please help me im struggling in math

The volume of air supplied to the plant is 105.12 times the ultimate BOD.

Given the BOD5 as 67.5% of ultimate BOD and ultimate BOD as BODu.

So BOD5 = 0.675 BODu.

Here, it is assumed that the BOD of the waste is completely degraded.

Now, oxygen demand, L per day = [0.68 BODu (kg/day)] / [(kg/m3 ) (kg O2/kg BOD)]

= (0.68 BODu)/ 2

= 0.34 BODu.

The weight of air required for oxygen demand is given by:

Weight of air = L/day x 24 hr/day x 1.3 kg air/kg O2

= 0.34 BODu x 24 x 1.3

= 10.512 BODu.

Now, oxygen transfer efficiency is 10%.

Hence, the volume of air required is given by:

Air supply = Weight of air / Oxygen transfer efficiency

= 10.512 BODu/ 0.1

= 105.12 BODu.

Therefore, the volume of air supplied to the plant is 105.12 times the ultimate BOD.

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Answer:

SAS

Step-by-step explanation:

pretty sure since the angle z is connected to both right triangles the sides become congruent.

The most general real-valued solution to the given linear system of differential equations is a combination of exponential terms involving eigenvalues and eigenvectors of the matrices A and B.

To find the most general real-valued solution to the linear system of differential equations:

x⃗ ′ = [12 − 25]x⃗

x→′ = [1 − 225]x→

Let's denote the matrix [12 − 25] as A and the matrix [1 − 225] as B. The system of differential equations can be written as:

x⃗ ′ = Ax⃗

x→′ = Bx→

To find the general solution, we need to solve the system of differential equations. Let's start with the first equation:

x⃗ ′ = Ax⃗

We can solve this equation by finding the eigenvalues and eigenvectors of matrix A. The eigenvalues, λ, are the solutions to the characteristic equation:

det(A - λI) = 0

where I is the identity matrix.

Solving this equation will give us the eigenvalues λ1 and λ2.

Once we have the eigenvalues, we can find the corresponding eigenvectors, v1 and v2.

The general solution for the first equation is then given by:

x⃗ = c1 * e^(λ1t) * v1 + c2 * e^(λ2t) * v2

where c1 and c2 are constants.

Now, let's move on to the second equation:

x→′ = Bx→

Similarly, we find the eigenvalues μ1 and μ2 of matrix B and the corresponding eigenvectors w1 and w2.

The general solution for the second equation is:

x→ = k1 * e^(μ1t) * w1 + k2 * e^(μ2t) * w2

where k1 and k2 are constants.

Combining the solutions for both equations, the most general real-valued solution to the given linear system of differential equations is:

x⃗ = c1 * e^(λ1t) * v1 + c2 * e^(λ2t) * v2

x→ = k1 * e^(μ1t) * w1 + k2 * e^(μ2t) * w2

where c1, c2, k1, and k2 are constants, and λ1, λ2, v1, v2, μ1, μ2, w1, and w2 are determined by the eigenvalue-eigenvector analysis of matrices A and B, respectively.

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Given,

Side = 7 cm

We know that,

Volume of a cube = side³

So, volume of Harry's cube

= (7 cm)³

= 343 cm³

Hi, here's a quick explanation;

if the given length is 7, and your object is a cube,

you'd cube 7,

which is =  7³

aka:   7 × 7 × 7

therefore,

Hope this helps you out!!    :D

Answer:

40%

Step-by-step explanation:

20-15 = 5, 2 students passed and did the assignment, 0.4 = 40%

Answer:

17=x

Step-by-step explanation:

In this case, we need to use Vertical Angles Theorem to solve this problem. Basically, because of the position of the angles, they are congruent.

68-x = 3x

Add x to both sides

68=4x

Divide by 4

17=x

Hope this helps!

Answer:

The value of 'x' is: 17°

Step-by-step explanation:

From what is being shown, there are two angles that are given:

(68 - x)°

3x°

Since they are congruent angles, meaning they are equal to each other, they will be put into a(n) equation such like shown below:

(68 - x)° = 3x°

(Then remove the parenthesis)

68° - x° = 3x°

     + x°=+3x°

------------------

68° = 4x°

------------------

(Divide both sides by 4)

\(\frac{68}{4} = \frac{4x}{4}\)

------------------

17° = x

------------------

Your value of 'x' is 17.

