In the figure, AE and BD intersect at C.
Prove that a + b = d + e.​

The formula for the area of a regular octagon in proportion to its Apothem, which in this case is 18, is used to arrive at the following result. As a result, the area of the Octagon provided is 1,446.

An apothem is  a line from the center of a regular polygon at right angles to any of its sides.

This shape's computation utilizing solely its apothem features several curved bends. To calculate the area, we first divide the octagon into triangles.

We may get the area of the Octagon by multiplying the area of the triangles by the total number.

As a result, the area of the Octagon (A) = (1/2b*h)n.

Where b is the base

          height = h

          n is the number of triangles.

Remember that the total angle in a circle is 360°, thus if all the triangles are equal, we must divide 360° by 8 triangles to find the angle in each triangle's vertex.

Thus, 360°/8 = 45°

As a result, we obtain the angle of our triangle opposite the base.

Remember that the triangle is divided in two such that each triangle is a right-angled triangle.

As a result, for each right angle triangle, the angle opposite the base is given as:

45°/2 = 22.5°

So we use the rule of tangents to calculate the length of the opposite side (x):

That is to say:

x = 18 Tan 22.5°

= 18 * 0.55785173935

≈ 10.04

As a result, if x equals 10.04, the area of that triangle is

= 1/2 * 10.04 * 18 (which is 1/2bh)

= 90.3792

We may deduce from the foregoing that the Area of the triangle with the Apothem is

= 90.3792 * 2

= 180.74

Recall our formula for finding the area of the octagon:

A = (1/2bh)n

A = (108.74) *8

A = 1,445.95

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To find the area of the regular octagon with center O, divide it into smaller shapes, calculate their areas, and sum them up: (8 * side length^2) + (2 * side length^2 * √2) ≈ 11.3 * side length^2 (rounded to the nearest tenth).

To find the area of a regular octagon with center O, you can divide it into smaller shapes and then sum up their areas.

A regular octagon can be divided into eight congruent isosceles triangles and a square at the center.

Let's assume the side length of the octagon is "s."

Each of the eight isosceles triangles has two equal sides, which are also radii of the octagon, and one base.

The angle between these two radii is 45 degrees because there are 360 degrees in an octagon, and each interior angle of a regular octagon is 135 degrees (360°/8).

This makes each of the two equal angles in the isosceles triangle 67.5 degrees (half of 135 degrees).

You can find the area of one of these isosceles triangles using the formula for the area of a triangle:

Area = (1/2) * base * height

The base is "s," and the height can be calculated using trigonometry:

height = s * sin(67.5 degrees)

Now, you can find the area of one isosceles triangle:

Area of one triangle = (1/2) * s * s * sin(67.5 degrees)

There are eight such triangles in the octagon, so the total area contributed by the triangles is:

Total area of triangles = 8 * (1/2) * s * s * sin(67.5 degrees)

Next, you need to find the area of the square at the center.

The diagonals of this square are equal to the sides of the octagon (s).

The area of the square is:

Area of square = s * s

Now, add the areas of the triangles and the square to find the total area of the octagon:

Total area of octagon = Total area of triangles + Area of square

Total area of octagon = 8 * (1/2) * s * s * sin(67.5 degrees) + s * s.

Now, you can calculate the area of the octagon by plugging in the values:

Total area = 8 * (1/2) * s^2 * sin(67.5 degrees) + s^2

Using the value of sin(67.5 degrees) ≈ 0.9239 (rounded to four decimal places):

Total area ≈ 8 * (1/2) * s^2 * 0.9239 + s^2

Simplify:

Total area ≈ 4 * s^2 * 0.9239 + s^2

Total area ≈ 3.6956s^2 + s^2

Total area ≈ 4.6956s^2

Now, you can round this to the nearest tenth if necessary.

The area of the regular octagon with side length "s" is approximately 4.7s^2 square units.

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10220 meters Juanita swim in those 2 weeks.

Given that,

Juanita practiced her swimming for a competition by swimming 0.73 kilometers in the pool every day for two weeks.

We have to find Juanita swam how many meters in those two weeks? 1 km = 1,000 m

First, we multiply the number of days swam by the amount of kilometers swan each day.

