Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?

The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.

The endpoints are (2, -5) and (-3,1).

The standard form equation for a circle is known as

\((x-a)^2+(y-b)^2=r^2\)

where (a, b) are the center's coordinates and (r) is the radius.

Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.

Calculating the midpoint is as follows:

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)\)

where, \((x_{1},y_{1})\) and \((x_{2},y_{2})\) are two points.

Now putting the values

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)\)

Now we determine the equation of circle.

The center (2, 1) and the terminal are the two points (-2, 3).

r = \(\sqrt{(-2-1)^2+(3-1)^2}\)

r =\(\sqrt{(-3)^2+(2)^2}\)

r = \(\sqrt{9+4}\)

r = √13

Now we can write the equation of circle as:

(x - 1)^2 + (y - 1)^2 = (√13)^2

(x - 1)^2 + (y - 1)^2 = 13

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The complete question is:

Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).

Write the standard equation for the circle.

The values of the expressions A and B after substitution are both -3

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

A. m(2 - m)

B. m(-m + 2)

The value of m is given as

m = -1

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

A. m(2 - m) = -1(2 + 1)

B. m(-m + 2) = -1(1 + 2)

Evaluate the expressions

A. m(2 - m) = -1(2 + 1) = -3

B. m(-m + 2) = -1(1 + 2) = -3

Hence, the values of the expressions after substitution are both -3

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Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.

The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.

Therefore, the ratio of the dimensions of the actual room to that of the scale model is:

length: 15m / 5m = 3 : 1

width: 9m / 3m = 3 : 1

height: 12m / 4m = 3 : 1

So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)

The ratio of the dimensions of the scale model to that of the actual object is 1:16

so to find the length and width of the actual object, you can use this relation

length = scale model length * 16 = 2.416 = 38.4m

width = scale model width * 16 = 1.816 = 28.8m

So the length and width of the actual object are 38.4m and 28.8m respectively.

Step-by-step explanation:

There are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

1. First we need to identify the total number of seats in the lecture hall which is 200.

2. Then we need to identify the number of seats with folding arm tablets that are designed for wheelchair users which is 30.

3. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats.

4. Therefore, 200 - 30 = 170, which means there are 170 seats with folding arm tablets that are not designed for wheelchair users.

The lecture hall in question has a total of 200 seats, with 30 of those seats having folding arm tablets that are designed for wheelchair users. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats. This means that 200 - 30 = 170, which means there are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

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It took Paul a total of 12 hours and 40 minutes to complete all three parts of the Ironman triathlon.

Paul’s time for swimming in the Ironman triathlon was 1 hour 25 minutes. Her time for biking was 5 hours longer than her swimming time, so her biking time was (1 hour + 5 hours) = 6 hours 25 minutes. She ran for 4 hours 50 minutes. The total time it took her to complete all three parts of the race is (1 hour 25 minutes) + (6 hours 25 minutes) + (4 hours 50 minutes) = 12 hours 40 minutes.

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onde esta a altenaativas

Answer:

9

Step-by-step explanation:

You know AB=CB because all 3 arcs are equal, therefore:

5x + 8 = 53

5x = 53 - 8

5x = 45

x = 45/5 = 9

Answer: 2007<y

Step-by-step explanation:

the years after 2007, like 2008, 2009 are greater than 2007

Answer:

A, B, D, and E

Step-by-step explanation: Hope it helps ^w^

Step-by-step explanation: I hope this helps.

Answer:

\(We \: \: \: \: know \\ mean \: \: = \frac{sum \: \: \: of \: \: \: the \: \: \: terms}{number \: \: \: of \: \: \: terms} \\ \)

\(Given \: \: \: here \: \: the \: \: \: mean \\ of \: \: \: 3y + 1 \: \: \: and \: \: \: 4y + 9 \: \: \: is \: \: \: 2y + 11.\)

\(Therefore \\ \frac{(3y + 1) + (4y + 9)}{2} = 2y + 11 \\ = > \frac{7y + 10}{2} = 2y + 11 \\ = > 7y + 10 = 2(2y + 11) \\ = > 7y + 10 = 4y + 22 \\ = > 7y - 4y = 22 - 10 \\ = > 3y = 12 \\ = > y = \frac{12}{3} \\ = > y = 4\)

\(Your \: \: \: answer \: \: \: is \: \: \: 4.\)

Answer:

To find the amount of money the Schaeffer family wants to save next year, we need to calculate 15% of their combined income of $80,000:

15% * $80,000 = $12,000

Therefore, the answer is $12,000, and the correct option is B.

