What is the significance of SS in water and in the mixed liquor of the activated sludge aeration tank?

Answer:

The ordered pair for the vertices for r₍₁₈₀ ₀₎(QRST), is given as follows;

Q' = (-1, -3) R' = (-3, 3) S' = (0, 2) T' = (2, -1)

Step-by-step explanation:

The coordinates of he vertices of the triangle QRST are;

Q(1, 3), R(3, -3), S(0, -2), T(-2, 1)

A rotation of a point with coordinates (x, y) 180° about the origin gives;

The coordinate of the point of the preimage before the rotation = (x, y)

The coordinate of the point of the image after the rotation = (-x, -y)

Therefore we have;

The image of point Q(1, 3) after 180° rotation = Q'(-1, -3)

The image of point R(3, -3) after 180° rotation = R'(-3, 3)

The image of point S(0, -2) after 180° rotation = S'(0, 2)

The image of point T(-2, 1) after 180° rotation = T'(2, -1)

The ordered pair for the vertices for r₍₁₈₀ ₀₎(QRST), is therefore, Q'(-1, -3), R'(-3, 3), S'(0, 2), and T'(2, -1);

Q' = (-1, -3) R' = (-3, 3) S' = (0, 2) T' = (2, -1).

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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There are different consecutive ways that the flowers can be planted:

3,9,15,21 and so on.

Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written sequentially, where the difference between the numbers is fixed and no number in between is skipped.

Given that:

Roses plants in 1st, 2nd, row are:

3,9 ,.....

Since difference between consecutive terms is same:

It is an AP

We have to find number of row in the flower bed:

Lets assume there are n rows in the flowers bed.

We know that:

    aₙ = a + (n-1)d

and d = 9-3 = 6

Therefore, the next numbers can be:

3,9,15 ,21 ......

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Answer:

Step-by-step explanation:

REcall that the triangular numbers are obtained by summing up the integers up to x. For example, the value of the function at x=2 is 1+2 = 3. At x=3 it is 1+2+3 = 6. So, at x we should add the first x integers. There is a formula for that, which is \(\sum_{i=1}^{x} i = \frac{x(x+1)}{2}\) which is equivalent to 0.5x^2+0.5x

So none of the options is the answer

Answer:d on edg

Step-by-step explanation:

Answer:

y=7x+14

Step-by-step explanation:

-y=14-7x

y=-14+7x

y=7x-14

Answer:

25.2% of the boys want to play inside

Step-by-step explanation:

Answer:

1/125 probability for each student so, a 0.8 percent probably of winning per student.

Step-by-step explanation:

The mathematically possible value of Pr(A and B) is either a) 0, b) 0.2, d) 0.8, or e) 0.5, depending on the specific probabilities of events A and B and their overlap.

For the first question, we need to find the mathematically possible value of Pr(A U B), which represents the probability of either event A or event B occurring. Since events A and B are not mutually exclusive (it is possible for a student to wear glasses and be less than 6 feet tall), we can use the formula Pr(A U B) = Pr(A) + Pr(B) - Pr(A and B) to find the desired probability.

Given that Pr(A) = 0.3 and Pr(B) = 0.8, we can substitute these values into the formula and rearrange it to solve for Pr(A and B): Pr(A U B) = Pr(A) + Pr(B) - Pr(A and B) => Pr(A and B) = Pr(A) + Pr(B) - Pr(A U B).

Now, let's analyze the options:

a) 0.4: This value is not possible since probabilities cannot exceed 1.

b) 0.2: This value is possible depending on the values of Pr(A) and Pr(B) and their overlap.

c) 0.6: This value is not possible since probabilities cannot exceed 1.

d) 0.9: This value is not possible since probabilities cannot exceed 1.

e) 0.5: This value is possible depending on the values of Pr(A) and Pr(B) and their overlap.

Therefore, the mathematically possible value of Pr(A U B) is b) 0.2.

For the second question, we need to find the mathematically possible value of Pr(A and B), which represents the probability of both event A and event B occurring.

Again, using the formula Pr(A U B) = Pr(A) + Pr(B) - Pr(A and B), we can rearrange it to solve for Pr(A and B): Pr(A and B) = Pr(A) + Pr(B) - Pr(A U B).

