Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1

an = n​

Answer:

the two numbers are 10 and 12.

Step-by-step explanation:

Let’s assume that the two numbers are 5x and 6x respectively. Then we can write:

5x/6x = 5/6

Multiplying both sides by 6x gives:

5x = (5/6) * 6x = 5x - (5/6) * 8

Simplifying gives:

30x = 30x - 20

Therefore, x = 2.

So the two numbers are:

5x = 10

6x = 12

If we subtract 5 from each number, we get:

10 - 5 = 5

12 - 5 = 7

Therefore, the two numbers are 10 and 12.

I hope this helps! Let me know if you have any other questions.

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The mean number of correct answers that the student can expect to guess correctly is 9, and the variance of the number of correct answers is 7.2.

The mean and variance of this binomial distribution can be calculated using the formula:

where n is the number of trials, and p is the probability of success (i.e. guessing the correct answer) on each trial.

In this case, n = 45 (the number of questions) and p = 1/5 (the probability of guessing the correct answer on each question, assuming all choices are equally likely).

Thus, the mean is:

mean = n * p = 45 * (1/5) = 9

And the variance is:

variance = n * p * (1 - p) = 45 * (1/5) * (4/5) = 7.2

Therefore, the mean number of correct answers that the student can expect to guess correctly is 9, and the variance of the number of correct answers is 7.2.

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An inequality that is represented by this graph include the following: C. y ≤ (4 - x)/2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 3)/(2 + 2)

Slope (m) = -2/4

Slope (m) = -1/2.

At data point (2, 1) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -1/2(x - 2)

y = -x/2 + 1 + 1

y = -x/2 + 2

y ≤ (4 - x)/2 (since the solid line is shaded below)

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The circle's circumference is approximately 43.96 kilometers.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and d is the diameter of the circle.

Substituting the given value for the diameter (d = 14 kilometers) into the formula, we get:

C = 3.14 × 14 km

C = 43.96 km

Therefore, the circle's circumference is approximately 43.96 kilometers.

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The ideal way to organize electronically the raw data for a study is to create a structured database or spreadsheet that can easily and efficiently store, sort, and analyze the data.

This will allow for easy retrieval and manipulation of the data, as well as the ability to perform statistical analysis and generate reports. It is important to ensure that the data is accurately recorded and labeled to prevent errors and ensure consistency. Additionally, proper data security measures should be in place to protect the confidentiality and integrity of the data.

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The ideal way to organize electronically the raw data for a study is to use a standardized format, such as a spreadsheet or database, with clear and consistent labeling for each variable.

It is important to ensure that the data is accurate, complete, and easily accessible, and to maintain appropriate security and privacy measures to protect the confidentiality of study participants. Additionally, it is recommended to create a data management plan outlining the procedures for data collection, storage, and sharing throughout the study. This plan should be reviewed and updated regularly to ensure that it remains effective and compliant with relevant regulations and ethical standards. The ideal way to organize electronically the raw data for a study is to use a structured and systematic approach, such as creating a well-designed database or spreadsheet. This allows for efficient data management, easy access, and accurate analysis.

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Since Diego and Armando were known to have attended the Regional Congress of Indigenous Languages for Latin America as well as the Caribbean, and thus they were able to write the conclusion that is "If people respect differences and act with justice, then human beings will not harm others."

In terms of a) Symbolization:  we can make p to be the proposition that is "people respect differences", and also q to be the proposition that is "people act with justice", and lastly, r can act as the proposition "human beings harm others". Hence the conclusion will be: p ∧ q → ¬r.

In terms of question 2, the Translate situations:

a) The problem scenario is about the Regional Congress of Indigenous Languages that is made for Latin America and the Caribbean, and it is one that is aimed to set up responsible commitments for the promotion, safeguarding, etc.

b) The statement in the underlined text is one tht is said to be: "If people respect differences and act with justice, then human beings will not harm others."

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See text below

1. Analiza la situación.

En el mes de septiembre del ano 2019 se llevó a cabo, en el Cusco, el Congreso Regional de Lenguas Indigenas para América Latina y el Ca ribe, cuyo fin era establecer compromisos responsables de promoción, salvaguardia, uso y desarrollo de las lenguas originarias a nivel regio nal. Diego y Armando, estudiantes universitarios, asistieron a dicho evento y al finalizar escribieron algunas conclusiones, entre ellas:

"Si las personas respetan las diferencias y actúan con justicia, enton- ces el ser humano no danara al prójimo".