0.73×2 week

0.73×14days

10.22

The kilometers are then multiplied by the conversion rate to convert them to meters.

10.22 kilometers multiplied by a 1000 m to m conversion factor results in 10220 m.

Therefore, 10220 meters Juanita swim in those 2 weeks.

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The wingspan height is 12 feet.

The correct option is (D)

In general, the term "proportion" refers to a part, share, or amount that is compared to a total. According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Height of plane= 20 feet

Wingspan height= 16 feet.

Model height= 15 feet

Model wingspan height= x

Now, using proportion

20/16 = 15/x

20x= 16 x 15

20x= 240

x= 240/20

x= 12 feet.

Hence, the wingspan height is 12 feet.

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The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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The point (-3, -1) satisfies the parametric equations x = 2t, y = 8t^2 + 10t - 3 and lies on the plane curve defined by these equations. The other points (2,1), (1,2), and (-1,3) do not satisfy the equations and do not lie on the curve.

Among the given options, the point (-3, -1) is the only one that lies on the plane curve defined by the parametric equations x = 2t, y = 8t^2 + 10t - 3.

To determine if a point is on the plane curve, we substitute the x and y values of the point into the parametric equations and check if they satisfy the equations.

For the point (-3, -1), substituting x = -3 and y = -1 into the parametric equations:

-3 = 2t

-1 = 8t^2 + 10t - 3

Solving the first equation gives t = -3/2, and substituting it into the second equation gives -1 = 8(-3/2)^2 + 10(-3/2) - 3. Simplifying the equation, we get -1 = 9 + (-15) - 3, which is true.

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Answer:

15.60

Step-by-step explanation:

23.31/18=1.30 (for one gallon)

1.30*12=15.60 (for twelve gallons)

Answer:

$15.54

Step-by-step explanation:

Divide $23.31 by 18 to find the cost of 1 gallon, then multiply this by 12.

$23.31 ÷ 18 = $1.295 , then

12 gallons costs = 12 × $1.295 = $15.54

Answer:

r = 5 units

Step-by-step explanation:

One way is to use the Pythag Theroem

12 ^2 + r^2 = (8+r)^2

144 + r^2 = 64 + 16r + r^2

80 = 16 r      r = 5

Answer:

c because I did this one an yeah

Answer:

Mr Bean will get 1000 naira.

Step-by-step explanation:

They invested in the ratio of 5:3:2 , meaning that Mr Bean will get half the profit. 1/2 X 2000 = 1000

Answer:
The statement "The number 4 is D ∩ (E ∩ F)" is true.

Step-by-step explanation:

Firstly, let's find E ∩ F:

E = {1, 4, 9}

F = {2, 4, 6, 8}

E ∩ F = {4}

Now we can find D ∩ (E ∩ F):

D = {..., -2, -1, 0, 1, 2, 3, 4, 5, 6, ...}

D ∩ (E ∩ F) = {4}

Therefore, the statement is true.

The statement "D ∩ F is {4, 6}" is false.

Let's find D ∩ F:

D = {..., -2, -1, 0, 1, 2, 3, 4, 5, 6, ...}

F = {2, 4, 6, 8}

D ∩ F = {2, 4, 6}

Therefore, the statement is false.

Answer:

its 12.03

have a great dayy

Answer:

12:40

hope this will help you have a great day

When you develop an argument with a major premise, a minor premise, and a conclusion, you are using deductive reasoning. When constructing an argument using deductive reasoning, three components are involved: a major premise, a minor premise, and a conclusion.

Deductive reasoning is a logical process where the conclusion is derived from the major and minor premises. The major premise is a general statement or principle that establishes a broad context or rule.

The minor premise is a specific statement or evidence that relates to the major premise. Finally, the conclusion is the logical inference or outcome that follows from the combination of the major and minor premises.

Deductive reasoning allows for the logical progression from general principles to specific conclusions, making it a valuable tool in fields such as mathematics, logic, and philosophy.

