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As per the permutation, there are 5040 number of different ways are available for seating.

The term permutation in math is known as  a mathematical calculation of the number of ways a particular set can be arranged

Here we know that there are 8! ways that you can arrange 8 people.

Now here we have to imagine a specific arrangement.

Here we have consider that everyone get up and move one seat to their right.

Then in that arrangement was counted separately from the first one in the 8!

Here have to know that it’s really the same since if each person looks to their left and their right and here they’re sitting next to the same person. Then here there are 8 such “identical rotations” for each possible seating arrangement so the total number of seating's is calculated as,

=> 8! / 8

=> 7! = 5040.

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c. The mode is the best measure to describe the typical or central value in this data set.

The data set consists of qualitative values, which means they are not in numerical form and cannot be used to calculate the mean or median. The mode is the best measure to describe the typical or central value because it identifies the value that occurs most often in the data set.

In this case, the value that occurs most often is ‘blonde’, which would be the mode. The mean and median cannot be used because they require quantitative data, such as numerical values, to be calculated.

Additionally, the data set does not have outliers, which would cause the mean to be skewed. By using the mode, we can accurately describe the typical or central value of this data set.

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A gas occupies 4.23 l at 2.25 atm. 2.75 L is the volume at 3.46 atm. This can be solved using the concept of Boyle's law.

Boyle's law gives the relationship between pressure and volume of gas.

It states that at constant temperature pressure in inversely proportional to volume.

PV = k

where P - pressure V - volume and k - constant

P₁V₁ = P₂V₂

Given that,

initial pressure (P₁) = 2.25 atm

final pressure (P₂) = 3.46 atm

initial volume (V₁) = 4.23 L

final volume (V₂) = ?

where parameters for the first instance are on the left side and parameters for the second instance are on the right side of the equation

substituting the values in the equation

2.25 atm x 4.23 L = 3.46 atm x V

V = 2.75 L

Thus, the final volume is 2.75 L

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Answer:

V = 17 m3

Step-by-step explanation:

The area of the base (triangular) is multiplied by the height, resulting in the volume

[tex]V=\frac{(2)(1)}{2} (17)=(\frac{2}{2})(17)=(1)(17)=17[/tex]

Hope this helps

Conversion of pressure of 1379 torr to atm= 1.814474

Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.

Additionally, choosing the right number of significant digits and rounding may be necessary during the process.

The multi-step process of unit conversion involves multiplying or dividing by a numerical factor.

Weight, distance, and temperature can all be measured in a variety of ways.

Temperature is expressed in degrees Celsius, weight is expressed in kilos, and distance is measured in kilometers.

Imagine you are on vacation in India and are informed that the two cities are 100 kilometers apart.

Hence, Conversion of pressure of 1379 torr to atm= 1.814474

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The gallons of blue paint he needs to make the green paint is 6 gallons.

This is a problem in ratios. Let's look into what we know.

Volume of green paint needed = 10 gallons

Parts of blue paint needed = 3

Parts of yellow paint needed = 2

Total number of parts = parts of blue paint + parts of yellow paint

                                    3 + 2 = 5

So fraction of blue paint needed = parts of blue paint / total parts

                                                       = 3/5

Volume of blue paint needed = [tex]\frac{3}{5}[/tex] × 10

                                                 = 6 gallons

Volume of yellow paint needed = [tex]\frac{2}{5}[/tex] ×10

                                                      = 4 gallons.

So we need 6 gallons of blue paint and 4 gallons of yellow paint to make 10 gallons of green paint.

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The probability that 3 hearts are chosen if 7 cards are selected from a well-shuffled deck of 52 playing cards is  [tex]\\& =0.175823334\end{aligned}[/tex]

The probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging between 0% to 100% can be used to describe probabilities.

Although a quasiprobability distributed enables a negative probability, called quasiprobability, for some events, the probability of the result of an experiment is never negative. These distributions may be applicable to conditional probability or unobservable occurrences.