Simboliza el texto subrayado, elabora su tabla de verdad y determi- na si se trata de una tautologia, contingencia o contradicción.

2. Traduce situaciones.

a. ¿De qué se trata la situación problemática? Explica brevemente.

CONGRESO REGI DE LENGUAS INDIGENA AMERICA LATINA Y EL

b. Identifica, en el texto subrayado, algunos enunciados y escribelos.

3. Comunica su comprensión sobre situaciones.

a. Representa de forma simbólica las proposiciones encontradas.

b. Representa las proposiciones usando los conectivos lógicos.

4. Usa estrategias y procedimientos.

¿Qué estrategia utilizarías para resolver la situación problemática?

5. Argumenta afirmaciones.

a. Explica cómo identificas a una proposición.

b. Una tautologia se reconoce porque todos los valores de verdad de su matriz principal son falsos.

c. ¿Por qué crees necesario saber reconocer una proposición simple de una compuesta?

1. Analyze the situation.

In the month of September of the year 2019, the Regional Congress of Indigenous Languages ​​for Latin America and the Caribbean was held in Cusco, the purpose of which was to establish responsible commitments for the promotion, safeguarding, use and development of native languages ​​to regional level. Diego and Armando, university students, attended said event and at the end they wrote some conclusions, among them:

"If people respect differences and act with justice, then human beings will not harm others."

Symbolize the underlined text, create its truth table, and determine if it is a tautology, contingency, or contradiction.

2. Translate situations.

to. What is the problem situation about? Explains briefly.

REGI CONGRESS OF INDIGENOUS LANGUAGES IN LATIN AMERICA AND THE

b. Identify, in the underlined text, some statements and write them.

3. Communicates understanding of situations.

to. Symbolically represents the propositions found.

b. Represent statements using logical connectives.

4. Use strategies and procedures.

What strategy would you use to solve the problematic situation?

5. Argue affirmations.

to. Explain how you identify a proposition.

b. A tautology is recognized because all the truth values ​​of its main matrix are false.

c. Why do you think it is necessary to know how to recognize a simple proposition from a compound one?

Required sum of interior angles of the kite is 360°.

What is kite?

A quadrilateral with two pairs of adjacent sides which are congruent is called kite. Total number of sides are four.

Let the kite has vertices A, B, C,D and the lengths of its diagonals are d_1 and d_2.

The interior angles of a kite can be found using the following formulas:

[tex]∠A = ∠C = \frac{(180° - ∠B - ∠D)}{ 2} \\ ∠B = ∠D = \frac{(360° - (∠A + ∠C)) }{2}[/tex]

We know sum of interior angles = (n-2) × 180°

Where n is number of sides.

Here number of sides are 4.

So, sum of interior angles of kite = (4-2)×180° = 2×180° = 360°

Therefore required sum of interior angles is 360°.

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Correct question is " What is the sum of interior angles of a kites for A,B,C,D ?"

(a) The initial value of water in the tank is 88 gallons, and the rate of change is -6 gallons per minute (since the water is being drained). Therefore, the function that represents the amount of water in the tank, Y, after X minutes is: Y = -6X + 88.

(b) We know that the amount of water left in the tank is 34 gallons. To find out how long the tank has been draining for, we can plug in 34 for Y in the function and solve for X:

34 = -6X + 88

-6X = -54

X = 9

Therefore, the tank has been draining for 9 minutes.

The amount of income tax for a couple claiming married filing jointly status for a year would be = $108,124.75

To calculate the income tax first determine the range where the salary of the each individual falls using the table given above.

That is;

For Mr Slater, his salary income of $57,235, fell within $18,501 to $75,300 and the percentage tax income = 15%

That is, 15/100 × 57,235/1

= 858525/100

=$8,585.25

Therefore the income of Mr Slater after tax = 57,235- 8,585.25 = $48,649.75

For Mrs Slater, her salary income of $79,300 fell within range of $75,301 to $151,900 and the tax percentage = 25%.

That is , 25/100 × 79,300

= 1982500/100

= $19,825

Therefore the income of Mrs Slater after tax = 79,300-19,825 = $59,475

Therefore, the amount of income tax for a couple claiming married filing jointly status for a year would be =$48,649.75+$59,475

= $108,124.75

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The angle taken in a clockwise direction from north to southeast is 135 degrees

When measuring angles, it is common to use a reference direction, such as north, as a starting point. In this case, we are measuring an angle in a clockwise direction from north to southeast. Southeast is located halfway between the directions of south and east, which means it is at a 45-degree angle from each of those directions.