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Answer:

The vertex is (3,4)

Step-by-step explanation:

f (x) = x^2 - 6 x + 13

Completing the square

-6/2 = -3 and squaring it = 9

    = x^2 -6x +9 +4

   = ( x-3) ^2 +4

The equation is now in vertex form

a( x-h) ^2 +k

where the vertex is ( h,k)

The vertex is (3,4)

Answer:

C on edge

Step-by-step explanation:

Final Answer: \(y = \frac{1}{3}x + 4\)

Steps/Reasons/Explanation:

There are two methods of solving this problem. Slope-intercept form and Point-slope form. I will be using the Slope-intercept form to solve this problem.

Step 1: Substitute slope from the original line (\(\frac{1}{3}\) in this case) into the slope-intercept equation.

\(y = \frac{1}{3}x + b\)

Step 2: Substitute the given point \((-3, 3)\) into the x and y values.

\(y = \frac{1}{3}x + b\)

\(3 = \frac{1}{3}(-3) + b\)

Step 3: Solve for b (the y-intercept).

\(3 = \frac{1}{3}(-3) + b\)

\(3 = -1 + b\)

\(+1\) = \(+1\) \(+\) \(b\)

\(4 = b\)

Step 4: Substitute this value for b in the slope-intercept form equation.

\(y = \frac{1}{3}x + 4\)

~I hope I helped you :)~

Answer:

y = 1/3x + 5

Step-by-step explanation:

(-3, 3)

x  ,  y

x1 = -3

y1 = 3

The formula we will use is y - y1 = m ( x - x1)

We will now replace y1 and x1 with the coordinate points (-3, 3).

We will keep x1 = -3, and y1 = 3.

then you will plug in the numbers giving you an equation like:

y - (3) = 1/3 (x -(-3))

y - 3 = 1/3 (x + 3)

y - 3 = 1/3x +1

  + 3          + 3

y = 1/3x + 4

I am 100% sure I am correct.

If you want free answers to your questions you can use math

way, which is  a free website

It gives you FREE answers to math problems and they are always reliable.

I always use it to check my answers as I did with this problem too you may go there to check my answer if you would like just type in y = 1/3x + 5 , (-3, 3)

then when options pop up select parallel, because you want to solve for a parallel line.

I hope I helped you a lot and my answer is correct.

Please mark me as brainliest and have a good day!

The 5 cm distance of the point of intersection from the plane and the angles of 45° and 30° formed by the lines and the plane give the distance between the points of intersection of the lines and the plane as approximately 13.66 centimeters

A point of intersection is the point where two figures meet (intersect).

The distance between the point of intersection of the line and the plane = 5 cm

The angles formed by the lines and the plane = 45° and 30°

The distance between the point of intersection of the lines and the plane is found by taking the figure formed by the two lines and the line joining their points of intersection with the plane as a triangle that has an altitude of 5 cm.

The distance, d, between the points of intersection of the lines and the plane is found using the trigonometric ratio for tangent as follows;

\(tan(\theta) = \dfrac{Opposite \, side}{Adjacent \, side}\)

Therefore;

\(d = \dfrac{5}{tan(45^{\circ}) } +\dfrac{5}{tan(30^{\circ})} = 5 + 5\cdot \sqrt{3}\)

The distance between the points, d = (5 + 5·√3) cm ≈ 13.66 cm

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Answer:

Step-by-step explanation:

Area of rhombus = (small diagonal · big diagonal)/2

small diagonal = AH +AH = 6+6 = 12

big diagonal = BH +BH = 10+10 = 20

Area of rhombus = (12·20)/2 = 120 units²

Answer:

The answer is x=14

Step-by-step explanation:

8=5x-34-2x

8=3x-34

8+34=3x

42=3x

42/3=x

14=x

x=14

Answer: 42=3x divide 3 to 42= 14

Step-by-step explanation: ANSWER IS 14=X

a. The test could be conducted on the mean of one sample or two samples of observations.

The statement "The test could be conducted on the mean of one sample or two samples of observations" is not related to statistics associated with cross-tabulation.

Cross-tabulation, also known as a contingency table or a crosstab, is a statistical technique used to analyze the relationship between two categorical variables. It is commonly used to examine the association between two variables and determine if there is a significant relationship between them.