The number of choosing  cards out of 52 is = ⁵²C₃

Number of ways of choosing 3 cards of heart out of 13 cards and 4 out of remaining 39 cards = ¹³C₅ × ³⁹C₃

Probability of choosing 5 hearts =  ¹³C₃ × ³⁹C₄ /  ⁵²C₃

[tex]\begin{aligned}\frac{13 \times 2 \times 11 \times 13 \times 19 \times 3 \times 9}{26 \times 17 \times 10 \times 7 \times 2 \times 47 \times 46} & =\frac{23523786}{133784560} \\& =0.175823334\end{aligned}[/tex]

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Step-by-Step Explanation:

We know,

[tex] \cos(angle) = \frac{base}{hypotenuse} [/tex]

Here, angle = 60°, base = 5, hypotenuse = x

Therefore,

[tex] \cos(60) = \frac{5}{x} \\ = > \frac{1}{2} = \frac{5}{x} \\ = > x = 5 \times 2 \\ = > x = 10[/tex]

Answer:

10

Hope it helps.

The solution for x in triangle is,

⇒ x = 10

We have to given that;

A triangle is shown in figure.

Since, A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Now, We can use the trigonometry formula to find the value of x as;

⇒ cos a = Base / Hypotenuse

Substitute a = 60°, base = 5 , hypotenuse = x in above equation,

⇒ cos 60° = 5 / x

⇒ 1 / 2 = 5 / x

⇒ x = 5 × 2

⇒ x = 10

Thus, The solution for x in triangle is,

⇒ x = 10

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The z score for the value 66, when the mean is 51 and the standard deviation is 1 is 15.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

Given that:

mean = 51, standard deviation = 1. For a value of 66:

z = (66 - 51) / 1 = 15

The z score is 15.

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The exponential function graphed is given as follows:

y = 2^x.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the parameters are given as follows:

When x increases by one, the output is multiplied by 2, hence the parameter b is given as follows:

b = 2.

The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:

a = 1.

Hence the function is defined as follows:

y = 2^x.

The graph is given by the image presented at the end of the answer.

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The force that a simple machine applies to an object is known as output force. The mechanical advantage exceeds one if the output force exceeds the input force.

A basic machine's output force is indeed the pressure it puts on an item. The mechanical advantage exceeds 1 when the output force exceeds the input force. Output force minus input force equals the mechanical advantage ratio. Work is made easier by increasing the mechanical advantage.

A 630 N input force is therefore necessary.

a 3 percent mechanical advantage

It can be represented mathematically as follows:

M=f 1/f 2

the output force F1 is

The input force is F2,

and thus

F1=1890 N and 3=F1/630 N

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Answer:

the answer is D. 1,890 N!!!

The Price of an Orange is $2 and the price of an Apple is $3.3.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let us assume that,

Apple price =  A  $

Orange price = B  $

$5.30 for 1 apple and 1  orange

=> A + B  = 5.30    Equation 1

$7.30 for 1 apple and 2 oranges.

=> A  + 2B = 7.30   Equation 2

Equation 2 - Equation 1

=> B = 2

Thus, the Price of an Orange = $2

A + 2 = 5.30

=> A=  $3.30

Price of Apple  = $3.3

Therefore, The Price of an Orange is $2 and the price of an Apple is $3.3

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Answer:

13.75 m.

Step-by-step explanation:

We can start by calculating the total area of the walls of the room by subtracting the area of the door and window from the total area of the room.

The total area of the room is 20m * 14m = 280 m^2

The area of the door is 1m * 1.7m = 1.7 m^2

The area of the window is 1.8m * 1.8m = 3.24 m^2

The total area of the walls is 280m^2 - 1.7m^2 - 3.24m^2 = 275.06 m^2

Now that we have the total area of the walls, we can divide it by the cost of painting per m^2 to find the height of the room.

The cost of painting per m^2 is $12165.9 / 275.06 m^2 = $44.32/m^2

So we can find the height of the room by dividing the cost by the rate of painting, $12165.9 / $44.32/m^2 = 275.06 m^2 / (20m * h) = 275.06 / 20 = 13.75m

Therefore, the height of the room is approximately 13.75 m.

Answer: 1/4

Step-by-step explanation: He plants 3/4 of the flowers in one garden. There are 1/4 left. 4/4 - 3/4= 1/4

The volume of the composite solid 28.26 cm³

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The volume is the space occupied for a solid figure.