1. A∪B = {b, c, d, e, f, g}

A∩B = {d, f, g}

2. B' = { a, b, h , l)

From the information given, we have that:

A∪B = {The sum of sets in A and B without repetition}

Then we have:

A∪B = {b, c, d, e, f, g}

A∩B = {Sets found in both A and B}

Then, we have:

A∩B = {d, f, g}

2. B' = { sets found in the universal set and not in B}

We have:

B' = { a, b, h , l)

Thus, we can see that union and intersection of sets give different subsets from the two original sets.

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Answer:

\(0.625kg\)

Step-by-step explanation:

we are given half-life of PO-210 and the initial mass

we want to figure out the remaining mass after 420 days

in order to solve so we can consider the half-life formula given by

\( \displaystyle f(t) = a {0.5}^{t/T} \)

where:

since it halves every 140 days our T is 140 and t is 420. as the initial mass of the sample is 5 our a is 5

thus substitute:

\(\displaystyle f(420)=5\cdot{0.5}^{420/140}\)

reduce fraction:

\(\displaystyle f(420)=5\cdot{0.5}^{3}\)

By using calculator we acquire:

\(\displaystyle f(420)=0.625\)

hence, the remaining sample after 420 days is 0.625 kg

The albedo (a)in this case is approximately 0.4231.

To compute the albedo (a), we need to understand the terms given.

Albedo is the measure of reflectivity of a surface, expressed as the ratio of the reflected solar radiation (st) to the incoming solar radiation (51).

Here, 51 = 650 W/m² represents the total solar radiation, and st = 275 W/m² represents the reflected solar radiation.

Additionally, L1 = 94 W/m² and L1 = 395 W/m² seem to be irrelevant to the calculation of albedo, as they don't represent incoming or reflected solar radiation.

Therefore, we can disregard these terms for this calculation.

Now, we can calculate the albedo (a) using the formula:

a = (reflected solar radiation) / (incoming solar radiation) a = (st) / (51)

By substituting the given values:

a = (275 W/m²) / (650 W/m²) a ≈ 0.4231

Remember, albedo values range from 0 to 1, where 0 indicates no reflectivity and 1 indicates total reflectivity.

In this case, just provide the numerical value as the answer: 0.4231

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Answer:

\(a_n=-\frac{9}{4} +\frac{1}{4} *n; \ a_{45}=9.\)

Step-by-step explanation:

1. the difference between two sequent term is: 2- 7/4=7/4 - 3/2 = 3/2 - 5/4=... = 1/4.

2. using the value of the calculated difference it is possible to make up the formula of the given sequence ('n' - the number of term):

\(a_n=-\frac{9}{4}+\frac{1}{4} n.\)

3. for n=45:

\(a_{45}=-\frac{9}{4}+45*\frac{1}{4}=9.\)

The equation that relates M to R is M = 13 - R

From the question, we have the following parameters:

The total number of new magazines is the sum of the number of magazines read and the number of magazines left

This is represented as

Total number of new magazines = Number of magazines read + Number of magazines left

Substitute the known values in the above equation

13 = R +M

Make M the subject

M = 13 - R

Hence, the equation is M = 13 - R

See attachment for the graph

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Answer:

They sold 17 purses

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

For F  - Median For Class 1 is 52.5 Median for Class 2 is 75 ( False )

For G - Range for class 2 is 75 Range for class 1 is 45.9 ( False )

For H - IQR for class 1 is 30.45 IQR for class 2 is 60 ( True )

For J - Minimum for Class 2 is 30 Minimum for Class 1 is 30 ( False )

The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²

After folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.

An equilateral triangle is a type of triangle where by all the three sides are equal.

To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.

Using the formula for the area of an equilateral triangle,

A = √¾ a²

a= 12 inches

A = √¾ ×12²

A = 62.35 inches ²

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Answer:

Its 78!!!!

Solution:

1/2(12 * 18 - 5 * 12) = 78

Answer:

i dont know because u didnt give me how many numbers

Step-by-step explanation:

nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine

Step-by-step explanation:

we know that

The Power of a Power Property , states that :To find a power of a power, multiply the exponents

so

In this problem we have

Remember that

Raise to the third power

Applying the power of power property

therefore

nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine

Answer:

You’re already a hero!

