If these two shapes are similar, what is the measure of the missing length d? d 84 cm 10 cm 35 cm

the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours

If person 1 can do a task in x hours and person 2 can do the same task in y hours, then the combined rate at which they can complete the task is:

rate = 1/x + 1/y

This is because each person's rate of completing the task is the reciprocal of their time to complete the task, and their combined rate is the sum of their individual rates.

To find the time it would take for both persons to complete the task working together, we can use the formula:

time = 1 / rate

Substituting the expression for the rate above, we get:

time = 1 / (1/x + 1/y)

Simplifying this expression, we can use the formula for the harmonic mean of two numbers:

time = 2xy / (x + y)

Therefore, the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours

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∠1 ≅ ∠2 ⇒ given

∠1 ≅ ∠3 ⇒ Vertical angles theorem.

∠2 ≅ ∠4 ⇒ Vertical angles theorem.

∠3 ≅ ∠4 ⇒ Transitive property of congruence

Given, ∠1 ≅ ∠2

∠2 ≅ ∠3 ⇒ Transitive property of congruence

We have to prove that ∠3 ≅ ∠4.

For that, here given the flow chart.

We have to complete the flow chart by using the given statements.

That is,

∠1 ≅ ∠2 ⇒ given

∠1 ≅ ∠3 ⇒ Vertical angles theorem.

∠2 ≅ ∠4 ⇒ Vertical angles theorem.

∠3 ≅ ∠4 ⇒ Transitive property of congruence

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The probability of picking a tile that is the letter N as a fraction 23/50.

We know that the probability of an event is a number between 0 and 1, where, 0 indicates impossibility of the event to happen and 1 indicates certainty of the event to happen.

From the question it is said that a bag of 50 letter tiles in it and 23 of the tiles are the letter N. If you pick a letter tile at random from the​ bag, the probability that it is the letter N is 3 50. Suppose another bag has 400 letter tiles in it and 256 of the tiles are the letter N.

23/50= 0.46 or 46%

And if the bag contain 400 letter tiles in it and 256 of the tiles are the letter N.  then the probability to pick N is 256/400

256/400 =0.64 or 64%

Thus the 1st bag probability is 46% and for 2nd bag is 64%. Hence choose 2nd bag

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It should be noted that a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Positive numbers are plotted to the right of the origin while negative numbers are plotted to the left of the origin. Arrows are put on the ends of the horizontal line to show that the line continues to infinity.

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The value of f ( -1 ) when evaluated is C. 1

The value of f ( - 4 ) would be A. -2

The value of x would be B. 1.7.

The question asking to evaluate f ( -1  ) is basically asking for the value of y, when the line on the graph is at the value of x in the bracket. The value of y at - 1 is 1. By this same notion, the value of y when x is - 4, according to the graph, is - 2.

The value of x however, when given f (x) = 3 would then be the value on the graph, when y is 3. We can see that this value is 1. 7.

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From the expansion of the algebraic expression (x + 9) (x + 4) (x + 10), the values of q, r, and t are:

The value of the expansion of the algebraic expression (x + 9) (x + 4) (x + 10) is given below as follows:

(x + 9) (x + 4) (x + 10) = (x + 9)(x + 4)(x + 10)

(x + 9) (x + 4) (x + 10) = (x + 9)(x² + 14x + 40)

(x + 9) (x + 4) (x + 10) = x(x² + 14x + 40) + 9(x² + 14x + 40)

(x + 9) (x + 4) (x + 10) = x³ + 14x² + 40x + 9x² + 126x + 360

(x + 9) (x + 4) (x + 10) = x³ + 23x² + 166x + 360

Comparing this expression with the given form x³ + qx² + rx + t, we can see that:

q = 23

r = 166

t = 360

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If a is a positive integer and if the unit's digit of a2 is 9 and (a+1)2 is 4, then the unit's digit of (a+2)2 is 1.

We are given that a is a positive integer, and we need to find the unit's digit of (a+2)². To solve this problem, let's first analyze the information provided:
1. The unit's digit of a² is 9.
2. The unit's digit of (a+1)² is 4.
From the first piece of information, we can conclude that the unit's digit a must be either 3 or 7, as 3² = 9 and 7² = 49 (the unit's digit is 9).
Now, let's check the second piece of information. If the unit's digit of a is 3, then the unit's digit of (a+1) would be 4. Since 4² = 16 (unit's digit is 6), this doesn't match the given condition that the unit's digit of (a+1)² is 4.
So, the unit's digit must be 7. In this case, the unit's digit of (a+1) is 8. Since 8² = 64 (unit's digit is 4), this matches the given condition.
Now that we know the unit's digit of a is 7, let's find the unit's digit of (a+2)². If the unit's digit of a is 7, then the unit's digit of (a+2) is 9. Since 9² = 81 (unit's digit is 1), the unit's digit of (a+2)² is 1.
Therefore, the correct answer is:
A) 1

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Answer: 88

Step-by-step explanation:

First, separate into familiar shapes

The area of the triangles at each side is 10 because the formula is length times times width divided by 2, when you plug the numbers in, 5 times 4 divided by two, times 2 because there are two triangles which equals 20.