Therefore, the angle from north to southeast is 45 degrees more than a right angle, which is 90 degrees. This gives us a total of 135 degrees. Visualizing this on a compass rose can help to understand the direction and angle more clearly.

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The given question is incomplete, the complete question is:

What is the angle taken in a clockwise direction from north to southeast ?

The z-scores for each situation are given as follows:

a) 35% of the data is to the left: z = -0.385.

b) 18% of the data is to the right: z = 0.915.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

From the second bullet point, we have that the z-score for which 35% of the data is to the left of the Z-score is z with a p-value of z = 0.35, hence z = -0.385.

The z-score for which 18% of the data is to the right of the data-set, is z with a p-value of 1 - 0.18 = 0.18, hence it is z = 0.915.

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Volume is the amount of space an object takes up, and is calculated by multiplying the object's length, width, and height together

Volume is calculated in units cubed because it is a measure of how much three-dimensional space an object occupies.

Volume = Length×Width×Height

=3×3×3

=27 cubic units

Volume is the amount of space an object takes up, and is calculated by multiplying the object's length, width, and height together.

This is why it is usually represented in units cubed.

Hence, Volume is the amount of space an object takes up, and is calculated by multiplying the object's length, width, and height together

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Answer:

Step-by-step explanation:

6.   There are 9 total possible outcomes, out of those 9, 5 are possibilities with burgers or salads so answer is"

5/9

 1.  There are at total of 8 possible outcomes, out of those 8, 7 are possibilities.  so answer is

7/8

Because "7 feet 14 inches" is not a conventional or usual method to describe measurements, you would use the measurement "8 feet 4 inches" instead.

REASONS FOR USING 8 feet 4 inches:

For a few reasons, the measurement of 8 feet 4 inches is more frequently used than 7 feet 14 inches. First off, compared to 7 feet 14 inches, 8 feet 4 inches is a more common unit of measurement. Based on multiples of 12 inches, the imperial system of measurement is widely used in the United States and other regions of the world. This standard is followed by 8 feet 4 inches because 8 feet is equal to 96 inches and 4 inches is an extra increment. On the other hand, because 7 feet 14 inches is not a common unit of measurement, figuring out the entire length in inches needs an additional step.

Second, when converting to other units of measurement, utilizing 7 feet 14 inches can be confusing. For instance, it would be more challenging to translate 7 feet 14 inches to meters or centimeters than it would be to convert 8 feet 4 inches to meters. This is due to the ease with which 8 feet 4 inches may be converted to inches, which can then be transformed using normal conversion factors to centimeters or meters. However, in order to convert 7 feet 14 inches to inches, an additional step of taking 2 inches away from 8 feet to get to 6 feet 10 inches is needed.

Thirdly, a measurement of 8 feet 4 inches is more accurate than one of 7 feet 14 inches. When 7 feet 14 inches is used, it suggests that the measurement is rounded to the nearest inch, which may result in some measurement error. A more accurate measurement, however, is 8 feet 4 inches, which implies that the post office's length was calculated to the nearest inch.

Using 8 feet 4 inches is also more in line with how dimensions are typically expressed. The simplest version of a measurement should always be used, without any extraneous fractions or decimals. The less usual method of describing an object's length is 7 feet 14 inches, however, this adds an extra fraction to the measurement. Therefore, stating the length of the smallest post office in the United States using 8 feet 4 inches is more accurate and consistent.

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Using sine rule, the distance of the ship from point y is 306.42m

To find the value of x which is the distance of the ship from y

Using alternating angle theorem and sum of angles in a triangle, we can draw the diagram of the problem properly.

Since we have the value of 3 angles and one side and we need to find a side length, we have to use sine rule;

a / sin A = b / sin B = c / sin C

x / sin 80 = 200 / sin 40

cross multiply both side;

x = 200 * sin 80 / sin 40

x = 306.42m

The distance of the ship from y is 306.42m

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The gradient of line A is 8, and the gradient of line B is -4.

We have,

To find the gradient of a line, we use the formula:

Gradient = (change in y) / (change in x)

For line A:

Between (1, 2) and (1.5, 6), the change in y is 6 - 2 = 4, and the change in x is 1.5 - 1 = 0.5.

So the gradient between these two points is 4 / 0.5 = 8.

Between (1.5, 6) and (2, 10), the change in y is 10 - 6 = 4, and the change in x is 2 - 1.5 = 0.5.