For the composite:

Volume of composite = volume of cylinder + volume of cone

For cylinder:

height is 2.5, radius : 3 inches

Volume of cylinder = π * radius² * height = π * (3)² * 2.5 = 70.65 cm³

For cone:

height is 3, radius : 3 inches

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (3)² * 3 = 28.26 cm³

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The best estimate of the system solution to the nearest integer values is (2,3).

The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis. A point's Cartesian coordinates (also known as rectangular coordinates) are a pair of integers (in two dimensions) or a triplet of numbers (in three dimensions) indicating signed distances from the coordinate axis. A point's coordinates are a pair of integers that define its precise location on a two-dimensional plane. Remember that the coordinate plane contains two axes that are perpendicular to each other, known as the x and y axes.

Here,

This question is asking us what the coordinates are for the point of intersection. Since the point is not directly on the grid lines, we must approximate.

The point is closest to the value "2" on the x axis.

The point is closest to the value "3" on the y axis.

This means the correct point is (2,3).

The best approximation of the solution to the system to the nearest integer values is (2,3).

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Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.

here,

rate = 10%

Time = 1 year

Principle = 12000

=>SI = PRT/100

=> SI =  10*1*12000/100

=> SI = 1200

and

=>  After 1 year = 12000 -1200 = 10800

and

for five  years

=> SI = PRT/100

=> SI = 10800 * 7.2 * 4 / 100

=> SI = 3110.4

After 5 year = 10800 - 3110.4  = 7,689.6

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There are 14 quarters and 25 number of pennies

Two or more expressions with an Equal sign is called as Equation.

Given that some quarters and pennies worth $3.75

0.25x+0.01y=3.75

There are 39 coins altogether

x+y=39

x=39-y

Now plug in x value in 0.25x+0.01y=3.75

0.25(39-y)+0.01y=3.75

9.75-0.25y+0.01y=3.75

9.75-0.24y=3.75

9.75-3.75=0.24y

6=0.24y

Divide both sides by 0.24

25=y

x+y=39

x=14

Hence, there are 14 quarters and 25 number of pennies

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The fate of the 22 checked bags can be considered the Bernoulli trials.

A Bernoulli trial is a random experiment with two possible outcomes, often referred to as a "success" or "failure." In the context of the lost luggage problem, success would be a checked bag that is not misplaced, and failure would be a checked bag that is misplaced.

For a set of trials to be considered Bernoulli trials, the following conditions must be met:

In this case, the fate of the 22 checked bags can be considered Bernoulli trials if the following conditions are met:

Therefore, the fate of the 22 checked bags can be considered Bernoulli trials.

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The proportion that represents kilometers Halona walks is 193 kilometers in 2300 minute, that is 193/ 2300.

1 kilometer / x minutes = 1.93 kilometers / 23 minutes

Let x be the kilometers Halona walks in 1 minute. If she walks at a constant speed, as speed is rate of distance covered in unit time

x kilometer / 1 minute = 1.93 kilometers / 23 minutes

So the proportion is:

x kilometer / 1 minutes = 1.93 kilometers / 23 minutes

x kilometer / 1 minutes = 193/ 2300

This proportion represents how many kilometers Halona walks per minute. To find her speed in kilometers per hour, we can multiply the proportion by 60 minutes/hour.

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Honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty, ranking their fellow participants in terms of honesty, conducting a polygraph test to assess physiological responses when presented with specific questions, and conducting interviews to assess how forthright people are in their answers.

An operational definition of honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty. This would allow participants to self-assess their own level of honesty and provide a baseline for comparison. By observing how often people tell the truth in a given situation, one can measure the level of honesty of a person.

Additionally, a polygraph can be used to measure physiological responses when asking a series of specific questions. This can provide a more accurate measurement of a person’s honesty in comparison to a self-reported scale.

Lastly, conducting interviews with participants can help to assess how forthright people are in their answers. This allows for a more in-depth assessment of honesty by allowing interviewers to observe and assess the sincerity of participants’ answers.

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To have a 50% chance of probability finding a secretary who knows Tex, at least 50 out of 100 applicants should be interviewed.

In order to determine the least number of applicants that should be interviewed to have a 50% chance of finding one secretary who knows the word processor language Tex, we can use the binomial probability formula. This formula states that the probability of finding at least one success out of a certain number of trials is given by P(X ≥ 1) = 1 – P(X = 0). Assuming that there are 100 applicants, the probability of finding at least one secretary who knows Tex is given by 1 – (98/100)^50, which is approximately 0.5. Therefore, at least 50 out of 100 applicants should be interviewed to have a 50% chance of finding a secretary who knows the language Tex.

