We need to simplify it. How would I do this

Para entender mejor esta función, podemos expandirla y simplificarla:

f(x) = (x+2)(-x+6)

f(x) = [tex]-x^2 + 4x + 12[/tex]

Esta es una función cuadrática, lo que significa que tiene la forma de una parábola. El término cuadrático ([tex]-x^2[/tex]) hace que la parábola tenga una concavidad hacia abajo, lo que significa que el valor máximo de la función se encuentra en el vértice de la parábola.

Podemos encontrar el valor del precio de venta que maximiza la ganancia utilizando la fórmula x = -b/(2a), donde "a" es el coeficiente del término cuadrático y "b" es el coeficiente del término lineal.

En este caso, a = -1 y b = 4, por lo que:

x = -4/(2-1)

x = -4/-2

x = 2

Por lo tanto, el precio de venta que maximiza la ganancia es de 2 por unidad. Si se venden las unidades a este precio, la ganancia total sería de:

f(2) = [tex]-2^2 + 4(2) + 12[/tex]

f(2) = -4 + 8 + 12

f(2) = 16 dólares

Es importante tener en cuenta que la función f(x) también puede ser utilizada para calcular la ganancia total para cualquier precio de venta "x". Por ejemplo, si se venden las unidades a 3 por unidad, la ganancia sería:

f(3) = [tex]-3^2 + 4(3) + 12[/tex]

f(3) = -9 + 12 + 12

f(3) = 15 dólares

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Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

Using the standard normal distribution, we find that approximately 73.8% of workers receive wages between $4.75 and $5.69 per hour. Using the inverse of the standard normal distribution, we find that the highest 5% of hourly wages are greater than approximately $6.09.

Using a standard normal distribution table or calculator with a mean of 5.25 and a standard deviation of 0.60, we can find that approximately 79.42% of workers receive wages between $4.75 and $5.69 per hour.

Using a standard normal distribution table or calculator, we can find the z-score corresponding to the highest 5% of wages, which is approximately 1.645.

Then, we can solve for x in the equation z = (x - μ) / σ, where z is the z-score, μ is the mean of 5.25, and σ is the standard deviation of 0.60. This gives us x = zσ + μ, which is approximately $6.09 per hour. Therefore, the highest 5% of hourly wages are greater than $6.09 per hour.

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a) Classroom:

Perimeter = 2(length + breadth) = 2(10m + 8m) = 36m

Area = length x breadth = 10m x 8m = 80m^2

Volume = length x breadth x height = 10m x 8m x 3m = 240m^3

b) Box:

Perimeter = 2(length + breadth) = 2(40cm + 25cm) = 130cm

Area = 2(length x breadth + length x height + breadth x height) = 2(40cm x 25cm + 40cm x 30cm + 25cm x 30cm) = 41500cm^2

Volume = length x breadth x height = 40cm x 25cm x 30cm = 30000cm^3

c) Cabinet:

Perimeter = 2(length + breadth) = 2(80cm + 70cm) = 300cm

Area = 2(length x breadth + length x height + breadth x height) = 2(80cm x 70cm + 80cm x 2m + 70cm x 2m) = 12640cm^2

Volume = length x breadth x height = 80cm x 70cm x 2m = 112000cm^3

Note: It's important to use consistent units in calculations. In this case, I converted the dimensions to a common unit (meters or centimeters) before performing the calculations.

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Answer:52.5

Step-by-step explanation:

Multiply

the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

How to solve the question?

To determine whether a triangle can be formed using the given side lengths, we need to apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Let's check each option:

A. XY = 11 mm, YZ = 12 mm, XZ = 18 mm

To form a triangle, we need to check whether the sum of any two sides is greater than the third side. Let's check:

XY + YZ = 11 mm + 12 mm = 23 mm > XZ = 18 mm

YZ + XZ = 12 mm + 18 mm = 30 mm > XY = 11 mm

XY + XZ = 11 mm + 18 mm = 29 mm > YZ = 12 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

B. XY = 16 mm, YZ = 12 mm, XZ = 23 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 12 mm = 28 mm > XZ = 23 mm

YZ + XZ = 12 mm + 23 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 23 mm = 39 mm > YZ = 12 mm

Again, all the combinations are greater than the third side, so a triangle can be formed with these side lengths.

