v₂ = 0

-16 = 0

This equation has no solution. However, this means that v₂ can take any value. Let's choose v₂ = 1 for simplicity.

So, for λ₂ = 3, the corresponding eigenvector is v₂ = [1, 1].

The general solution of the system of differential equations can be expressed as:

X(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂

where c₁ and c₂ are constants that need to be determined.

We are given the initial conditions x₁(0) = 1 and x₂(0) = 5. Substituting these values into the general solution, we get two equations:

x₁(0) = c₁e(λ₁(0))v₁ + c₂e(λ₂(0))v₂

x₂(0) = c₁e(λ₁(0))v₁ + c₂e(λ₂(0))v₂

Simplifying, we have:

1 = c₁v₁ + c₂v₂

5 = c₁v₁ + c₂v₂

Solving this system of equations, we can find the values of c₁ and c₂.

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Answer:

Equation = 298.56=6(0.07m+23.90+0.10(23.90))

Minutes = 335

Step-by-step explanation:

Okay, so first simplify to get 298.56=0.52m+172.08

Next subtract to get 0.52m=126.48

Then divide 0.52 to get 335

I hope this helps ! :)

Answer:

894

Step-by-step explanation:

58,110 divided by 65 is 894

The quotient of the given numbers 58,110 and 65 would be equal to  894.

Quotients are the number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

The quotient of the given numbers is 58,110 and 65.

58,110 divided by 65

58,110 /65

= 894

Thus, the quotient of the given numbers is 894.

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Answer:

√89

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(9 - 1)² + [-6 - (-1)]²

√(8)² + (-5)²

√64 + 25

√89

The 90% confidence interval for the mean score for all students is [79.35, 86.75].

A 90% confidence interval was calculated to estimate the mean score for all students based on a sample of six students' scores. The sample mean was found to be 82.83, and the standard deviation was 3.67.

Using a t-distribution with five degrees of freedom (n-1), the critical value for a 90% confidence level was determined to be 2.571. By applying the formula for confidence intervals, the lower bound of the interval was calculated as 82.83 - (2.571 * (3.67/√6)) = 79.35, and the upper bound was calculated as 82.83 + (2.571 * (3.67/√6)) = 86.75.

This means that we can be 90% confident that the mean score for all students falls within the range of 79.35 to 86.75.

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The formulas below that are true in the domain.

The correct answer is (A, B, C, E, F). A. Vay P(x,y) B. ByVx P(x,y) C. 3xVy P(x,y) E. 3xVy - P(x, y) F. ByVx - P(x, y)

Let's evaluate each formula to determine which ones are true in the given domain:

A. Vay P(x, y): This formula states that for all y, there exists an x such that x + 1 > y. Since there is no restriction on x, this formula is true in the given domain.

B. ByVx P(x, y): This formula states that for all x, there exists a y such that x + 1 > y. Since there is no restriction on y, this formula is true in the given domain.

C. 3xVy P(x, y): This formula states that there exists an x such that for all y, x + 1 > y. Since there is no restriction on y, this formula is true in the given domain.

D. Vyc P(x, y): This formula states that for all y, there exists a constant c such that x + 1 > y. However, there is no mention of c in the given domain, so this formula is not true.

E. 3xVy -P(x, y): This formula states that there exists an x such that for all y, x + 1 ≤ y. This is the negation of the original condition x + 1 > y. Since there is no restriction on y, this formula is true in the given domain.

F. ByVx -P(x, y): This formula states that for all x, there exists a y such that x + 1 ≤ y. This is again the negation of the original condition x + 1 > y. Since there is no restriction on x, this formula is true in the given domain.

G. Vzy -P(x, y): This formula states that for all z, there exists a y such that x + 1 ≤ y. However, there is no mention of z in the given domain, so this formula is not true.

H. -3xVy P(x, y): This formula states that there does not exist an x such that for all y, x + 1 > y. Since the original condition x + 1 > y is true for any value of x and y in the given domain, this formula is not true.

Based on the evaluations above, the formulas that are true in the given domain are:

A. Vay P(x, y)

B. ByVx P(x, y)

C. 3xVy P(x, y)

E. 3xVy -P(x, y)

F. ByVx -P(x, y)

Therefore, the correct answer is (A, B, C, E, F).

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Answer: 1/9

Step-by-step explanation: 9(1/3)^5-1, which is  9(1/3)^4.

Solve and you get 1/9.

Answer:

8/10 or 4/5 as a fraction. the percentage is 80%

Step-by-step explanation:

The initial concentration of the solution in the tank is 0.036 kg of salt per liter.

Initially, the tank contains 90 kg of salt and 1000 liters of water, resulting in a total volume of 1000 liters. A solution with a concentration of 0.045 kg of salt per liter enters the tank at a rate of 8 liters per minute. Since the solution is mixed and drains from the tank at the same rate, the concentration remains constant throughout the process.

To find the initial concentration, we can calculate the amount of salt in the tank after a certain time period. After 1.5 hours, the solution has been entering and draining from the tank for 90 minutes (1.5 hours * 60 minutes/hour). During this time, the total volume of the solution that has entered and drained is 90 minutes * 8 liters/minute = 720 liters.

The amount of salt that has entered the tank is 720 liters * 0.045 kg/liter = 32.4 kg. Since the initial amount of salt in the tank was 90 kg, the amount of salt remaining after 1.5 hours is 90 kg - 32.4 kg = 57.6 kg.

To find the concentration, we divide the remaining amount of salt (57.6 kg) by the remaining volume of the solution (1000 liters - 720 liters = 280 liters). The concentration of the initial solution in the tank is 57.6 kg / 280 liters ≈ 0.206 kg of salt per liter.