Options (b), (c), and (d) are all related to statistics associated with cross-tabulation. The chi-square statistic is commonly used to measure the statistical significance of the observed association. The statement in option (c) correctly highlights that the strength of association is of interest only if it is statistically significant. Option (d) mentions several measures that can be used to quantify the strength of association in cross-tabulation, including the phi correlation coefficient, the contingency coefficient, Cramer's V, and the lambda coefficient.

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The results of given question's parts based on hypothesis testing.

a) Null and Alternative hypothesis

H₀ : p = 0.8

H₀ : p = 0.8 Hₐ : p < 0.8

b) test statistic (z value ) is Z = -2.25.

c) P- value ( Z꜀ ) is - 1.64

d) Rejected the null hypothesis.

We have given that

Sample size, n = 900

Hypothesis population proportion, p₀ = 0.80

Sample proportion , p-hat = 0.77

favourable cases, X = 693

significance level, α = 0.05

a) The following null and alternative hypothesis for population proportion needs to be tested :

H₀ : p = 0.8

Hₐ : p < 0.8

This is corresponding to a left tailed test for a z test for one population will used .

c) we have given that, Significance level is α=0.05 and the critical value for a left tailed test is Z꜀ = - 1.64

so, the rejection region for left tailed test R = { Z Z<- 1.64 }

b) Z- statistic value :

Z = (p-hat - p₀)/√p₀(1-p₀)/n

=> Z = ( 0.77 - 0.8 )/√0.8×0.2/900

=> Z = -2.25

d) Decision about Null hypothesis,

Since, it is observed that Z = - 2.25 < Z꜀ = - 1.645 it is then concluded that the null hypothesis is rejected. Reject the null hypothesis. There is not enough evidence to conclude that the percentage of infants who receive immunization s is less than 80%.

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Answer: Since this is the right triangle so

\(Sin B = \frac{AC}{AB} =\frac{AC}{6} \\=> AC = sin(20) * 6 = 5.478 = 5.48\)

Apply Pythagorean theorem:

\(AC^{2} +CB^{2} =AB^{2} \\5.48^{2} +CB^{2} =6^{2}\)

\(CB = \sqrt{6^{2} -5.48^{2} } = 2.44\)

The answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

A combination of numbers, variables, and operators that represents a quantity or mathematical relationship is called an expression.

First, divide sextillion (10²¹) by nonmillion (10⁶) to get 10¹⁵.

Next, multiply 10¹⁵ by 10,000 to get 10¹⁹.

Subtract 200 million (2 x 10⁸) from 10¹⁹ to get 9.9998 x 10¹⁸.

Finally, add 5,000 to get the result of approximately 9.9998 x 10¹⁸ + 5,000 = 9.9998 x 10¹⁸ + 0.0005 x 10¹⁸ = 9.9998 x 10¹⁸.

Therefore, the answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

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Answer:

The question is incomplete

We have to find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1.

To find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1, we have to integrate x^(1/2) and x^(1/3) with respect to x. That is, Area = ∫0¹ [x^(1/2) - x^(1/3)] dx= [2/3 x^(3/2) - 3/4 x^(4/3)] from 0 to 1= [2/3 (1)^(3/2) - 3/4 (1)^(4/3)] - [2/3 (0)^(3/2) - 3/4 (0)^(4/3)]= 0.2857 square units

Therefore, the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1 is 0.2857 square units. Note: The question  but the answer has been provided in the format requested.

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Step-by-step explanation:

Number of boxes that will fit =2340

Step-by-step explanation:

The shipping box volume can be calculated by the formula V = Lxwxh ,where L ,w ,h are length ,width and height of the box.

The length of the shipping box =3\frac{3}{4} =\frac{15}{4} ft.

Width = 3 ft.

Height =3\frac{1}{4} =\frac{13}{4} ft.

Volume of shipping box =\frac{15}{4} .3 .\frac{13}{4} =\frac{585}{16} = 36.6 ft.cubic ft.

Volume of shipping box can also be calculated by multiplying base area with the height of box.

Base area of box = \frac{15}{4} .3=\frac{45}{4} square ft.

Volume of box = base area x height =\frac{45}{4} .\frac{13}{4} = 36.6 cubic ft.

Volume of packing cubes =\frac{1}{4} .\frac{1}{4} .\frac{1}{4} =\frac{1}{64} cubic ft.