The Phillips curve describes the relationship between the unemployment rate and the rate of change of wages. Option C is the correct option.

What is  Phillips curve?

The relationship between the rate of inflation and the unemployment rate is represented by the Phillips curve. The analysis of wage inflation and unemployment in the United Kingdom from 1861 to 1957 by A. W. H. Phillips, despite having forerunners, is a significant development in the field of macroeconomics. When unemployment was high, wages rose slowly; when unemployment was low, wages rose quickly, according to Phillips' research.

According to Phillips' hypothesis, as the unemployment rate declines, the labor market becomes more competitive and firms are forced to raise wages more quickly in order to recruit qualified workers. The pressure decreased as unemployment rates rose. The average relationship between wage behavior and unemployment over the course of the business cycle was represented by Phillips' "curve."

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Answer:

x=2

Step-by-step explanation:

X=2 is the answer because the line touches downward from x-axis

so we can say that the answer is x=2

Step-by-step explanation:

I think you mean relation

Relation is the way in which two or more people or things are connected; a thing's effect on or relevance to another.

When a distribution is shown as a symmetrical bell-shaped curve then the mean, median, and mode are equal i.e., option (a) is correct.

A symmetrical bell-shaped curve, also known as a normal distribution or Gaussian distribution, is characterized by its symmetry around the mean.

In this type of distribution, the mean, median, and mode all coincide at the center of the curve.

This means that the central tendency measures, such as the mean (average), median (middle value), and mode (most frequent value), are all equal.

Option (a) states that the mean, median, and mode are equal, which aligns with the properties of a symmetrical bell-shaped curve. This equality occurs because the data is evenly distributed on both sides of the mean, resulting in a balanced distribution.

Options (b) and (d) suggest that the mean is either less than or greater than the median and mode, which does not hold true for a symmetrical distribution.

In a symmetrical distribution, the mean is located at the center of the data, and the median and mode share the same value as the mean.

Option (c) mentions moderate uniformity, but a symmetrical bell-shaped curve does not specifically indicate uniformity. Uniformity refers to a distribution where all data points have equal probability, resulting in a flat line.

In contrast, a symmetrical bell-shaped curve indicates a normal distribution with the majority of data concentrated around the mean, gradually decreasing towards the tails.

Therefore, based on the given options, option (a) is the correct conclusion when the distribution is shown as a symmetrical bell-shaped curve.

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Answer:

16

Step-by-step explanation:

(if u are 4, i'm gonna scream)

Answer:

16

Step-by-step explanation:

If you are 4, just no.

The problem is asking us to prove that there is only one polynomial of degree n-1 or less that passes through all n points. This can be done using the concept of linear independence and the basis of a polynomial space.

First, let's consider a polynomial of degree n-1:
P(x) = a0 + a1x + a2x^2 + ... + an-1x^(n-1)
We can write this polynomial in the form of a linear combination of basis vectors:
P(x) = a0(1) + a1(x) + a2(x^2) + ... + an-1(x^(n-1))

The basis vectors of the polynomial space are 1, x, x^2, ..., x^(n-1). These basis vectors are linearly independent, which means that no linear combination of the basis vectors can equal zero unless all the coefficients are zero.
Now, let's plug in the n points into the polynomial:
P(x1) = a0(1) + a1(x1) + a2(x1^2) + ... + an-1(x1^(n-1)) = y1
P(x2) = a0(1) + a1(x2) + a2(x2^2) + ... + an-1(x2^(n-1)) = y2...
P(xn) = a0(1) + a1(xn) + a2(xn^2) + ... + an-1(xn^(n-1)) = yn

This gives us a system of n linear equations with n unknowns (the coefficients a0, a1, ..., an-1). Since the basis vectors are linearly independent, the system of equations has a unique solution. This means that there is only one polynomial of degree n-1 or less that passes through all n points.

Therefore, we have proved that there is exactly one polynomial of degree n-1 or less which passes through all n points.

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Answer:

7 students

Step-by-step explanation:

1+2+4=7students

9514 1404 393

Answer:

  6. step 2; terms are improperly combined; it should be -61n-8=-8

  7. no; point (2, 5) is not part of the solution in the left graph

Step-by-step explanation:

6. Step 2 should be ...

  -61n -8 = -8 . . . . . because -5n-56n = -61n, not -51n

__

7. The boundary lines of both graphs go through the point (2, 5). In the left graph, the line is dashed, indicating that points on the line are not part of the solution set. The point (2, 5) on the dashed line is not a solution to that inequality.

The solid boundary line indicates that the points on the line are part of the solution set. The point (2, 5) on the solid line is a solution to that inequality.