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The correct answer is option d) 9x² + 12xy + 4y². To simplify the expression (3x + 2y)² using the square of a binomial formula, we need to apply the formula (a + b)² = a² + 2ab + b². In this case, a = 3x and b = 2y.

Using the formula, we have:

(3x + 2y)² = (3x)² + 2(3x)(2y) + (2y)²

= 9x² + 12xy + 4y²

So the simplified form of (3x + 2y)² is 9x² + 12xy + 4y².

Now let's analyze the given options:

a) 9x² + 4y²: This option is incorrect because it is missing the term 12xy.

b) 9x² + 5xy + 4y²: This option is also incorrect because it contains an additional term, 5xy, which is not present in the simplified expression.

c) 9x² + 6xy + 4y²: This option is incorrect because it also contains an additional term, 6xy, which is not present in the simplified expression.

d) 9x² + 12xy + 4y²: This option is correct because it matches the simplified form we obtained using the square of a binomial formula.

Therefore, the correct answer is option d) 9x² + 12xy + 4y².

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Answer:

Well what's the question lol

Answer:

show the question

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The symbolic argument ~p -> q is valid.

To determine the validity of the argument ~p -> q using a truth table, we need to consider all possible combinations of truth values for p and q and evaluate the truth value of the implication ~p -> q.

The symbolic form of the argument is ~p -> q, which can also be written as ¬p → q.

A truth table for this argument would have columns for p, ~p, q, and ~p -> q.

Let's construct the truth table:

|   p      |  ~p    |   q      |  ~p -> q |

| True  | False | True  |   True    |

| True  | False | False |   False   |

| False | True  | True  |   True    |

| False | True  | False |   True    |

In the truth table, we consider all possible combinations of true (T) and false (F) for p and q. For ~p, we negate the value of p.

For the implication ~p -> q, it is true (T) if either ~p is false (F) or q is true (T). In all other cases, it is false (F).

Looking at the truth table, we can see that in all rows where ~p -> q is true (T), the corresponding conclusion q is true (T). Therefore, the argument ~p -> q is valid because whenever ~p is true (F), the conclusion q is also true (T).

In summary, the symbolic argument ~p -> q is valid.

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Answer:

x = − 9 , − 4 , 4

Step-by-step explanation:

Each crate is in the shape of a rectangular solid. Its dimensions are length, width, and height. The rectangular solid shown in the image below has a length  

4  units, width  2  units, and height  3

units. Can you tell how many cubic units there are altogether? Let’s look layer by layer.

Breaking a rectangular solid into layers makes it easier to visualize the number of cubic units it contains. This  

4  by  2  by  3  rectangular solid has  24 cubic units.

A rectangular solid is shown. Each layer is composed of 8 cubes, measuring 2 by 4. The top layer is pink. The middle layer is orange. The bottom layer is green. Beside this is an image of the top layer that says  

Altogether there are  24  cubic units. Notice that  24  is the  length × width × height .

The top line says V equals L times W times H. Beneath the V is 24, beneath the equal sign is another equal sign, beneath the L is a 4, beneath the W is a 2, beneath the H is a 3.

The volume,  V , of any rectangular solid is the product of the length, width, and height.

V = L W H

We could also write the formula for the volume of a rectangular solid in terms of the area of the base. The area of the base,  B , is equal to  length × width . B = L ⋅ W

We can substitute  

B  for  L ⋅ W  in the volume, formula to get another form of the volume formula.

The top line says V equals red L times red W times H. Below this is V equals red parentheses L times W times H. Below this is V equals red capital B times h.

We now have another version of the volume formula for rectangular solids. Let’s see how this works with the  

4 × 2 × 3

rectangular solid we started with. See the image below.

 Besides the solid is V equals Bh. Below this is V equals Base times height. Below Base is parentheses 4 times 2. The next line says V equals parentheses 4 times 2 times 3. Below that is V equals 8 times 3, then V equals 24 cubic units.

Answer:

e^12

Step-by-step explanation:

Write the problem as a mathematical expression.

e^3 ⋅ e^9

Use the power rule and combine the exponents.

e^3 + 9^e

Add 3 and 9.

e^12

The result can be shown in multiple forms.

Exact Form:

e^12

If not the answer

The Decimal Form:

162754.79141900…

There is not sufficient evidence to conclude that the proportion of union members differs from 13.7% at the 0.01 level of significance.

To determine if there is sufficient evidence to conclude that the proportion of union members differs from 13.7%, we can perform a hypothesis test using the given sample data.

Let's define the hypotheses:

Null Hypothesis (H0): The proportion of union members is equal to 13.7%.

Alternative Hypothesis (H1): The proportion of union members differs from 13.7%.

We can set up the test using the z-test for proportions. The test statistic is calculated as:

z = (p(cap) - p) / √(p × (1 - p) / n)

where p(cap) is the sample proportion, p is the hypothesized proportion, and n is the sample size.

Given that the sample size is 200 and 30 workers belonged to a union, the sample proportion is p(cap) = 30/200 = 0.15.

The hypothesized proportion is p = 0.137.

Let's calculate the test statistic:

z = (0.15 - 0.137) / √(0.137 × (1 - 0.137) / 200)

z ≈ 1.073

To determine if there is sufficient evidence to conclude that the proportion differs from 13.7%, we compare the test statistic to the critical value.

At a significance level of 0.01, the critical value for a two-tailed test is approximately ±2.576 (obtained from a standard normal distribution table).

Since |1.073| < 2.576, the test statistic does not fall in the rejection region. Therefore, we fail to reject the null hypothesis.

Conclusion: Based on the given sample data, there is not sufficient evidence to conclude that the proportion of union members differs from 13.7% at the 0.01 level of significance.

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