A ball is thrown into the air with an initial upward velocity of 48 ft/s. Its height (h) in feet after t seconds is given by the function h=-16t^2+48t+64. After how many seconds will the ball hit the ground?

Answer:

Y= 2m + 6

Step-by-step explanation:

A system of equations that model the situation are e = a - 12 and a + e = 100.

The number of tickets Alberto won is 56 tickets.

The number of tickets Elian won is 44 tickets.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of tickets Alberto won and number of tickets Elian won, and then translate the word problem into an algebraic equation as follows:

Since Alberto won 12 tickets less than Elian, a linear equation that models this situation is given by:

e = a - 12     .....equation 1.

Additionally, when they put their tickets together they have exactly 100 tickets;

a + e = 100     .....equation 2.

By solving the system of linear equations simultaneously, we have:

a + a - 12 = 100

2a = 112

a = 112/2

a = 56 tickets.

For the number of tickets (e) Elian won, we have:

e = a - 12

e = 56 - 12

e = 44 tickets.

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The correct answer is (A) IQR, because Sunny Town is symmetric.

The Interquartile Range (IQR) is a measure of variability that is based on the spread of the middle 50% of the data. It is less affected by extreme values and outliers compared to the range, which is the difference between the highest and lowest values in a dataset.

According to the given information:

In this case, since the data in Sunny Town is symmetric, meaning it is evenly distributed around the center without any skewness, the IQR would be an appropriate measure of variability. The symmetric distribution indicates that the data points are equally distributed on both sides of the central tendency, and the IQR would provide a good measure of the spread of the middle 50% of the data.

On the other hand, if the data in Beach Town was skewed, meaning it is not evenly distributed and has a longer tail on one side, the IQR may not be as reliable, and the range might be affected by extreme values. In such cases, using the range as a measure of variability may not be as accurate.

So, the correct answer is (A) IQR, because Sunny Town is symmetric.

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The possible types of triangles that can be formed with the given side lengths are: equilateral triangles (if all sides are equal), and isosceles triangles (if two sides are equal).

Based on the given side lengths of 2 cm, 3 cm, 4 cm, and 5 cm, the possible types of triangles that can be formed are:

For side length 2 cm:

a) Equilateral triangle: All three sides are equal, so a triangle with side lengths 2-2-2 cm is possible.

For side length 3 cm:

a) Equilateral triangle: All three sides are equal, so a triangle with side lengths 3-3-3 cm is possible.

b) Isosceles triangle: Two sides are equal, so triangles with side lengths 3-3-2 cm and 3-3-4 cm are possible.

For side length 4 cm:

a) Equilateral triangle: All three sides are equal, so a triangle with side lengths 4-4-4 cm is possible.

b) Isosceles triangle: Two sides are equal, so triangles with side lengths 4-4-3 cm and 4-4-5 cm are possible.

For side length 5 cm:

a) Equilateral triangle: All three sides are equal, so a triangle with side lengths 5-5-5 cm is possible.

b) Isosceles triangle: Two sides are equal, so triangles with side lengths 5-5-4 cm are possible.

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True. The question states that ten families were randomly selected and their daily water usage (in gallons) before and after viewing a conservation video was recorded.

The sample mean difference was found to be 4.8 and the corresponding standard deviation 5.25, with differences

calculated as (before - after).

Assuming the data is normally distributed, the resulting 95% confidence interval is (1.04, 8.55).

Since the entire 95% confidence interval is positive (i.e., all values are greater than zero), this indicates that there is a

significant difference between water usage before and after viewing the conservation video.

This provides evidence to suggest that the conservation videos would be effective in reducing water use in the general population.

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The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.

The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.

The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.

Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

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S is a subspace of the vector space V.

For four conditions are satisfied,

The set S is a subspace of C3(1)

The set S is a subspace of Mn(R)

The set S is a subspace of C2(I)

The set S is a subspace of [tex]R^n[/tex]

The set S is not a subspace of P5(R) because it is not closed under scalar multiplication.

