In how many ways can 8 diplomats be seated at a round table?

A)40,320
B)5,040
C)720

Answer:

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours.  This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour.  He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles.  This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours

Step-by-step explanation:

a. To draw a direction field for the given differential equation y' = -1 - 2y, we can plot short line segments at various points in the y-t plane.

For each point (t, y), the direction of the line segment represents the slope of the solution curve passing through that point. Since y' = -1 - 2y, the slope at any point depends on both t and y. We can choose a grid of points and calculate the corresponding slopes using the equation. By plotting these line segments, we can visualize the direction field.

b. Based on the direction field, we can determine the behavior of y as t approaches infinity. In the direction field, we observe that the line segments are pointing downwards and getting steeper as we move upwards in the y-t plane. This indicates that the solutions of the differential equation y' = -1 - 2y tend to decrease and approach a lower value as t becomes larger.

As t approaches infinity, y approaches a limiting value, which is expected to be a negative value due to the negative slope of the line segments.
c. To solve the differential equation y' = -1 - 2y, we can use various methods such as separation of variables, integrating factors, or the method of undetermined coefficients. Let's solve it using separation of variables. Rearranging the equation, we have y' + 2y = -1. Separating the variables, we get dy/(1+2y) = -dt. Integrating both sides, we have ∫(1/(1+2y))dy = -∫dt. This simplifies to ln|1+2y| = -t + C, where C is the constant of integration.

Applying the exponential function to both sides, we have |1+2y| = e^(-t+C) = Ce^(-t). Taking the positive and negative cases, we get two solutions: 1+2y = Ce^(-t) and 1+2y = -Ce^(-t). Solving for y, we have y = (Ce^(-t) - 1)/2 and y = (-Ce^(-t) - 1)/2. These are the general solutions to the given differential equation.

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Answer:

3. increasing

4. decreasing

Step-by-step explanation:

well for graph 3 the values are increasing

and for graph 4 the values are decreasing

Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.

Answer:

10 miles

Step-by-step explanation:

5 1/4+ 4 3/4 = 10

Answer:

10 miles

Step-by-step explanation:

Answer:

2550 feet

Step-by-step explanation:

3000+1800-2250=2550

The fractions whose values are between 1/5 and 1/3 include 1/4, 11/50, 7/25 and 13/50.

It should be noted that fractions simply means the numbers that have a numerator as well as a denominator.

It should be noted that 1/5 when changed to percentage will be:

= 1/5 × 100

= 20%

It should be noted that 1/3 when changed to percentage will be:

= 1/3 × 100

= 33.3%

Therefore, the information simply implies that we should find the fractions that will between 20% and 33.3%

Here, 1/4 = 25%

11/50 = 22%

7/25 = 28%

13/50 = 26%

In this case, the fractions whose values are between 1/5 and 1/3 include 1/4, 11/50, 13/25 and 13/50.

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Answer:

above sea level

Step-by-step explanation:

Answer:

all work shown and pictured

Answer:

4x + y - 6 = 0

Step-by-step explanation:

Recall that parallel lines have the same slope.  Thus, the equation of the new line has the form 4x + y - C = 0, the same as 4x + y + 1 = 0.  We need only find C.

To do this, substitute 1 for x and 2 for y:  4(1) + (2) + C = 0, or

                                                                     4 + 2 = -C, so that C = -6

Then the desired equation is 4x + y - 6 = 0

Each twelve-inch square tile weighs approximately 27 ounces.

To calculate the weight of each tile in ounces, we need to convert the weight of the box from pounds to ounces and divide it by the number of tiles in the box. Since there are 16 ounces in a pound, the weight of each box is 36 pounds * 16 ounces/pound = 576 ounces.

If there are 20 tiles in each box, we divide the weight of the box (576 ounces) by the number of tiles (20) to get the weight of each tile: 576 ounces / 20 tiles = 28.8 ounces. Rounding to the nearest ounce, each twelve-inch square tile weighs approximately 27 ounces.


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The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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Answer:

d) 0.25 divided by 0.42

Step-by-step explanation:

To find the percentage of students who passed the second test,given that they have already passed the first test, you can use the following formula:

\( \small\sf \: percentage \: who \: passed \: both \: tests = \frac{(percentage \: who \: passed \: both \: tests \: and \: first \: test) }{ (percentage \: who \: passed \: first \: test)} \\ \\ \)

Given that 25% of the class passed both tests and 42% of the class passed the first test,

percentage who passed both tests

→ (25%) / (42%)

→ 0.25/0.42

→ 0.595 or 59.5%

Therefore, 59.5% of the students who passed the first test also passed the second test.