Helping others is the best! We’re sure you can give a great answer.

Step-by-step explanation:

Answer: x = \(\frac{ \sqrt{7}-5}{2}\)

              x = \(\frac{ -\sqrt{7}-5}{2}\)

Step-by-step explanation:

\((2x + 5)^{2} - 7 = 0\)

Add 7 to both sides of the equation.

\((2x + 5)^{2} - 7 + 7= 0 + 7\)

Subtracting 7 from itself leaves 0.

\((2x + 5)x^{2} =7\)

Take the square root of both sides of the equation.

\(2x + 5 = \sqrt{7} \\2x + 5 = -\sqrt{7}\)

Subtract 5 from both sides of the equation.

\(2x + 5 - 5 = \sqrt{7} - 5 \\2x + 5 - 5 = - \sqrt{7} - 5\)

Subtracting 5 from itself leaves 0.

\(2x = \sqrt{7} - 5 \\2x = - \sqrt{7} - 5\)

Subtract 5 from \(\sqrt{7}\).

\(2x = \sqrt{7} - 5\)

Subtract 5 from \(-\sqrt{7}\).

\(2x = -\sqrt{7} - 5\)

Divide both sides by 2.

\(\frac{2x}{2} =\frac{ \sqrt{7}-5}{2} \\\frac{2x}{2} =\frac{- \sqrt{7}-5}{2}\)

Dividing by 2 undoes the multiplication by 2.

\(x=\frac{ \sqrt{7}-5}{2}\\x=\frac{ -\sqrt{7}-5}{2}\)

Answer:

x < -5

Step-by-step explanation:

-0.6x > 3

=> Dividing 0.6 on both sides

=> -x > 3/0.6

=> -x > 5

=> x < -5     [When we multiply -1 on both sides the sign changes]

The solution to the inequality -0.6x > 3 is x < -5.

To solve for x in the inequality -0.6x > 3, we need to isolate x on one side of the inequality.

First, to divide both sides of the inequality by -0.6 to remove the coefficient in front of x.

Remember that when dividing or multiplying both sides of an inequality by a negative number, we need to reverse the inequality sign.

So, dividing both sides by -0.6 gives

x < 3 / -0.6

Simplifying the right side of the inequality, we have:

x < -5

Therefore, the solution to the inequality -0.6x > 3 is x < -5.

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y=-5x+5...(1)

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

subt (1)into (2)

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

2x-5x-5=3

2x-5x=3+5

-3x=8

divide by -3

x=-8/3

subt 2 into 1

y=-5(-8/3)+5

y=55/3

Answer:

C = 7.72 ~ 7.7

Step-by-step explanation:

So when you solve this equetion you must 1st find x then c

we can find x by using cos(60)

cos(60) = x/14

x = cos(60) × 14

x = 1/2 ×14

x = 7

so after we find x we are going to solve c by using cos (25)

cos (25) = X/C = 7/c

cos(25) × C = 7

C = 7/cos (25)

C = 7.72 ~ 7.7

so the solution is 7.7

Suppose x and y are proportional. 3rd , 4th and 5th options are correct.

What is proportional in an equation?

Given that  x and y are proportional ,

then ,    x = my  for some constant m

       Δx = Δ (my)   ⇒ m Δy

∴ 3rd option is correct .

          x = my

          y = 1/m x ⇒ kx

∴ 4th option is correct.

the points ( 0,0) satisfies x = my

the point ( 0, 0 ) is on the graph of y in terms of x .

∴ 5th option is correct .

  y = kx

Δy = Δ ( kx)  ⇒ k Δx

∴ 1st option is not true .

y = 2x also implies x and y are proportional .

∴ 2nd  option is not true .

∵ 3rd , 4th and 5th options are correct.

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The complete question is -

Suppose x and y are proportional. Which of the following statements are true? Select all that apply. Ay = kx, where k is constant Oy=3 D Ax = mAy, where m is constant Oy kä, where k is constant The point(0, 0) is on the graph of y in terms of

The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.

a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.

b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.