That leaves the rectangle and the formula for the area of a rectangle is length times width, 17 times 4 which equals 68.

Add them, 20 plus 68 equals 88.

A t-test to compare the purchase rates between the two career types. A t-test is appropriate when comparing the means of two groups.

We cannot use correlation because we are not looking for a relationship between two variables. We also cannot use ANOVA because ANOVA is used when we have three or more groups.
To determine if there is a significant difference in purchase rate between the two career types with the highest and lowest purchase rates on stats-2, I used a t-test. A t-test is appropriate because it compares the means of two groups and tests whether there is a significant difference between them. In this case, the two groups are the career types with the highest and lowest purchase rates.

Here is a step-by-step explanation of the analysis:
1. Identify the two career types with the highest and lowest purchase rates.
2. Collect the data on purchase outcomes for these two career types.
3. Calculate the means of purchase outcomes for each career type.
4. Perform a t-test to determine if there is a significant difference between the means of the two career types.
5. Examine the results, specifically the p-value, to determine if there is a significant difference. If the p-value is less than 0.05, it indicates a significant difference.
Correlation and ANOVA are not appropriate in this case because correlation measures the strength and direction of a relationship between two variables, and ANOVA is used to compare the means of three or more groups.

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The bookstore should 300 calendars in order to have the maximum expected monetary value of $252.

To determine this, we need to calculate the expected monetary value for each option.

For ordering 100 calendars:
- Expected revenue: $12 x 100 = $1200
- Expected cost: $4 x 100 = $400
- Probability of selling all calendars: 0.35
- Probability of selling some calendars back to a supplier: 0.65
- Expected revenue from selling some calendars back to supplier: $2 x (100 - sales) = $2 x (100 - 35) = $130
- Expected monetary value: (0.35 x $1200) - $400 + (0.65 x $130) = $370

For ordering 200 calendars:
- Expected revenue: $12 x 200 = $2400
- Expected cost: $4 x 200 = $800
- Probability of selling all calendars: 0.25
- Probability of selling some calendars back to the supplier: 0.75
- Expected revenue from selling some calendars back to a supplier: $2 x (200 - sales) = $2 x (200 - 50) = $300
- Expected monetary value: (0.25 x $2400) - $800 + (0.75 x $300) = $350

For ordering 300 calendars:
- Expected revenue: $12 x 300 = $3600
- Expected cost: $4 x 300 = $1200
- Probability of selling all calendars: 0.40
- Probability of selling some calendars back to a supplier: 0.60
- Expected revenue from selling some calendars back to a supplier: $2 x (300 - sales) = $2 x (300 - 120) = $360
- Expected monetary value: (0.40 x $3600) - $1200 + (0.60 x $360) = $252

Based on these calculations, we can see that ordering 300 calendars gives the highest expected monetary value of $252.

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The amount of money saved by Kaitlin is $6.

We have,

Cost of Game= $12

Amount Kaitlin saved= 1/2 of total money

So, She saved

= 12 x 1/2

= 12 x 1/2

= 6 x 1

= $6

Thus, Kaitlin saved $6.

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The value of fraction which is equal to 2/-7 are,

⇒ - 4/14, - 6/21, - 8/28, ..

We know that;

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 2/- 7

Now, We can find all the fractions which is equal to 2/-7 as,

⇒ 2/- 7 = - 2/7

           =  - 4/14,

⇒ - 2/7 = - 6/21,

⇒ - 2/7 =  - 8/28,

Thus, the value of fraction which is equal to 2/-7 are,

⇒ - 4/14, - 6/21, - 8/28, ..

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The first four non-zero terms of the Taylor series expansion of f(x)=e^x sin x, centered at c=0, are: f(x) = x + x^2/2 + x^3/3! + ...

To find the Taylor series expansion of f(x)=e^x sin x, we need to first find the Taylor series expansions of e^x and sin x centered at c=0.

The Taylor series expansion of e^x centered at c=0 is:

e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...

And the Taylor series expansion of sin x centered at c=0 is:

sin x = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...

