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The relation R on the set of natural numbers (N) is defined as (a, b) ∈ R if and only if a/b is a natural number. This relation exhibits the properties of reflexivity, symmetry, and transitivity.

Reflexivity: For any natural number a, a/a = 1, which is a natural number. Therefore, (a, a) ∈ R for all a ∈ N. Hence, R is reflexive.Symmetry: If (a, b) ∈ R, then a/b is a natural number. This implies b/a is also a natural number since the division is commutative. Thus, (b, a) ∈ R. Therefore, R is symmetric.

Transitivity: Let (a, b), (b, c) ∈ R, which means a/b and b/c are natural numbers. As the division operation is closed under natural numbers, a/c = (a/b) * (b/c) is also a natural number. Therefore, (a, c) ∈ R, and R is transitive. In summary, the relation R on the set of natural numbers is reflexive, symmetric, and transitive, making it an equivalence relation.

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Answer:

Step-by-step explanation:

w is the width of the rectangle, then the length would be 3w - 1.

A = lw

A = w(3w - 1)

A = 3w² - w

The fluid has a mass density of 1060 kg/m³, we can multiply the net volume by 1060 to obtain the net mass of fluid passing through the hemisphere in 1 second.

To find the net volume of fluid passing through the hemisphere, we need to calculate the flux of the velocity vector across the surface. The flux is given by the surface integral of the dot product of the velocity vector and the outward unit normal vector. Since the velocity vector is F(x, y, z) = -yi + zj + 3xk, we can calculate the dot product as -y(-y) + z(0) + 3x(√(9 - x² - y²)). Simplifying, we have F · dS = y² + 3x√(9 - x² - y²).

To evaluate the flux over the surface, we need to parameterize the hemisphere. Let's use spherical coordinates: x = r sinθ cosϕ, y = r sinθ sinϕ, and z = r cosθ, where 0 ≤ r ≤ 3, 0 ≤ θ ≤ π/2, and 0 ≤ ϕ ≤ 2π. The outward unit normal vector is given by n = (sinθ cosϕ)i + (sinθ sinϕ)j + (cosθ)k. Now, we can evaluate the flux by taking the surface integral: ∫∫(F · dS) = ∫∫(y² + 3x√(9 - x² - y²)) dA, where dA is the differential area element in spherical coordinates. Integrating over the appropriate limits, we can find the net volume of fluid passing through the hemisphere in 1 second.

To determine the net mass of fluid passing through the surface, we need to multiply the net volume by the fluid's mass density. Given that the fluid has a mass density of 1060 kg/m³, we can multiply the net volume by 1060 to obtain the net mass of fluid passing through the hemisphere in 1 second.

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Answer:

0.82

Step-by-step explanation:

82/100 as a fraction is equal to 0.82

Answer:

68%

Step-by-step explanation:

85 divided by 125 = .68 * 100 = 68

Answer: The sale price is 40 percent of the regular price

Step-by-step explanation:

Answer:

y+3=2*(x+1)

Step-by-step explanation:

Answer:y=2+2x

Step-by-step explanation:

Perpendicular means the slope is the opposite reciprocal of the red line’s. Opposite reciprocal means that if the red line has a negative slope the blue line will have a positive one, and you flip the fraction of the red line from 1/2 to 2. The y intercept is at 2 so that’s why there is a +2

Answer:

Below

Step-by-step explanation:

Every triangle should add up to 180 degrees,

This is a right triangle because it has the square in the corner meaning it is 90 degrees.

39 + 90 = 129

180 - 129 = 51 degrees

A: 51 degrees

C: 90 degrees

Answer:

a. 51 degrees

c. 90 degrees

I think

Answer:

Dena's answer

14ft^2

Step-by-step explanation:

Her answer is correct because area of triangle is base times height divided by two. Base is 7 and height is 4

From there, you can find the area which is 14.

hope this is correct

Answer:

Step-by-step explanation:

When doing synthetic division, if the remainder is zero, we know that the divisor is a root of the polynomial.  If the remainder is not zero, the remainder is the function vaue for that divisor.

Answer:

its c kiddos

Step-by-step explanation:

The required ordered pair for the solution of an equation  [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).

An ordered pair from the options is the solution of the equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] to be determined.

An ordered pair is defined as the coordinates when put into the equation giving the solution of the equation.

While plotting the curve of the given equation on the graph and also plotting the ordered pair on the graph. It is seen that points (2, –3.5), (2, 5.5), and (1.5, –5) lie on the unshaded portion. While ordered pair (-7.5, -5) lies on the shaded portion.