C. XY = 16 mm, YZ = 17 mm, XZ = 18 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 17 mm = 33 mm > XZ = 18 mm

YZ + XZ = 17 mm + 18 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 18 mm = 34 mm > YZ = 17 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

D. XY = 11 mm, YZ = 12 mm, XZ = 28 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 11 mm + 12 mm = 23 mm < XZ = 28 mm

YZ + XZ = 12 mm + 28 mm = 40 mm > XY = 11 mm

XY + XZ = 11 mm + 28 mm = 39 mm > YZ = 12 mm

The first combination is less than the third side, so a triangle cannot be formed with these side lengths.

Therefore, the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

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A statement that is best supported by the data in the box plots include the following: H. the interquartile range of the data for the community college is greater than the interquartile range of the data for the university.

In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.

Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of university = Q₃ - Q₁

Interquartile range (IQR) of university = 15 - 9

Interquartile range (IQR) of university = 6.

For the community college, we have;

Interquartile range (IQR) = 15 - 6

Interquartile range (IQR) = 9.

Therefore, 9 is greater than 6.

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In a normal distribution with a mean of 75 and a standard deviation of 5, the approximate value of the median is 75 and approximately 68% of the scores fall between 70 and 75 while 95.45% of the scores lie between two standard deviations below and two standard deviations above the mean.

Standard deviation is a measure of how much variation exists in a set of data. It is used to measure the spread of the data, or how far the data is dispersed from the average. A low standard deviation indicates that data points are close to the average, while a high standard deviation means that the data points are spread out over a wide range of values. Standard deviation is calculated by taking the square root of the variance of the data.

1) The approximate value of the median in a normal distribution with a mean of 75 and a standard deviation of 5 is 75.

2) Approximately 68% of the scores fall between 70 and 75. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of 70 is 0.5 and the cumulative probability of 75 is 0.8413, so the difference of 0.3413 gives the approximate percentage of scores between 70 and 75.

3) Approximately 95.45% of the scores would lie between two standard deviations below and two standard deviations above the mean. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of two standard deviations below the mean is 0.02275 and the cumulative probability of two standard deviations above the mean is 0.97725, so the difference of 0.9545 gives the approximate percentage of scores between two standard deviations below and two standard deviations above the mean.

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Complete questions as follows-
Given a normal distribution with a mean of 75 and a standard deviation of 5, answer the following questions:

1) What is the approximate value of the median?

2) What percentage of scores fall between 70 and 75?

3) What percentage of the scores would lie between two standard deviations below and two standard deviations above the mean?

Answer:

Answer is 20

Step-by-step explanation:

When two lines intersect each other as a result of that, every opposite angles are equal

so,

6x+20 = 140

6x = 120

x = 120/6

x = 20

Answer:

x = 20

Step-by-step explanation:

Vertically opposite are equal

therefore

6x + 20 = 140

6x = 140-20

6x = 120

6x/6 = 120/6

x = 20

Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar

(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:

Therefore, the blank spaces should be filled as follows:

Translate the solid circle 2 units to the left and 2 units down.

Dilate the solid circle by a scale factor of 2.

(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.

This is because all circles are similar

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Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.

According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.

Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.

In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.

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Hence correct option or expression are D and F.

its branches of mathematics. The  arithmetic deals with numbers and mathematical procedures. Math think how to add, subtract, multiply, and divide two or more  numbers. Shapes are the main focus  in geometry, which involves creating them with various instruments including a compass, ruler,  and pencil. Another fascinating area of study is algebra, where we use numbers and variables to represent the circumstances we encounter every day.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth,  and so forth. You will discover  the formulas, guidelines, characteristics, graphs, derivatives, exponential series, and examples of exponential functions in this article.

use,

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

so,

[tex]\frac{b^{-2} }{b^{-6} } =b^{-2+6}\\=b^{4} or \frac{1}{b^{-4} }[/tex]

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Answer:

Step-by-step explanation:

If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,

(x - 3) (x - 1)

x^2 - x - 3x + 3

x^3 - 4x + 3 = 0

Your answer is 3

Answer: 3 pieces

Step-by-step explanation:First, 6/8 can be converted into fourths by dividing the numerator and the denominator by 2 and we get 3/4. if we want 1/4 slices we divide 3/4 by 1/4 and get 3.

Answer: 207.338[tex]cm^2[/tex] or 66[tex]\pi[/tex]

Step-by-step explanation:

Lateral Area of a cylinder : 2[tex]\pi[/tex](radius)(height)

Surface Area of a cylinder : Lateral Area + 2 (base area)

LA= 48[tex]\pi[/tex]

= 150.79

SA= 150.79 + (2([tex]\pi[/tex]([tex]3^2[/tex])

= 207.338 [tex]cm^2[/tex]

: )))

The long-run fraction of time that there is exactly one lightbulb working (event O) is: 0.228.