To find the Taylor series expansion of f(x)=e^x sin x, we need to multiply these two series together. We can do this using the "r series" method, where we take the product of the first r terms of each series and then add up all the resulting terms.

So the first term of the series for f(x) is simply the product of the first term of each series:

f(x) = e^0 * sin(0) = 0

The second term is the sum of the product of the second term of the e^x series and the first term of the sin x series, and the product of the first term of the e^x series and the second term of the sin x series:

f(x) = e^0 * sin(x) + e^x * sin(0) = x

The third term is the sum of the product of the third term of the e^x series and the first term of the sin x series, the product of the second term of the e^x series and the second term of the sin x series, and the product of the first term of the e^x series and the third term of the sin x series:

f(x) = e^0 * sin(x) + e^x * sin(0) + (x^2)/2! * sin(x) = x + x^2/2

The fourth term is the sum of the product of the fourth term of the e^x series and the first term of the sin x series, the product of the third term of the e^x series and the second term of the sin x series, the product of the second term of the e^x series and the third term of the sin x series, and the product of the first term of the e^x series and the fourth term of the sin x series:

f(x) = e^0 * sin(x) + e^x * sin(0) + (x^2)/2! * sin(x) + (x^3)/3! * sin(0) = x + x^2/2 + x^3/3!

So the first four non-zero terms of the Taylor series expansion of f(x)=e^x sin x, centered at c=0, are:

f(x) = x + x^2/2 + x^3/3! + ...

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It will take x/n hours to complete the painting at this rate

From the question, we have the following parameters that can be used in our computation:

1/x of the fence in 1/n of the hour

This means that

Time = 1/n hour

Length = 1/x fence

So, we have

Unit rate = Hour/Length

Substitute the known values in the above equation, so, we have the following representation

Unit rate = (1/n)/(1/x)

Evaluate the expression

Unit rate = x/n

Hence, the time taken is x/n hour

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The point estimate of the difference between the two population means is -51.975.

The point estimate of the difference between the two population means can be calculated by finding the difference between the sample means. From the given samples, the sample mean for the first sample is (-20 + 30 + (-223))/3 = -71, and the sample mean for the second sample is (-20.1 -24 + 5 - 40)/4 = -19.025.

It is important to note that this is only an estimate and may not perfectly represent the true difference between the two population means.

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Answer:

Firstly, it is essential to remain calm and composed. Reacting with anger or frustration can escalate the situation and make it worse. Instead, try to approach the person and speak to them calmly and respectfully. Explain how their behavior is affecting others and the overall atmosphere of the game or event.

If the person continues to display poor sportsmanship despite your attempts to communicate with them, it may be necessary to involve a coach, referee, or authority figure who can address the situation more effectively. It's important to remember that poor sportsmanship not only ruins the game for others but also reflects poorly on the individual displaying it.

In some cases, it may be best to simply ignore the behavior and focus on the game or event. As difficult as it may be, sometimes the best course of action is to rise above the negativity and continue playing with good sportsmanship. This can set a positive example for others and show that poor sportsmanship will not be tolerated.

Overall, it's important to handle poor sportsmanship with maturity, respect, and a focus on creating a positive and enjoyable experience for everyone involved.

At maturity, using the U.S. rule, the interest calculated from the last partial payment is subtracted from beginning balance added to adjusted balance.

Here, we have,

The payment of money above the principal amount (the amount borrowed) at a predetermined rate to a lender or depositor by a borrower or deposit-taking financial institution is referred to as paying interest in the fields of finance and economics.

It is different from a fee that the borrower may pay to the lender or another entity.

It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve, but not at a set rate predetermined beforehand, but rather on a pro rata basis as a portion of the rewards received by risk-taking businesspeople when revenue is earned that exceeds all costs.

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False. The slope of the line is actually -0.5.

Let's determine the slope of the line that passes through the points (20, 5) and (10, 10). To find the slope, we can use the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (10 - 5) / (10 - 20) = (5) / (-10) = -1/2

The slope of the line is -1/2. Therefore, the statement "If a line passes through the points (20, 5) and (10, 10), then the slope of the line is -2" is FALSE.

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Simple linear regression is a statistical method used to model the relationship between an independent variable (x) and a dependent variable (y).

In this analysis, a one-unit change in the independent variable (x) is assumed to result in the same consistent change in the dependent variable (y). This relationship is represented by a straight line, also known as the regression line, which is mathematically defined as y = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line. The main goal of simple linear regression is to find the best-fitting line that minimizes the differences between the observed values and the predicted values of the dependent variable (y).