Analyzing the options:

a) 0: This value is possible if events A and B are mutually exclusive, meaning they cannot occur together.

b) 0.2: This value is possible depending on the values of Pr(A), Pr(B), and their overlap.

c) 0.6: This value is not possible since probabilities cannot exceed 1.

d) 0.8: This value is possible depending on the values of Pr(A), Pr(B), and their overlap.

e) 0.5: This value is possible depending on the values of Pr(A), Pr(B), and their overlap.

Therefore, the mathematically possible value of Pr(A and B) is either a) 0, b) 0.2, d) 0.8, or e) 0.5, depending on the specific probabilities of events A and B and their overlap.

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Answer:

Which number is missing?

40   38   35   31   26   20   13   5

Pattern: ( -2, -3, -4, etc)

40 - 2 = 38

38 - 3 = 35

35 - 4 = 31

31 - 5 = 26

26 - 6 = 20

20 - 7 = 13

13 - 8 = 5

Step-by-step explanation:

You're welcome.

The domain on which the graph described as in the image is increasing is to be determined; (-4, ∞).

It follows from the task content that the domain for which the function described by the graph is increasing is to be determined.

Since the graph is a quadratic function which opens upward and whose minimum point is at; x = -4.

Also, since a graph of a function, f(x) is increasing when f'(x) > 0.

Therefore, by observation the graph is increasing on the domain defined by; (-4, ∞).

Put simply, the function is increasing in the Domain; x > -4.

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Probability that three of them were born in the same month is 8.8737104e-21.

Total students present in class = 25.

What is the probability such that three of them were born in the same month?

Numerous applications can be made of the mathematical computation of probability. Probability can be used, for instance, to forecast sales growth or to estimate the likelihood that a particular marketing strategy would be successful in attracting new clients. The probability of something happening can also be calculated using mathematical formulas.

The probability that an event will occur is determined by probability:

P(A) = f / N = favourable outcomes/ total number of outcomes.

Probability and odds are related, but probability determines what the odds are. Probability is required before calculating the likelihood of an event.

we have total 12 months in a year.

total sample space for 25 students = 12^25

3 studnets were born in same month

3 have to choose 1 month we have 12 ways. to choose.

22 have to choose remaining 11 months 22C11

P(A) = 12*22C11/12^25

= 8465184/12^25

=8.8737104e-21

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A general equation for the line with vector equation is expressed in the form ax + by + c = 0, where a, b, and c are constants. This is known as the standard form of a linear equation.

Here, x and y represent variables in a two-dimensional plane.To find the standard form of a linear equation, you need to follow the steps listed below:

1. Start by assuming a vector equation.

2. Convert the vector equation to a parametric equation.

3. Obtain the slope of the line from the parametric equation.

4. Use the slope and a given point to find the intercept.

5. Finally, write the standard form by replacing the variables x and y with constants.

The standard form of a linear equation is the most general form that can be used to describe a line. A line that is vertical will have an undefined slope, and therefore, the equation cannot be written in slope-intercept form.

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Answer:x=\frac{b-1}{a-d}

Step-by-step explanation:

If Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits

Number of dog biscuits that Mandi has = 8 dog biscuits

Number of dog bowls that Mandi has =  7 dog bowls

Each dog bowl get the same number of dog biscuits.

To find the number of dog biscuits in each bowl we have to do the division

Number of dog biscuits in each bowl = Number of dog biscuits that Mandi has ÷ Number of dog bowls that Mandi has

Substitute the values in the equation

= 8/7

= 1.14 biscuits

Hence, if Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits

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Step-by-step explanation:

x1 y1 = -3,-3

x2 y2= 4,-3

now using slope formula(m),

(m)= y2-y1

x2-x1

= -3+3

4+3

= 0

7

= 0

hope it helped !!!!!

Answer:

Simplifying

3x + 77 = 4x + 54

Reorder the terms:

77 + 3x = 4x + 54

Reorder the terms:

77 + 3x = 54 + 4x

Solving

77 + 3x = 54 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

77 + 3x + -4x = 54 + 4x + -4x

Combine like terms: 3x + -4x = -1x

77 + -1x = 54 + 4x + -4x

Combine like terms: 4x + -4x = 0

77 + -1x = 54 + 0

77 + -1x = 54

Add '-77' to each side of the equation.