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it would take the object approximately 11.51 seconds to reach the ground.

Generally, Time is a concept used to describe the progression of events, or the duration of those events. It is often measured in units such as seconds, minutes, hours, days, and years.

Time can also be described as a continuum, with past events on one end and future events on the other.

Time is a fundamental aspect of the universe and is closely related to concepts such as causation, change, and entropy.

The time it would take the object to reach the ground can be found by setting the distance from the ground, s, to 0 and solving for t.

0 = -16t^2 + 2120

t^2 = (2120/16)

t = [tex]\sqrt{(2120/16)}[/tex]

t = approximately 11.51 seconds

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Answer:

1/ 14^4

Step-by-step explanation:

Rules of Exponents

We know that a^-b = 1/a^b

14^-4  = 1/ 14^4

Answer:

[tex]{14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]

Step-by-step explanation:

To find the answer for this, you have to follow the negative rule of exponents.

That is,

1) If the number with a negative power is in it's numerator, the number with a negative exponent should be put to the denominator and make the power positive.

2) If the number with a negative power is in it's denominator, the number with a negative exponent should be put to the numerator and make the power positive.

Here, we have follow the rule 1.

Ex:

[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]

Accordingly, let us find the answer for the question.

[tex] {14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]

Let x1, x2, x3,x4,x5 be 5 nos in increasing order.

Median of 5 nos =[(5-1)/2 +1 ] th value =

3rd value = 8

x3 = 8 ........(0)

Range = Max - Min = x5 - x1

x5 - x1 = 11

x5 = 11 + x1. .......(1)

Mean = sum of values/ no. of values

(x1+x2+x3+x4+x5)/5 = 9

x1+ x2 +8 +x4+ 11+x1 = 45 _____(using (1) and (0))

2*x1 + x2 + x4 = 45-8-11

2*x1+ x2 + x4 = 22-------------(2)

Now mode = value that occurs most number of times

Mode = 4. -------(3)

Using (3) in (2) we get

2*x1 + 4 + 4 = 22

2*x1 = 14

x1 = 7

From (1)

x5 = x1+ 11 = 7+11= 18

So

x1 = 7, x2 = 4, x3 = 8, x4 = 4, x5 = 18

Answer:

To work out the cost of the council tax bill before the increase, we can use the formula:

Original cost = New cost / (1 + increase percentage)

We know that the council tax bill increased by 5% and the increase is £62. So the new cost of the council tax bill is £62 more than the original cost.

We can use the formula above to find the original cost:

Original cost = £62 / (1 + 0.05)

Original cost = £62 / 1.05

Original cost = £59.04

So the cost of the council tax bill before the increase was £59.04.

Answer:

[tex]72cm^{2}[/tex]

Step-by-step explanation:

9/3=3

12/3=4

(4x9)+(4x6)+(4x3)=

=36+24+12

=[tex]72cm^{2}[/tex]

If the artist makes a triangle from three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. The triangle will not be a right triangle because the values are not Pythagorean triple

Pythagorean triples are b² + a² = c² where b, a and c are all positive integers.

These triples are represented as (b, a, c).

Here, b is perpendicular (or right angel) to a, a is the base and the hypotenuse of the right - angled triangle is labeled .

The most known and smallest triplets are (3, 4, 5).

In the problem, the values  4 inches, 5 inches and 7 inches cannot make a Pythagorean triple since

c² = 4² + 5²

c² = 16 + 25

c² = 41

c = √41 ≠ 7

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The probability of the top card being red and the second card being black is P(A and B) =  0.0650.

The probability that the top card is red and the second card is black can be calculated using the formula P(A and B) = P(A) x P(B)

Let A be the event of the top card being red and B be the event of the second card being black.

The probability of the top card being red is P(A) = (26/52), since there are 26 red cards in the deck.

The probability of the second card being black is P(B) = (26/51), since there are 26 black cards left in the deck after taking away the red card from the top.

Therefore, the probability of the top card being red and the second card being black is P(A and B) = (26/52) x (26/51) = (169/2612) = 0.0650.

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