Using Euler's method with two steps of equal size, we can approximate f(1) as follows:

f(0.5) = f(0) + (1/2)dy/dx|t=0

= 8 - (1/2)(1/6)*8

= 7.333...

f(1) = f(0.5) + (1/2)dy/dx|t=0.5

= 7.333... - (1/2)(7.333.../8)*(6-7.333...)

= 6.636...

Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.

c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.

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Answer:

B. 171.74 cm²

Step-by-step explanation:

Area of a sector = \( \frac{\theta}{360} \times \pi r^2 \).

Where,

\( \theta = 260 \)

radius (r) = 8.7 cm

Plug in the values into the formula

Area of sector = \( \frac{260}{360} \times \pi 8.7^2 \)

Area of sector = \( \frac{260 \times \pi 75.69}{360} \)

Area of sector = 171.74 cm² (approximated)

Answer:

B. 171.69 cm²

Step-by-step explanation:

Answer:

NO is answer I believe if you rotate the figure such that the similar sides IJ and MN are on top.

Step-by-step explanation:

Exact value of the definite integral is 320. Comparing the results: Exact value of the definite integral = 320, Trapezoidal Rule approximation (n = 4) = 340, Simpson's Rule approximation (n = 4) ≈ 246.6667.

What is trapezoid?

A trapezoid is a quadrilateral (a polygon with four sides) that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs.

To approximate the value of the definite integral ∫[0, 4] 5x * x^2 dx using the Trapezoidal Rule and Simpson's Rule, we need to specify the value of n, which represents the number of subintervals.

Let's calculate the approximations using n = 4 for both methods:

Trapezoidal Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using the Trapezoidal Rule is given by:

\(T_4 = (h/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)]\)

Plugging in the values:

\(T_4 = (1/2) * [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]\\\\= (1/2) * [5(0)(0^2) + 2(5)(1)(1^2) + 2(5)(2)(2^2) + 2(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/2) * [0 + 10 + 80 + 270 + 320]\\\\= (1/2) * 680\\\\= 340\)

Simpson's Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using Simpson's Rule is given by:

\(S_4 = (h/3) * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4)]\)

Plugging in the values:

\(S_4 = (1/3) * [f(0) + 4f(1) + 2f(2) + 4f(3) + f(4)]\\\\= (1/3) * [5(0)(0^2) + 4(5)(1)(1^2) + 2(5)(2)(2^2) + 4(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/3) * [0 + 20 + 40 + 360 + 320]\\\\= (1/3) * 740\\\\= 246.6667\)

Exact value of the definite integral:

∫[0, 4] 5x * \(x^2\) dx = [(5/4) * \(x^4\)] evaluated from 0 to 4

\(= (5/4) * 4^4 - (5/4) * 0^4\\\\= (5/4) * 256 - (5/4) * 0\\\\= 320 - 0\\\\= 320\)

Comparing the results:

Exact value of the definite integral = 320

Trapezoidal Rule approximation (n = 4) = 340

Simpson's Rule approximation (n = 4) ≈ 246.6667

As we can see, the Trapezoidal Rule approximation is slightly greater than the exact value, while Simpson's Rule approximation is less than the exact value.

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Without additional information, it is not possible to say whether Suan's sample of 145 math problems is likely to be biased or not.

It is difficult to say whether this sample of math problems is likely to be biased without more information. A sample is considered biased if it is not representative of the larger population from which it was taken.

In this case, we do not know how many math books there are in the library or how many math problems each book contains. If there are only a few books in the library, then a sample of 145 problems is likely to be biased as it may not accurately reflect the range of difficulty levels in the library as a whole.

On the other hand, if there are many books in the library, a sample of 145 problems may be representative of the larger population and not biased.

Therefore, without additional information, it is not possible to say whether Suan's sample of 145 math problems is likely to be biased or not.

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--The given question is incomplete; the complete question is

"Suan did 145 random math problems from each math book in her library. Each math book in the library has an equal number of problems. Is this sample of the math problem in the library likely to be biased?"--

2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.

The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.

The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.

\((Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}\)

                        \((2.5)^{2}+(6)^{2}=(6.5)^{2}\)

                            6.25 + 36 = 42.25

                                  42.25 = 42.25

The sides offered satisfy the specifications for a right triangle.

Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.

Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.

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