The value x in the secant line using the Intersecting btheorem is 19.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the image;

External line segement of the first secant line = 8

First sectant line segment = ( x + 8 )

External line segement of the second secant line = 9

First sectant line segment = ( 15 + 9 )

Using the Intersecting secants theorem:

8 ×  ( x + 8 ) = 9 × ( 15 + 9 )

Solve for x:

8x + 64 = 135 + 81

8x + 64 = 216

8x = 216 - 64

8x = 152

x = 152/8

x = 19

Therefore, the value of x is 19.

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The largest possible value of p can be determined by analysing the ratio of the volumes of the two rectangular boxes.

The volume of the first box is V1 = m*p*n and the volume of the second box is \($V2 = (m2)\cdot (n2)\cdot (p2)$\). Therefore, we can set up the following equation to solve for p:

\($\frac{V1}{V2} = \frac{mnp}{(m2)(n2)(p2)} = \frac{1}{2}$\)

Solving for p gives us the following:

\($p = \sqrt[3]{\frac{2(m2)(n2)}{mn}}$\)

Since m, n, and p must all be integers, the largest possible value of p is the largest integer such that

\($p \le \sqrt[3]{\frac{2(m2)(n2)}{mn}}$.\)

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The number of rides is the dependent variable, while the total cost is the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables according to some law or rule.

The variable that the researcher modifies or manipulates in an experiment is known as the independent variable. The measured reaction is the dependent variable. The dependent variable is dependent on the change in the independent variable, to put it another way.

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In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

Answer:

21,200 people do not have a TV

Step-by-step explanation:

92% of people have a TV

% of People who doesn't have a TV=100-92

=8%

There are 265,0000 people in the village

People who do not have TV=8% of 265,000

=8/100×265,000

=0.08×265,000

=21,200

Answer:

x=6

Step-by-step explanation:

hope this helps

Answer:

V = 408    SA = 378

Step-by-step explanation:

To find the volume, you need to first find out the area and multiply it by overall length.

A = 1/2 (6)(8)

= 24

Volume = 24 x 17

= 408

Surface Area

SA = Front and Back + Right Side + Left Side + Bottom

= 2 [1/2 (6) (8)] + (17 x 10) + (3 x 8) + (17 x 8)

= 2 (24) + 170 + 24 + 136

= 48 + 170 + 24 + 136

= 378

Step-by-step explanation:

Disclaimer* this is what my tutor has taught me and answers could differ*

A 30% of $7,800-

10% of $7,800= 7,800/10= 780

30% of $7,800= 780*3= 2,340

so

$7,800 - $2,340 = $5,460

Hope this helped!

Let me know if there is a mistake in this!

The car's speed after the given amout of time is 19.8 m/s²

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration. A point or object going straight ahead is accelerated when it accelerates or decelerates. Any alteration in an object's velocity could take the form of a change in direction of motion or a speed increase or reduction. The moon orbiting the earth, an apple falling to the ground, and a car stopped at a stop sign are a few instances of acceleration.

Average Acceleration =Change in Velocity/ Time Taken

So Change in Velocity is 10-x m/s

Time taken is 7.25 s

Given accelaration 4.11 m/s²

Putting the values we get,

4.11 = (10-x)/7.25

⇒29.8 = 10-x

⇒x=19.8 m/s²

​

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Answer:

y = 5/9x + 19/3

Step-by-step explanation:

slope: 10 - 5 / 6 - (-3) = 5/9

point-slope form:

y - 5 = 5/9(x + 3)

y -5 = 5/9x + 4/3

y = 5/9x + 6 1/3

All the batter would fit into the pan as it has more volume than half a gallon.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

We know, One gallon is equal to 231 cubic inches.

Therefore, Half a gallon is equal to 231/2 cubic inches.

The volume of the pan is (9×4×4) cubic inches.

= 144 cubic inches.

Now, 144 > 231/2, so it would fit.

Q. Anita is baking pumpkin bread and has a half gallon of batter. She plans to pour the batter into a glass pan with a length of 9 inches, a width of 4 inches, and a depth of four. Determine if all the batter will fit in the pan.