Let's use the following notation:

Let W denote the event that both lightbulbs are working,

let O denote the event that one lightbulb is working, and

let B denote the event that both lightbulbs are burnt out.

We are given that when both lightbulbs are working (event W), one of them will go out with probability 0.03.

Therefore, the probability that both lightbulbs will still be working on the next day is 1 - 0.03 = 0.97.

On the other hand, when only one lightbulb is working (event O), it will burn out with probability 0.07, and the other lightbulb is already burnt out.

Hence, the probability of moving from O to B is 1.

We can set up the following system of equations to model the probabilities of being in each state on the next day:

P(W) = 0.97P(W) + 0.5P(O)

P(O) = 0.03P(W) + 0.93P(O) + 1P(B)

P(B) = 0.07P(O)

Note that in the first equation, we use 0.97 because the probability of staying in W is 0.97, and the probability of moving to O is 0.5 (because there are two ways for one of the lightbulbs to go out).

Simplifying the system of equations, we get:

0.03P(W) - 0.5P(O) = 0

-0.03P(W) + 0.07P(O) - 1P(B) = 0

0P(W) - 0.07P(O) + 1P(B) = 0

Solving for P(O), we get:

P(O) = 0.3P(W)

Substituting this into the second equation, we get:

-0.03P(W) + 0.07(0.3P(W)) - P(B) = 0

Simplifying, we get:

P(B) = 0.004P(W)

We also know that the sum of the probabilities of being in each state must be 1:

P(W) + P(O) + P(B) = 1

Substituting the expressions for P(O) and P(B), we get:

P(W) + 0.3P(W) + 0.004P(W) = 1

Solving for P(W), we get:

P(W) = 0.762

Therefore, the long-run fraction of time that there is exactly one lightbulb working (event O) is:

P(O) = 0.3P(W) = 0.228.

Approximately 22.8% of the time, there will be exactly one lightbulb working.

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Answer:

The comparison that is not correct is:

C. -8 > -6

This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.

The other comparisons are correct:

A. 1 > -9 (true, because 1 is greater than -9)

B. 3 < 6 (true, because 3 is less than 6)

D. -3 < 4 (true, because -3 is less than 4)

The reasonableness of the estimate depends on the quality and reliability of the data sources and methodology used to arrive at the estimate.

In order to determine whether 12% is a reasonable estimate of the proportion of all Americans who eat chocolate

frequently, we would need to define what is meant by "frequently."

If we define "frequently" as "at least once a week," then 12% may or may not be a reasonable estimate, depending on

the data source and methodology used to arrive at that estimate.

For example, if the estimate is based on a small sample size or a non-representative sample of the population, then it

may not be a reliable estimate of the true proportion of Americans who eat chocolate frequently. Additionally, if the

estimate is several years old, it may not accurately reflect current trends and habits.

On the other hand, if the estimate is based on a large, nationally representative sample of the population, and is

relatively recent, then 12% could be a reasonable estimate of the proportion of Americans who eat chocolate

frequently.

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Trigonometric functions are used to model relationships between angles and sides of a right triangle. They are particularly useful in solving problems that involve angles, distances, heights, and lengths that are difficult to measure directly.

For example, consider a problem that involves finding the height of a building. By measuring the length of the shadow cast by the building at a particular time of day, the angle of the sun's rays can be calculated using trigonometry. Once the angle is known, the height of the building can be determined using the tangent function.

In contrast, a non-trigonometric function may not be able to model the relationship between the given quantities in such problems, and may not provide an accurate solution. Therefore, when a problem involves angles or distances that are not directly measurable, trigonometric functions are typically the best tool for setting up and solving the problem.

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The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.

If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000

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There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.

To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.

There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
 a) Pennies (P)
 b) Nickels (N)
 c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
 Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.

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The probability of selecting such a permutation is very low, only about 0.31%.

The probability of the event when we randomly select a permutation of the 26 lowercase letters of the English alphabet where 'm' immediately precedes 'n', which immediately precedes 'o' can be calculated as follows:

Firstly, we need to determine the total number of permutations of the 26 letters. Since there are 26 letters in the alphabet, there are 26! ways to arrange them.