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To determine the relationship between drag force and speed, you can conduct an experiment using 5 coffee filters and a motion detector. First, set up the motion detector to track the speed of the coffee filters as they fall through the air. Then, drop each coffee filter one at a time and record the drag force measured by the motion detector.

Plot the drag force on the y-axis and the speed on the x-axis, and you should be able to observe a relationship between the two variables. As the speed of the coffee filter increases, the drag force will also increase. This relationship is due to air resistance, which causes the coffee filter to experience a drag force as it falls through the air.

By analyzing the data and creating a graph, you can determine the specific relationship between drag force and speed for these coffee filters. This information can be useful in understanding how air resistance affects the motion of objects and in designing experiments or models that take air resistance into account.

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If in 2007, the population of the city was about 166,025, then K is approximately 0.0454.

The term "population" refers to the total number of humans, animals, or other living things in a certain area or region. When referring to human populations, it means the whole population of a certain city, state, nation, or even the entire planet. Births, deaths, immigration, and emigration are a few examples of things that might have an impact on a region's population.

We are given that the population of the city in 2007 was about 166,025. Since t = 0 corresponds to the year 2000, this means that in 2007, t = 7.

So we have P = 166.025 and t = 7, and the equation is:

P = 120.8[tex]e^{kt}[/tex]

Substituting these values, we get:

166.025 = 120.8[tex]e^{k*7}[/tex]

Dividing both sides by 120.8, we get:

166.025/120.8 =[tex]e^{k * 7}[/tex]

Taking the natural logarithm of both sides, we get:

ln(166.025/120.8) = k× 7

Simplifying the left-hand side, we get:

ln(1.372) = k× 7

Using a calculator to evaluate ln(1.372), we get:

0.3188 ≈ k × 7

Dividing both sides by 7, we get:

k ≈ 0.0454

Hence, if in 2007, the population of the city was about 166,025, then K is approximately 0.0454.

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The solution is, 20th term of the sequence is:  161.

We know that,

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

The nth term of AP : a_n = a + (n – 1) × d

here, we have,

the sequence:

-10, -1, 8, 17, 26

so, 1st term = a = -10

then, common difference = d

so, d = -1 - (-10)

        = 9

now, 20th term of the sequence is:

taking n = 20,

we get,

a_20 = a + (20 – 1) × d

or, a_20 =  -10 + (20 – 1) × 9

              = 161

Hence, The solution is, 20th term of the sequence is:  161.

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Based on the given information, the company estimates its sales to be 200,000 units in the first quarter. Assuming a 20,000 unit increase each quarter over the year, the second quarter's sales would be 220,000 units, the third quarter's sales would be 240,000 units, and the fourth quarter's sales would be 260,000 units.

To calculate the desired ending inventory of finished goods, we take 25% of the expected sales for the next quarter. For example, to determine the desired ending inventory for the first quarter, we take 25% of 220,000 units (the expected sales for the second quarter), which equals 55,000 units.

Each unit sells for $35, so the total sales revenue for the first quarter would be 200,000 units x $35 = $7,000,000.

Of the sales, 70% are for cash, so the company would receive $4,900,000 in cash for the first quarter's sales. The remaining 30% of sales are credit sales, and assuming that 70% of credit customers pay within the quarter, the company would receive an additional 21,000 units x $35 = $735,000 in the first quarter. The remainder of the credit sales, which is 30% x 30,000 units = 9,000 units, would be received in the following quarter.

Overall, the company expects to have increasing sales throughout the year and desires to maintain a 25% ending inventory of finished goods. The company also expects a mix of cash and credit sales, with 70% of credit customers paying within the quarter and the remainder paying in the following quarter.

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The functions represented by the graphs are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

f(x) = |x|

The function g(x) is a translation down two units of the parent function f(x), hence it is given as follows:

g(x) = |x| - 2.

The function h(x) is a translation up three units of the parent function f(x), hence it is given as follows:

h(x) = |x| + 3.

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The solution is : the measure of angle A is 150°.

We have,

First a diagram which looks like a 12 sided figure where all the sides are equal.

Now draw 2 consecutive radii.

There are 12 such triangles in a 12 sided polygon.

These triangles have an apex angle of 360 / 12 = 30 degrees.

The other two angles making up the triangle are both equal.

Therefore x + x + 30 = 180

2x = 150

x = 75

But 75 is 1/2 of the interior angle.

There are 2 such angles making up the interior angle 75 + 75 = 150.

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The requried value of x that satisfies the equation [tex]3^{(2x+1)} = 3^x+5[/tex] is x = 4.

If [tex]3^{(2x+1)} = 3^x+5[/tex], then we can use the rule that states: if [tex]a^b = a^c[/tex], where a is a non-zero number and b and c are any real numbers, then b = c.