77 + -77 + -1x = 54 + -77

Combine like terms: 77 + -77 = 0

0 + -1x = 54 + -77

-1x = 54 + -77

Combine like terms: 54 + -77 = -23

-1x = -23

Divide each side by '-1'.

x = 23

Simplifying

x = 23

Step-by-step explanation:

I hope its helps

Answer:

5(x-2)-(X+3)=x-8

5x-10-x-3=x-8

4x-13=x-8

4x-x=(-8)+13

3x=5

X=5/3

hope you like the answer

please mark the answer as brainliest

Answer:

-5

Step-by-step explanation:

Hello! :)

To solve your equation, we will first simplify both sides of the equation

-7 = -1 + x/3

-7 = -1 + 1/3x

-7 = 1/3x - 1

Next, we will flip the equation

1/3x - 1 = -7

Third, we will add 1 to both sides

1/3x - 1 + 1 = -7 + 1

1/3x = -6

Last, we will Multiply both sides by 3

3 * (1/3x) = (3) * (-6)

x = -18 (ANSWER)

That means -18 is you answer

Hope this helped you!

THEDIPER

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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Answer:

c

Step-by-step explanation:

The expression for the radius of the cylinder is r = 2x units

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be represented as V

Now , the value of V is

V = 4πx³ units

where the height of the cylinder is h = x units

So , the Volume of Cylinder = πr²h

On simplifying , we get

4πx³ = πr²h

Substituting for h , we get

4πx³ = πr² ( x )

Divide by πx on both sides , we get

r² = 4x²

Taking square roots on both sides , we get

r = 2x units

Therefore , the value of r is 2x units

Hence , the radius of the cylinder is 2x units

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Answer:

x=4

Step-by-step explanation:

5(2x-3)-(x+8)=13

10x-15-x-8=13

9x-23=13

9x=36

x=4

Answer:

Step-by-step explanation:

x= -90 degrees

Answer:

x = 10√2

Step-by-step explanation:

Taking the cosine value of the given angle :

The number of years that the deposit was held for is 3 years.

From the information, Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. and he received $360 as interest at the end of the tenure.

It should be noted that simple interest is Illustrated as:

I = PRT

Therefore, T = Interest / Principal × Rate

Time = 360 / (2000 × 6%)

Time = 360 / 120

Time = 3 years

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▹ Answer

y = 15, -15

▹ Step-by-Step Explanation

This is considered a 'square root' since we have to find y^2.

15 * 15 = 225

-15 * -15 = 225

Both of these values work for y, so the answer is 15, -15.

Hope this helps!

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Answer:

time to cry

Step-by-step explanation:

The statement "(X, T) is Hausdorff but not connected" is false. In the given set X = {1, 2, 3, 4, 5} and the topology T defined as T = {∅, X, {1}, {1, 4}, {1, 5}, {1, 4, 5}}, it can be observed that X with this topology is not Hausdorff.  

This is because there exist points in X that cannot be separated by disjoint open sets. For example, the points 4 and 5 cannot be separated by disjoint open sets since any open set containing 4 also contains 5, and vice versa.

Furthermore, X with the given topology T is also not connected. It can be partitioned into two non-empty disjoint open sets, namely {1} and {2, 3, 4, 5}, which demonstrates that X is not a connected space.

Therefore, the correct statement is neither "(X, T) is Hausdorff but not connected" nor "(X, T) is connected and Hausdorff"

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DCM, this is the solution:

According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.

Therefore,

KJ = 2 * GH

KJ = 2 * 30

KJ = 60 and FJ = 30

JL = 2 * FG

JL = 2 * 37

JL = 74

Answer:

$558.88

Step-by-step explanation:

Answer:

Rs. 6300

Step-by-step explanation:

Given that:

Land area = 63m²

Rate of paving brick = RS. 100 per m²

Hence, to pave bring on a 63m² land area ;

Total cost of paving brick will be :

Cost per m² * land area

Rs. 100 * 63

= Rs. 6300

Answer:

Step-by-step explanation:

\( {2x}^{4} = 50 \\ = > {x}^{4} = \frac{50}{2} \\ = > {x}^{4} = 25 \\ = > {x}^{4} - 25 = 0 \\ = > ( {x}^{2} + 5)( {x}^{2} - 5) = 0 \\ = > {x}^{2} - 5 = 0 \\ > (x - 5)(x + 5) = 0 \\ = > x = 5 \: \: and \: \: - 5\)

Answer:

5, -5

Hope it helps.

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