Next, we need to determine the number of permutations where 'm' immediately precedes 'n', which immediately precedes 'o'. To do this, we can consider 'mno' as a single unit and then there are 24! ways to arrange the 24 units (23 individual letters and 1 unit of 'mno').

However, there are 3! ways to arrange 'mno' within the unit, so we need to multiply by 3!. Therefore, the total number of permutations where 'm' immediately precedes 'n', which immediately precedes 'o' is 24! x 3!.

Thus, the probability of randomly selecting a permutation where 'm' immediately precedes 'n', which immediately precedes 'o' is:

P = (24! x 3!) / 26!

P ≈ 0.0031 or 0.31%

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The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UF × FS = VF × FT

8(10x - 1) = 9 × 16

80x - 8 = 144

80x = 144 + 8 {collect like terms}

80x = 152

x = 152/80 {divide through by 80}

x = 1.9

FS = 10(1.9) - 1 = 18

Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

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Answer:

19/14

Step-by-step explanation:

6/4+4/8

to solve that multiply the denominator on the left with 8 and the one on the right with 7 to make them equivalent and do the same for the numerator so now its 76/56 so now just simplified as much as possible will be 19/14

Answer:

Take your question 6/7 + 4/8, and find a common denominator. 7 and 8 both go in to 56, so set both denominators to 56.

The question now reads 6/56 + 4/56.

Multiply the numerator by the number of times the denominator was multiplied to get to the common denominator. 8 goes into 56 7 times, and 7 goes into 56 8 times.

Therefor:

7 x 8 = 56, and 8 x 7 = 56.

Now multiply  the numerator by the amount of times the denominator went into the common denominator.

8 x 6 = 48 and 7 x 4 = 28.

So 48/56 and 28/56.

We could then simplify, by dividing both sides by the same number.

12/14

7/14

Then add the numerators only.

That would give us 19/14

Hope that helps, :D.

Answer:

The y-intercept is at (0, 8).

Answer: (0,8)

Step-by-step explanation: The line only touches the Y-axis Once and its on 8

When a researcher uses the Pearson product-moment correlation, two highly correlated variables will appear on a scatter diagram as a tightly clustered group of points that form a linear pattern.

The scatter diagram is a visual representation of the correlation between two variables, where one variable is plotted on the x-axis, and the other variable is plotted on the y-axis. If the two variables have a high positive correlation, then the points on the scatter diagram will form a cluster that slopes upwards to the right.

On the other hand, if the two variables have a high negative correlation, then the points will form a cluster that slopes downwards to the right. The tighter the cluster of points, the higher the correlation between the variables.

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Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:

sin^2(a) + cos^2(a) = 1

sin^2(a) + (-5/9)^2 = 1

sin^2(a) = 1 - (-5/9)^2

sin^2(a) = 1 - 25/81

sin^2(a) = 56/81

Taking the square root of both sides:

sin(a) = ±sqrt(56/81)

Since a is in quadrant III, sin(a) is positive. Therefore:

sin(a) = sqrt(56/81) = (2/3)sqrt(14)

Answer:

Kai is correct and Leila is incorrect. The movie is actually 10,800 seconds long.

Step-by-step explanation:

1 hour = 60 minutes

1 minute = 60 seconds

Therefore, 1 hour = 60 x 60 = 3600 seconds

So, the movie's length in seconds is:

3 hours x 3600 seconds/hour = 10,800 seconds

Leila says the movie is less than 10,000 seconds, which is not correct, since the movie is actually longer than 10,000 seconds.

Kai says the movie is more than 10,000 seconds, which is correct.

Answer:

Step-by-step explanation:

its a rectanlge

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman.

Numbers are mathematical units of measurement and labelling. It is a sign or collection of symbols that are used to represent a quantity, usually a real or integer number.

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman. The idea of combination can be used to arrive to this number.

Calculating the number of possible combinations of a given number of things is done mathematically using the concept of combination. C(n,r) = n! / (r! (n - r)!), where n is the total number of items and r is the number of things to be picked at a time, is the formula used to compute it. In this instance, r is the number of persons to be picked, which is 3, and n is the total number of people to be chosen from the group, which is 18, consisting of 10 males and 8 women.

As a result, there are a total of 10 ways for men and 8 ways for women to form a committee of two men and one woman C(18,3) = 18! / (3! (18 - 3)!) = 18! / (3! 15!) = 1320.

Thus, there are 1320 different methods to create a committee of two men and one woman out of a group of ten men and eight women.

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