So the gradient between these two points is 4 / 0.5 = 8.

Since the gradient is constant for a straight line, we can conclude that the gradient of line A is also 8.

For line B:

Between (2, 0) and (1, 4), the change in y is 4 - 0 = 4, and the change in x is 1 - 2 = -1. So the gradient between these two points is 4 / (-1) = -4.

Between (1, 4) and (0, 8), the change in y is 8 - 4 = 4, and the change in x is 0 - 1 = -1. So the gradient between these two points is 4 / (-1) = -4.

Again, since the gradient is constant for a straight line, we can conclude that the gradient of line B is also -4.

Therefore,

The gradient of line A is 8, and the gradient of line B is -4.

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Answer:

x = 7, y = -1

Step-by-step explanation:

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

10x = 70

x = 7

y = 7 - 8

y = -1

Answer:

Step-by-step explanation:

-1 is not a whole number so Karim is right.

-1 is an integer so Ali is also right.

The total amount of medication in blood stream after n number of doses is  19.44 milligrams, under the given condition that a  person repeatedly takes 20 milligrams of a prescribed medication every 4 hours.

Then the recursive rule for the amount of medication in the bloodstream after n dose is

A (n) = A (n-1) x 0.6

here

A (n) =  amount of medication in the bloodstream after the nth dose,

A (1) = 150 (the initial dose)

We can implement the values in the formula

A(5) = A(4) x 0.6

A(4) = A(3) x 0.6

A(3) = A(2) x 0.6

A(2) = A(1) x 0.6

A(1) = 150

Then,

A(2) = 150 x 0.6 = 90

A(3) = 90 x 0.6 = 54

A(4) = 54 x 0.6 = 32.4

A(5) = 32.4 x 0.6 = 19.44

The total amount of medication in blood stream after n number of doses is  19.44 milligrams, under the given condition that a  person repeatedly takes 20 milligrams of a prescribed medication every 4 hours.

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To find the difference between 87 and 12 12, we need to convert 12 12 to an improper fraction.

12 12 = (12 x 2 + 12) / 2 = 36/2 + 12/2 = 48/2 = 24

Now we can subtract the fractions:

87 - 24/12 = 87 - 2 = 85

Therefore, the difference between 87 and 12 12 is 85.

The data distribution is skewed and the mean of the number of emails is less than the median number of emails.

The median is equal to 22.

The mean is equal to 20.2.

In Mathematics, a median refers to the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

First of all, we would sort the 10 observations from the least to greatest as follows:

15, 16, 18, 19, 22, 22, 22, 22, 23, 23

Median = (22 + 22)/2

Median = 22.

In Mathematics, the mean for a set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Mean = [15+16+18+19+22+22+22+22+23+23]/10

Mean = 202/10

Mean = 20.2

In conclusion, we can logically deduce that the data distribution is skewed to the left because the mean is less than the median.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

3/1

Step-by-step explanation:

3/1 the ratio is 3:1

A 95% confidence interval estimate can be interpreted to mean that option (a) we are 95% confident that the true population mean is covered by the calculated confidence interval.

A 95% confidence interval is a range of values within which we are 95% confident that the true population mean lies. This means that if we take many random samples from the same population and calculate a 95% confidence interval for each sample, we would expect 95% of these intervals to contain the true population mean.

The 95% confidence level indicates the level of certainty we have in our estimate of the population mean, and it is a common statistical tool used in hypothesis testing and inferential statistics. However, it does not guarantee that the true population mean is within the calculated interval for a particular sample, as there is still a 5% chance of obtaining an interval that does not contain the true population mean.

Therefore, the correct option is (a) We are 95% confident that the true population mean is covered by the calculated confidence interval.

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Answer:

50 Starbusts in a bowl

Red = 20% of 50 = 10

Orange = 30% of 50 = 15

Yellow = 24% of 50 = 12

Pink = 50 - 15 - 12 - 10

= 13

Therefore, There are 13 pink Starbusts.

A displacement vector is a vector that represents the overall change in position of an object, taking into account both the direction and magnitude of the change. It is a measurement of the distance and direction from an object's initial position to its final position.

Distance, on the other hand, is a scalar quantity that refers to the total amount of ground covered by an object, regardless of its direction. It is simply a numerical value indicating the length of the path traveled by an object.

When considering velocity vs speed, velocity is also a vector quantity that includes both the speed and direction of an object's motion. Average velocity is calculated by dividing the total displacement of an object by the time it took to travel that distance.