If p(x) is a polynomial in S, then 2p(x) may not satisfy the condition. [tex]p(1) > p(0).[/tex]

The set S is a subspace of C3(1).

The differential equation [tex]y\prime\prime\prime + 2y = x^2[/tex] is linear and homogeneous, so the sum of two solutions is also a solution, and a constant multiple of a solution is also a solution.

S is closed under linear combinations.

The set S is a subspace of Mn(R) because it is closed under addition and scalar multiplication.

If A and B are skew-symmetric matrices, then[tex](A + B)^T = A^T + B^T = -A - B = -(A + B), so A + B[/tex]is skew-symmetric. Similarly, if c is a scalar, then [tex](cA)^T = cA^T = -cA, so c A[/tex] is skew-symmetric.

S is a subspace of C2(I) because it is closed under addition and scalar multiplication.

If y1 and y2 are solutions to[tex]y\prime\prime - 4y\prime+ 3y = 0, then y1\prime\prime - 4y\prime + 3y1 = 0[/tex] and [tex]y2\prime\prime - 4y2\prime + 3y2 = 0[/tex].

Adding these equations gives [tex](y1 + y2)\prime\prime - 4(y1 + y2)\prime + 3(y1 + y2) = 0,[/tex] so [tex]y1 + y2[/tex]is also a solution.

Similarly, if c is a scalar, then [tex](cy)\prime\prime - 4(cy)\prime + 3(cy) = c(y\prime\prime - 4y\prime+ 3y) = 0[/tex], so cy is also a solution.

The set S is a subspace of [tex]R^n[/tex]because it is the null space of a fixed matrix A.

The null space of a matrix is always closed under addition and scalar multiplication.

The set S is not a subspace of [tex]R^n[/tex]because it is not closed under addition. If (1, 1, 0) and (0, 2, 1) are in S, then their sum (1, 3, 1) is not in S because. [tex]1 - 4(3) + 1 \neq 3.[/tex]

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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:

It is located at point (-6,-4), and it can reach a distance of 6 units.

Step-by-step explanation:

The equation is a circle equation:

(x-a)²+(y-b)²=r², where a and b are coordinates and r is the radius

We easily see that point a is -6, and point b is -4.

Since the square root of 36 is 6, we see that the radius of the circle is also 6, which is also the signals maximum range.

Hope this helps!

1. The volume of the prism is 950.4m³

2. The volume of the prism is 16110m³

A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;

V = base area × height.

1. Volume of prism = base area × height

base area = l×w

= 11×16

= 176m²

height = 5.4m

v = 176 × 5.4

= 950.4 m³

2. Volume of the prism = base area × height

base area = 25×36 = 900m²

height = 17.9m

Volume = 900 × 17.9m

= 16110 m³

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The two fractions are greater than 3/4 are 4/5 and 7/8

There are infinitely many fractions greater than 3/4, but here are two examples of such fractions:

4/5: To see that 4/5 is greater than 3/4, we can convert both fractions to have a common denominator.

The least common multiple of 4 and 5 is 20, so we can write:

3/4 = 15/20

4/5 = 16/20

Since 16/20 is greater than 15/20, we can conclude that 4/5 is greater than 3/4.

7/8: We can again use the method of finding a common denominator to compare 3/4 and 7/8:

3/4 = 6/8

7/8 = 7/8

Since 7/8 is greater than 6/8, which is equivalent to 3/4, we can conclude that 7/8 is greater than 3/4.

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So the Tohoku earthquake was about 2.25 times more energetic than the Northridge earthquake.

An earthquake is a shaking or trembling of the earth's crust caused by the sudden release of energy in the Earth's lithosphere, usually by the movement of tectonic plates or by volcanic activity. Earthquakes can cause significant damage to buildings and infrastructure, trigger landslides and tsunamis, and have other destructive consequences. They are one of the most powerful and unpredictable natural phenomena on the planet.