Using this rule, we can equate the exponents of 3 on both sides of the equation:

2x + 1 = x + 5

Simplifying this equation, we can isolate the variable x by subtracting x from both sides and then subtracting 1 from both sides:

x = 4

Therefore, the value of x that satisfies the equation [tex]3^{(2x+1)} = 3^x+5[/tex] is x = 4.

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Answer:

p(blue) = 0.2

Step-by-step explanation:

A: "Pick 1 blue marble"

[tex]n(A)=C^{1}_3[/tex] = 3

n(Ω) = [tex]C^{1}_{15}[/tex] = 15

p(blue) = n(A)/n(Ω) = 3/15 = 0.2

The probability of selecting a blue marble is 0.20 expressed as a decimal.


To determine the theoretical probability of choosing a blue marble, follow these steps:
 
1. Count the total number of marbles in the bag: 3 blue + 5 red + 7 yellow = 15 marbles.
2. Identify the number of blue marbles: 3 blue marbles.
3. Calculate the probability of choosing a blue marble by dividing the number of blue marbles by the total number of marbles: 3 blue marbles / 15 total marbles.
4. Express this probability as a decimal by dividing 3 by 15: 3 ÷ 15 = 0.2.
5. Round the decimal to the nearest hundredth: 0.2 already falls at the hundredth place.
       
The theoretical probability of choosing a blue marble, expressed as a decimal rounded to the nearest hundredth, is 0.20 or simply 0.2.

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The probability that the article will have no errors is approximately 0.0233.

To solve this problem, we can use the formula for the probability of an event, which is the number of favorable outcomes divided by the total number of outcomes.

Let's first find the probability that the article is typed by the first typist. Since the article is equally likely to be typed by either typist, this probability is 1/2.

Now, we need to find the probability that the article has no errors given that it is typed by the first typist. We know that the average number of errors per article typed by the first typist is 3.5, so the probability that an article typed by the first typist has no errors is given by the Poisson distribution with λ = 3.5:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-3.5) * 3.5^0 / 1 = e^(-3.5) ≈ 0.0302

Similarly, we can find the probability that the article has no errors given that it is typed by the second typist. This probability is given by the Poisson distribution with λ = 4.1:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-4.1) * 4.1^0 / 1 = e^(-4.1) ≈ 0.0164

Finally, we can use the law of total probability to find the probability that the article has no errors:

P(X = 0) = P(X = 0 | typed by first typist) * P(typed by first typist) + P(X = 0 | typed by second typist) * P(typed by second typist)

= 0.0302 * 1/2 + 0.0164 * 1/2

= 0.0233

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In order to place 8 distinguishable rooks on an 8x8 chessboard without any of them being able to capture each other, you will need to ensure that each rook occupies a unique row and column.

Step 1: Place the first rook. There are 8 different locations to choose from (one in each row).
Step 2: Place the second rook. There are 7 remaining locations to choose from, as you cannot place it in the same row or column as the first rook.
Step 3: Place the third rook. There are 6 remaining locations to choose from, avoiding the rows and columns of the first two rooks.
Step 4: Continue this process until all 8 rooks have been placed.

To find the total number of ways to place the 8 distinguishable rooks, multiply the number of choices for each step:

8 (choices for rook 1) * 7 (choices for rook 2) * 6 (choices for rook 3) * 5 (choices for rook 4) * 4 (choices for rook 5) * 3 (choices for rook 6) * 2 (choices for rook 7) * 1 (choice for rook 8) = 40,320 ways.

To solve this problem, we can use the principle of multiplication. We start by placing the first rook in any of the 64 squares on the chessboard. There are 64 choices for the first rook.

Next, we need to place the second rook in a location that is not attacked by the first rook. Since rooks can attack any square in the same row or column as them, we need to choose a square that is not in the same row or column as the first rook. There are 7 rows and 7 columns remaining, so there are 14 squares in which the second rook can be placed.

For the third rook, we need to choose a location that is not attacked by either the first or second rook. This means we need to choose a square that is not in the same row or column as the first two rooks. There are 6 rows and 6 columns remaining, so there are 12 squares in which the third rook can be placed.

Continuing in this way, we see that the number of choices for the nth rook is equal to the number of rows and columns remaining after the (n-1)th rook has been placed. So, the total number of ways to place all 8 rooks on the chessboard is:

64 × 14 × 12 × 10 × 8 × 6 × 4 × 2 = 16,777,216

Therefore, there are 16,777,216 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.

To learn more about rook : brainly.com/question/14773695

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