Average speed, however, is calculated by dividing the total distance traveled by the time it took to travel that distance.

Instantaneous velocity refers to the velocity of an object at a specific point in time, while instantaneous speed refers to the speed of an object at a specific point in time.

Both of these values can be calculated by taking the derivative of the object's position vs time graph. Overall, the difference between displacement and distance is that displacement takes direction into account, while distance does not. And when considering velocity vs speed, velocity includes both direction and speed, while speed only includes the numerical value of the distance traveled over time.

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The following is the detailed proof of that ∠2 and ∠8 are supplementary.

What are parallel lines?

Parallel lines are two or more lines in a plane which never intersect, no matter how far they are extended. They always remain the same distance apart and have the same slope. Parallel lines can be found in many geometric figures, such as squares, rectangles, and parallelograms.

From the figure we can see that ∠2 and ∠4 are supplementary angles.

That is, ∠2 + ∠4 = 180°.

We can also see that ∠4 = ∠8, because they are corresponding angles.

That means if we substitute ∠8 instead of ∠4 we get,

∠2 + ∠8 = 180°

This gives us the result that ∠2 and ∠8 are supplementary.

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The commutative property of multiplication is used in -8/9x1=1x-8/9=-8/9

The commutative property, which states that changing the order of the factors in a multiplication expression does not change the result.

-8/9 x 1 = 1 x (-8/9)

Then, we can apply the commutative property again to switch the order of the factors:

1 x (-8/9) = (-8/9) x 1

Finally, we can simplify by multiplying the two factors:

(-8/9) x 1 = -8/9

Therefore, we have shown that -8/9 x 1 = 1 x (-8/9) = -8/9 using the commutative property of multiplication.

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The expression of the given polynomial 4x³ − 3x² + 16x − 12 in the form of

products of binomial terms is given by option c. (x² + 4)(4x − 3).

Polynomial is equal to ,

4x³ − 3x² + 16x − 12

Now to rewrite the polynomial in the form of a products of binomial terms.

Take out the common factors we get,

Common factors between first two terms 4x³ − 3x² is equal to x² .

Common factors between last two terms 16x − 12 is equal to 4

4x³ − 3x² + 16x − 12

⇒ x² ( 4x - 3 ) + 4 ( 4x - 3 )

⇒ ( x² + 4 )( 4x - 3 )

Therefore, the polynomial in the form of products of binomial  is written as option c. (x² + 4)(4x − 3).

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The above question is incomplete, the complete question is:

Given the polynomial 4x³ − 3x² + 16x − 12, rewrite the polynomial as a product of binomials.

a. (x² − 4)(4x + 3)

b. (x² − 4)(4x − 3)

c. (x² + 4)(4x − 3)

d. (x² + 4)(4x + 3)

Answer:

(x2 + 4)(4x − 3)

Step-by-step explanation:

bc i got it right on my quiz

We know that (A) ∠h = 28° as the angle pair ∠h and ∠I are alternate angles and hence they are equal.

The intersection of two parallel lines by a transversal produces alternate angles.

Because they are not additional angles, alternate angles often don't add up to 180 degrees, although they can if the transversal is perpendicular to the parallel lines.

So, by observing the figure we can easily state that:

∠h and ∠I are a pair of alternate angles and hence they must be equal.

So, according to this:

∠h = 28°

Therefore, we know that (A) ∠h = 28° as the angle pair ∠h and ∠I are alternate angles and hence they are equal.

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The probability of selecting a black marble, replacing it, then selecting a red marble is  7.0%.

The probability of selecting a yellow marble, not replacing it, then selecting another yellow marble is 2.2%.

The probability of selecting one yellow marble, not replacing it, then selecting a black marble is  15.6%.

There are 10 marbles in the bag, and 7 of them are black.

If we select a black marble and replace it, then there are still 10 marbles in the bag, but now only 6 of them are black and 1 is red.

Therefore, the probability of selecting a black marble, replacing it, then selecting a red marble is:

P(black, then red) = (7/10) × (1/10) = 0.07

P(black, then red) = 7 %

Therefore, the probability of selecting a black marble, replacing it, then selecting a red marble is approximately 7.0%.

P(yellow, then yellow) = (2/10) × (1/9) = 0.0222...

P(yellow, then yellow) = 2.2%

P(yellow, then black) = (2/10) × (7/9) = 0.1556...

P(yellow, then black) = 15.6%

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