In the given question,

The Tohoku earthquake had an energy release equivalent to about 3.6 x 10¹⁴ joules, while the Northridge earthquake had an energy release equivalent to about 1.6 x 10¹⁴ joules. Therefore, the ratio of the energies is:

Tohoku earthquake energy / Northridge earthquake energy = (3.6 x 10¹⁴J) / (1.6 x 10¹⁴ J) = 2.25

So the Tohoku earthquake was about 2.25 times more energetic than the Northridge earthquake.

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Answer:

f

Step-by-step explanation:

thats the explanation

The only statement that is true is b, which states that the quadrilateral is a rectangle.

A quadrilateral is a polygon with four sides and four vertices. The sum of the interior angles of a quadrilateral is always 360 degrees. Quadrilaterals can have sides of different lengths and angles of different measures, giving rise to many different types of quadrilaterals with different properties.

First, we find the lengths of the sides of the quadrilateral:

AB = √[(7-6)² + (-1+4)²] = √10

BC = √[(4-7)² + (0-0)²] = 3

CD = √[(3-4)² + (-3+0)²] = √10

AD = √[(6-3)² + (-4+1)²] = √26

Then, we find the slopes of each pair of opposite sides:

AB: (7-6)/(−1+4) = 1/3

BC: (4-0)/(0-(-1)) = 4/1 = 4

CD: (-3-(-4))/(0-(-3)) = 1/3

AD: (6-3)/(-4-(-1)) = -1/5

Now we can analyze each statement:

a.) Rhombus

A rhombus is a quadrilateral with all sides of equal length. We found that AB = CD and AD ≠ BC, so not all sides are of equal length. Therefore, statement a is false.

b.) Rectangle

A rectangle is a quadrilateral with all angles equal to 90 degrees. We can find the slopes of adjacent sides and check if they are opposite reciprocals:

AB: 1/3

BC: 4

CD: 1/3

AD: -1/5

We can see that AB and CD have slopes of 1/3 and are opposite reciprocals, and BC and AD have slopes of 4 and -1/5, respectively, and are also opposite reciprocals. Therefore, all angles of the quadrilateral are 90 degrees. Also, since AB = CD and AD ≠ BC, the quadrilateral is a rectangle. Therefore, statement b is true.

c.) Square

A square is a special type of rectangle with all sides of equal length. We found that AB ≠ AD, so not all sides are of equal length. Therefore, statement c is false.

d.) None

We have determined that the quadrilateral is a rectangle, so it is not "none". Therefore, statement d is false.

Therefore, the only statement that is true is b, which states that the quadrilateral is a rectangle.

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Answer:

[tex]f(x) = 500( {.89}^{x} )[/tex]

The correct option is - D. (1,5). The solution to the system of equations for the given graph is at (1,5).

A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

For the given graph, the solution of the system of equation is obtained as the point where the lines intersect.

The two lines in the graph intersect at the (1,5). Thus, the solution to the system of equations for the given graph is at (1,5).

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Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.

What is the rate of change?

The rate of change is the amount of change in the output (dependent variable) for a given change in the input (independent variable).

In this case, the input is the number of days ridden, and the output is the cost of transportation for a month.

For Function 1, the cost is $5.50 per day. Therefore, the rate of change is $5.50 per day.

For Function 2, the equation E = 8.25 + 1.50d represents the cost of transportation for a month, where d is the number of days ridden. The rate of change is the coefficient of d, which is $1.50 per day.

Hence, Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.

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Answer:

49

Step-by-step explanation:

3 x 8 - 5 x -5

24+25 = 49

By Pythagoras Hypotenuse for 1.   9.43 , 2.   9.22 , 3.    9.85 , 4.   12.37, 5.   14.87 , 6.   10.63

7. 9.85 ,   8. 13.04 ,  9. 19.85 ,  10.    7.81

The Pythagorean theorem, commonly referred to as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. It declares that the hypotenuse's square, which is the side that is opposite the right angle, is equal to the sum of the squares of the other two sides. In other words, if the hypotenuse is length c and the legs of a right triangle are lengths a and b, then a² + b² = c².