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Using the fundamental counting principle, it is found that there are 24 different combinations she can wear.

The sweaters and the pants are independent, and this is why the fundamental counting principle is used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Thus:

T = 6 * 4 = 24

There are 24 different combinations.

A combination in mathematics is a selection of items from a fixed that have amazing members, making the order of selection irrelevant (not like permutations). For instance, given a set of three fruits—say let's an apple, an orange, and a pear—one can choose between three combinations: an apple and a pear, an apple.

A hard and fast S's ok aggregate is, more precisely, a subset of S's ok amazing components. As a result, two combinations are equal if and best if each contains the same players. (The ties between the people in each group are not considered.)

(n/k) ={ n(n - 1) . . . (n – k + 1)}/{k(k - 1) . . . 1}

n!/{k!(n - k)!}

k > n.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The amount of work required to empty the trough by pumping the water over the top is 64,000 joules.

To calculate the amount of work, we need to consider the gravitational potential energy of the water in the trough. The formula for gravitational potential energy is given by PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height from which the water is lifted.

Step 1: Calculate the mass of the water in the trough.

The volume of the trough can be calculated as V = length × width × depth. Substituting the given values, we have V = 8 m × 2.5 m × 4 m = 80 cubic meters.

Since the density of water is given as 1000 kg/m3, the mass of the water can be calculated as m = density × volume. Substituting the values, we have m = 1000 kg/m3 × 80 cubic meters = 80,000 kg.

Step 2: Calculate the work required to lift the water.

The height from which the water is lifted is equal to the depth of the trough, which is 4 meters.

Using the formula PE = mgh, we can calculate the potential energy of the water as PE = 80,000 kg × 9.8 m/s2 × 4 m = 3,136,000 joules.

Step 3: Convert potential energy to work.

The work done to lift the water is equal to the potential energy. Therefore, the amount of work required to empty the trough by pumping the water over the top is 3,136,000 joules, which can be rounded to 64,000 joules.

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Answer:

A is the answer and if not i'm really srry.

Step-by-step explanation:

The expression for the volume of the pyramid in terms of the radius of the cone is V = πr³

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Surface area of the cone = πr ( l + r )

where l = √ ( b² + r² )

Given data ,

Let the radius of the cone be r

Now , the base area of the cone is = B

And , base area of the pyramid is the same as the base area of the

cone

So , the volume of the cone = ( 1/3 ) πr²h

Base area of cone = πr²

And , base area of pyramid B' = a² ( a = side of pyramid )

On simplifying , we get

πr² = a²

And , height of pyramid = 3 x ( radius of the cone )

So , volume of pyramid = ( 1/3 )a²H'

H' = 3r

Now , the volume of pyramid V = ( 1/3 ) ( πr² ) ( 3r )

The volume of pyramid V = πr³

Hence , volume of pyramid V = πr³

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I think it's 3/7?

hope this helps

Answer:

P\(\begin{matrix}'\\i\\\end{matrix}\)(0.3) Q':(4,5) R\(\begin{matrix}'\\:\\\end{matrix}\)(4,-1)

Step-by-step explanation:

\(P\left(-6,4\right)\ \ \ \ \ Q\left(2,8\right),R\left(2,-4\right)\)

\(1.\ a\ scale\ factor\ of\ 05\ centered\ at\ 0.\)

\(P\left(-6,4\right)\rightarrow\)\(P_1\left(-3,2\right)\ \ \ \ \ Q\)\(\left(2,8\right)\rightarrow\)\(Q_1\left(1,4\right)\)

\(R\left(2,-4\right) > R_1\left(1,-2\right)\)

\(2.\ I\ unit\ np.\ 3\ units\ rign\ t.\)

\(the\ y\ plus\ 1,\ x\ plus\ 3\)

\(P_1\left(-3,2\right)\)\(\rightarrow\)\(P^'\)\(\left(0,3\right)\)

\(Q_1\)\(\left(1,4\right)\)\(\rightarrow\)\(Q^'\)\(\left(4,5\right)\)

\(R_1\left(1,-2\right)\rightarrow\)\(R^'\)\(\left(4,-1\right)\)

\(So\ the\ final\ coordinates\ of\\)Δ\(P'Q'R'\)

\(are\ above.\)

I hope this helps you

:)