Number of fish boxes that will fit in the shipping box = volume of shipping box ÷ volume of fish food box = 36.6 ÷ \frac{1}{64} =2340 .

Answer:

2340

Step-by-step explanation:

Answer:

B. X = 2

Step-by-step explanation:

2(0)+7 = 7 --> 7<9 so no

* 2(2)+7 = 11 --> 9<11<15 so yes *

2(4)+7 = 15 --> 15 = 15 so no

2(6)+7 = 19 --> 19>15 so no

The molar composition of the product stream is: CO2: 68.65%, O2: 6.01%, and N2: 25.34%.

Given that a gas power plant combusts 600 kg of coal every hour in a continuous fluidized bed reactor that is at a steady state.

The composition of coal fed to the reactor is found to contain 89.20 wt% C, 7.10 wt% H, 2.60 wt% S, and the rest moisture.

Air is fed at 20% excess and that only 90.0% of the carbon undergoes complete combustion. The following are the answers to the questions that follow:

Calculate the air feed rate - The first step is to balance the combustion equation to find the theoretical amount of air required for complete combustion:

\(C + O2 → CO2CH4 + 2O2 → CO2 + 2H2OCO + (1/2)O2 → CO2C + (1/2)O2 → COH2 + (1/2)O2 → H2O2C + O2 → 2CO2S + O2 → SO2\)

From the equation, the theoretical air-fuel ratio (AFR) is calculated as shown below:

Carbon: AFR

1/0.8920 = 1.1214

Hydrogen: AFR

4/0.0710 = 56.3381

Sulphur: AFR

32/0.0260 = 1230.7692

The AFR that is greater is taken, which is 1230.7692. Now, calculate the actual amount of air required to achieve 90% carbon conversion:

0.9(0.8920/12) + (0.1/0.21)(0.21/0.79)(1.1214/32) = 0.063 kg/kg of coal

The actual air feed rate (AFR actual)

AFR × kg of coal combusted = 1230.7692 × 600

= 738461.54 kg/hour or 205.128 kg/s

The air feed rate is 205.128 kg/s or 738461.54 kg/hour.

Calculate the molar composition of the product stream

Carbon balance: C in coal fed = C in product stream

Carbon in coal fed:

0.892 × 600 kg = 535.2 kg/hour

Carbon in product stream

0.9 × 535.2 = 481.68 kg/hour

Carbon in unreacted coal = 535.2 − 481.68 = 53.52 kg/hour

Molar flow rate of CO2 = Carbon in product stream/ Molecular weight of CO2

= 481.68/(12.011 + 2 × 15.999) = 15.533 kmol/hour

Molar flow rate of O2:

Air feed rate × (21/100) × (1/32) = 205.128 × 0.21 × 0.03125 = 1.358 kmol/hour

Molar flow rate of N2:

Air feed rate × (79/100) × (1/28) = 205.128 × 0.79 × 0.03571 = 5.720 kmol/hour

Total molar flow rate:

15.533 + 1.358 + 5.720 = 22.611 kmol/hour

Composition of product stream: CO2: 15.533/22.611

0.6865 or 68.65%

O2: 1.358/22.611 = 0.0601 or 6.01%

N2: 5.720/22.611 = 0.2534 or 25.34%

Therefore, the molar composition of the product stream is: CO2: 68.65%, O2: 6.01%, and N2: 25.34%.

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The molar composition of the product stream is approximately:
- Carbon dioxide (CO2): 17.35%
- Water (H2O): 4.15%
- Sulfur dioxide (SO2): 0.19%
- Nitrogen (N2): 78.31%

To calculate the air feed rate, we need to determine the amount of air required for the complete combustion of carbon.

Calculate the moles of carbon in the coal:
  - The molecular weight of carbon (C) is 12 g/mol.
  - We know the weight percentage of carbon in the coal is 89.20 wt%.
  - Convert the weight percentage to mass: 600 kg * (89.20/100) = 534.72 kg of carbon.
  - Convert the mass of carbon to moles: 534.72 kg / 12 g/mol = 44.56 mol of carbon.