Thus, the required ordered pair for the solution of an equation  [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).

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Answer:

100°= angle b(VERTICAL OPPOSITE ANGLE)

100°+x°=180°[co interior angle]

x=180°-100°

x=80°

The Measure for angle x is 80 degree.

When two straight lines cross, they generate a pair of non-adjacent angles known as vertical angles. In the corners of the "X" created by two straight lines, or to put it another way, vertical angles are situated opposite one another. Due to their position opposite one another, they are also known as vertically opposite angles.

Given:

<CBD = 100 degree.

So, <ABF = <CBD (Vertical Opposite Angle)

<CBD = 100 degree.

Now, <ABF + <BFE = 180 (Angle on same side of Transversal)

<ABF + 100 = 180

<ABF = 180-100

x= 80 degree.

Hence, the measure for x is 80 degree.

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Answer:

A) 12 feet or d) 10 feet..

Answer:

each cookie was $0.94

Step-by-step explanation:

5.00 - 1.89 = 3.11

3.11 - 1.23 = 1.88

1.88 divided by 2 = 0.94

Answer:

x =5 & y =9

Step-by-step explanation:

let anumber x & y

-(x + 2y = 23)

4x + 2y = 38

-x -2y = -23

4x + 2y = 38

-x + 4x + 2y - 2y = 38-23

3x+0 = 15

3x /3 = 15/3

x = 5 then

5 + 2y = 23

2y = 23-5

2y/2 = 18/2

y = 9

therefore y =18 and x = 5

Answer:

D 240

Step-by-step explanation:

75÷15 to get the cost of each egg 5

5x12 to get 60

60x4 to get d 240

Answer:

Step-by-step explanation:

Correct choice is D

Answer:

140

Explanation: cause -180 + 40 = -140 (but absolute value is 140)

Answer:

let ABC be a right-angled triangle, where A is the right angle (left to right)

the original coordinates:

A (-8, 8)

B (-1, 8)

C (-8, 5)

by changing the coordinates from (x, y) to (-y, x)

A (-8, -8)

B (-8, -1)

C (-5, -8)

look attachment

Answer:

2^9 (2 to the 9th power) = 512

Step-by-step explanation:

Since 2 is multiplied by itself 9 times, it can be represented as 2^9, which evaluates to 512.

Hopefully this helps - let me know if you have any questions!

Answer:

3/2

Step-by-step explanation:

The ratio of perimeters of similar polygons is the same as the ratio of the lengths of corresponding sides.

WX/AB = 12/8 = 3/2

The 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).

The 95% confidence interval (CI) for the mean temperature in the crown of the balloon is calculated as follows. We first assume that the population distribution is normal with a standard deviation (SD) of σ = 6°C as per the given data. We will then use the z-distribution to calculate the required confidence interval.

The formula for calculating the 95% confidence interval is given by

CI (mean) = x ± z × (σ/√n)

Where 'x' is the mean, 'z' is the z-score associated with the 95% CI, 'σ' is the standard deviation, and 'n' is the number of samples taken.

For the given data the confidence interval is calculated as:

CI (Mean) = 97 ± 1.96 × (6/√59)

CI (Mean) = 97 ± 1.22

Therefore, the 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).

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Answer:

:c

Step-by-step explanation:

Answer:

x≤21

Step-by-step explanation:

x/3≤7

Multiply both sides by 3

3x/3≤7×3

Simplify

x≤21

Hope this helped!!!

The hexadecimal expansion [tex](A95E)_{16}[/tex] is equal to the decimal expansion 43358. This conversion is achieved by assigning the positional values of each digit in the hexadecimal number and evaluating the corresponding decimal values.

To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum up the results. Starting from the rightmost digit, the value of A in hexadecimal is equivalent to 10 in decimal. The next digit 9 represents the value of 9 in decimal. Continuing in the same manner, the digit 5 represents 5 in decimal, and the final digit E is equal to 14 in decimal.

Now, we calculate the decimal equivalent using the formula:

[tex](10 * 16^3) + (9 * 16^2) + (5 * 16^1) + (14 * 16^0) = 43486[/tex]

Therefore, the hexadecimal expansion [tex](A95E)_{16}[/tex] is equal to 43486 in decimal.

In conclusion, the decimal equivalent of the given hexadecimal expansion is 43486.

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Answer:

23

Step-by-step explanation:

GCF of 4 is 2 and GCF of 30 is 6.

2(2*x)-6(5*y)

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hope it helps