The point (2, 5) is not a solution to both inequalities.

Answer:

12x+5=162

Step-by-step explanation:

Over 10.144 years of age are found in 75% of firm employees' autos.

We need to identify the z-score that corresponds to the age of the cars driven by firm employees that are 75% older than the other cars of 75th percentile of the normal distribution.

A normal distribution calculator or statistical software programme can be used to find this z-score. As an alternative, we can look for the value using a z-distribution table.

The formula for the z-score is:

z = (x - μ) / σ

If x is the value we are looking for, is the distribution's mean, and is its standard deviation.

We can use the common normal distribution table or a calculator with a built-in function to determine the z-score corresponding to the 75th percentile  to a cumulative probability of 0.75. The table value is 0.67.

As a result, we can determine the age of the company vehicles that are approximately 75% older than the others as follows:

x = μ + zσ

= 8 + (0.67)(3.2)

= 10.144

As a result, more than 75% of the cars that firm employees drive are older than 10.144 years.

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Answer:

20 feet

Step-by-step explanation:

Height of the student = 68 inches

Length of the student's shadow = 17 inches

Length of the tree's shadow = 60 inches

Let's set up the proportion:

(T / 60) = (68 / 17)

Cross-multiply:

17T = 68 * 60

Simplify:

17T = 4080

Divide both sides by 17:

T = 4080 / 17

Calculate:

T ≈ 240 inches

To convert to feet, divide by 12:

T ≈ 240 / 12

T ≈ 20 feet

Therefore, the tree is approximately 20 feet tall.

chatgpt

bardAI

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Answer:

12

Step-by-step explanation:

Create a ratio

AB : DE

5 : 4

BC : EF

15: x

5/4 = 15/x

5x = 15*4

5x = 60

x = 12

EF = 12

Answer:

2/3

Step-by-step explanation:

1. (4/9)^1/2

2. 4/9 + 2/9 = 6/9

3. simplify it gives you 2/3

Answer:

D. 2/3

Step-by-step explanation:

\((\frac{4}{9} )^{\frac{1}{2} } = \frac{\sqrt{4} }{\sqrt{9}} = \frac{2}{3}\)

Los signos de puntuación adecuados son:

(El unicornio camina muy tranquilo en el bosque cuando de repente se encuentra con una Quimera).​

El uso de los signos de puntuación.

Los signos de puntuación, dependiendo del requerimiento del texto, la oración o la conversación, pueden servir para:

Como puedes ver, según cada tipo de expresión fue ubicado el signo dentro del diálogo, puedes identificarlo puesto que los signos, tanto de admiración como de interrogación añadidos, se encuentran en cursiva y los dos puntos están subrayados.

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The product of the terms   \((d - 9)\)  and  \((2d^{2} + 11d -4)\)  will be \((2d^{3} - 7d^{2} - 103d + 36)\).

We have to find the product of two terms.

First term = (d - 9)

Second term = \((2d^{2} + 11d -4)\)

To find the product of these two terms, we will be using the distributive property. According to the distributive property, when we multiply the sum of two or more addends by a number, it will give the same result as when we multiply each addend individually by the number and then add the products together.

We have to find :  \((d - 9) (2d^2 + 11d -4)\)

Using the distributive property,

\(d * 2d^{2} + d * 11 + d * (-4) - 9 * 2d^2 - 9 * 11d - 9 * (-4)\)

After further multiplication, we get

\(2d^{3} + 11d^2 - 4d - 18d^{2} - 99d + 36\)

Now, combine all the like terms.

\(2d^{3} + 11d^{2} - 18d^{2} - 4d - 99d + 36\)

\(2d^{3} - 7d^{2} - 103d + 36\)

Therefore, the product of d-9 and 2d^2 + 11d -4 is \(2d^{3} - 7d^{2} - 103d + 36\)

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The diameters of a strand of black hair and a strand of red hair is found to be 1.4×10⁻³.

Scientific notation is a method of expressing extremely large or extremely small numbers.

For the given question;

Convert the decimal value 0.001 in scientific notations;

= 0.001 inch

= 1×10⁻³ inch

Now, calculate the difference;

Difference in diameter = Black hair diameter - Red hair diameter

Difference in diameter =  2.4×10⁻³ - 1×10⁻³

Difference in diameter = 1.4×10⁻³

Therefore, the value of the difference in the diameter of red and black hair is found as 1.4×10⁻³.

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Answer:

x>-3

Step-by-step explanation:

Divide both sides by 5

x > -3

-15/5 = -3