Calculate the stoichiometric amount of air required for complete combustion:
  - The balanced equation for the combustion of carbon is: C + O2 -> CO2.
  - From the balanced equation, we see that 1 mole of carbon requires 1 mole of oxygen (O2) for complete combustion.
  - Since air contains 21% oxygen, we can calculate the moles of air required: 44.56 mol * (1/0.21) = 212.17 mol of air.

Calculate the excess air:
  - We are given that air is fed at 20% excess. Excess air is the additional amount of air supplied beyond the stoichiometric requirement.
  - Calculate the excess air: 212.17 mol * (20/100) = 42.43 mol of excess air.
  - Total moles of air required: 212.17 mol + 42.43 mol = 254.60 mol.

Calculate the air feed rate:
  - We are given that the gas power plant combusts 600 kg of coal every hour.
  - The rate of coal combustion is equal to the rate of carbon combustion since only 90.0% of the carbon undergoes complete combustion.
  - Convert the rate of carbon combustion to moles: 44.56 mol/hour.
  - The air feed rate is the same as the moles of air required per hour: 254.60 mol/hour.

To calculate the molar composition of the product stream, we need to determine the moles of each component in the product stream.

Calculate the moles of carbon dioxide (CO2):
  - From the balanced equation, we know that 1 mole of carbon produces 1 mole of carbon dioxide.
  - The moles of carbon in the coal is 44.56 mol.
  - Therefore, the moles of carbon dioxide produced is also 44.56 mol.

Calculate the moles of water (H2O):
  - The weight percentage of hydrogen (H) in the coal is 7.10 wt%.
  - Convert the weight percentage to mass: 600 kg * (7.10/100) = 42.60 kg of hydrogen.
  - The molecular weight of water (H2O) is 18 g/mol.
  - Convert the mass of hydrogen to moles: 42.60 kg / 2 g/mol = 21.30 mol of hydrogen.
  - Since water contains 2 moles of hydrogen per mole of water, the moles of water produced is 21.30 mol / 2 = 10.65 mol.

Calculate the moles of sulfur dioxide (SO2):
  - The weight percentage of sulfur (S) in the coal is 2.60 wt%.
  - Convert the weight percentage to mass: 600 kg * (2.60/100) = 15.60 kg of sulfur.
  - The molecular weight of sulfur dioxide (SO2) is 64 g/mol.
  - Convert the mass of sulfur to moles: 15.60 kg / 32 g/mol = 0.4875 mol of sulfur.
  - Since sulfur dioxide contains 1 mole of sulfur per mole of sulfur dioxide, the moles of sulfur dioxide produced is 0.4875 mol.

Calculate the moles of nitrogen (N2):
  - Nitrogen is the remaining component in the air after combustion.
  - Since air contains 79% nitrogen, the moles of nitrogen is 79% of the moles of air: 254.60 mol * 0.79 = 201.03 mol.

Calculate the total moles in the product stream:
  - The total moles is the sum of the moles of carbon dioxide, water, sulfur dioxide, and nitrogen: 44.56 mol + 10.65 mol + 0.4875 mol + 201.03 mol = 256.72 mol.

Calculate the molar composition of the product stream:
  - The molar composition of each component is the moles of that component divided by the total moles, multiplied by 100 to get a percentage.
  - Carbon dioxide (CO2): (44.56 mol / 256.72 mol) * 100 = 17.35%
  - Water (H2O): (10.65 mol / 256.72 mol) * 100 = 4.15%
  - Sulfur dioxide (SO2): (0.4875 mol / 256.72 mol) * 100 = 0.19%
  - Nitrogen (N2): (201.03 mol / 256.72 mol) * 100 = 78.31%

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Answer:

Explanation:

There are three right angled triangles are in the diagram of three different sizes.

Identify the right angles.

In the first triangle, the right angle is angle M. In the second one, the right angle is angle K and in the third triangle, it is angle K.

Now, identify the shortest sides of each.

The shortest side in the first triangle is MJ, in the second triangle, it is JK and in the third triangle, it is MK.

In the given triangle JKM, notice that JK is the shortest side and angle K is the right angle. Write the other two tringles also in the similar form with the first two letters gives the short side and middle letter represents the right angle.

So, the similarity statement is

Answer:

sum of two even numbers will always be even. conjecture just means to make a generalization based on patterns