The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the other two sides, can be used to determine the hypotenuse of a right triangle.

This theorem allows us to calculate the hypotenuse value for each of the right triangles presented as follows:

1. a = 5, b = 8

  c = √(a² + b²) = √(5² + 8²) = √(25 + 64) =√(89) ≈ 9.43

2. a = 6, b = 7

  c = √(a² + b²) = √(6² + 7²) = √(36 + 49) = √(85) ≈ 9.22

3. a = 4, b = 9

  c = √(a² + b²) = √(4² + 9²) = √16 + 81) = √(97) ≈ 9.85

4. a = 3, b = 12

  c =√(a² + b²) = √(3² + 12²) = √(9 + 144) = √(153) ≈ 12.37

5. a = 11, b = 10

  c = sqrt(a^2 + b^2) = sqrt(11^2 + 10^2) = sqrt(121 + 100) = sqrt(221) ≈ 14.87

6. a = 8, b = 7

  c = √(a² + b²)= √(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63

7. a = 9, b = 4

  c =√(a² + b²)=√(9² + 4²) = √(81 + 16) = √(97) ≈ 9.85

8. a = 7, b = 11

  c = √(a² + b²)= √(7² + 11²) = √(49 + 121) ≈√(170) ≈ 13.04

9. a=13,b=15

  c=√(a² + b²)=√((13²)+(15²))=√((169)+(225))=√(394))≈19.85

10.a=5,b=6

  c=√(a²+b²)=sqrt((5²)+(6²))=s√((25)+(36))=√(61))≈7.81

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Proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.

Given, mean (μ) = 266 days and standard deviation (σ) = 16 days.

Let X be the length of pregnancies, then X follows the normal distribution with mean (μ) = 266 and standard deviation (σ) = 16.

We need to find the probability that a pregnancy lasts fewer than 276 days i.e. P(X < 276).

To find this probability, we standardize the variable X using the standard normal distribution formula:

z = (x - μ) / σ

where z is the standard normal random variable.

Substituting the given values, we get:

z = (276 - 266) / 16 = 0.625

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being less than 0.625 is approximately 0.7340.

Therefore, the proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.

Explanation: This means that out of 100 pregnancies, around 73 pregnancies will last fewer than 276 days.

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The sample variances is calculated by option b, which is the sum of all squared differences between actual values and the overall mean divided by the total number of observations less one.

The sample variance is calculated by the sum of all squared differences between actual values and the overall mean divided by the total number of observations less than one.

The sample variance is a measure of the spread of a sample data set. It measures how far each value in the set is from the mean of the set. The formula for the sample variance involves taking the sum of the squared differences between each data point and the mean, and then dividing that sum by the total number of observations minus one. Dividing by the number of observations minus one instead of just the number of observations is known as Bessel's correction and is used to correct for bias in the sample variance calculation. The resulting value represents the average squared deviation from the mean, and is often used as an estimate of the population variance. Therefore, the sample variance is calculated by the sum of all squared differences between actual values and the overall mean divided by the total number of observations less than one.

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There are 12,620,256 different combinations of 31 balloons that can be chosen from the store's inventory of 8 colors, each with at least 31 balloons.

We can use the method of example 9.6.2, which involves using the combination formula. We know that there are 8 colors of balloons and at least 31 of each color. We have 8 options for the first balloon, 8 options for the second balloon, and so on, for a total of 8 options for each of the 31 balloons.

Using the combination formula, we can calculate the number of different combinations of 31 balloons that can be chosen as follows:

[tex]nCr = n! / (r! \times (n-r)!)[/tex]

where n is the total number of options (in this case, 8), and r is the number of items we are choosing (in this case, 31).

Plugging in these values, we get:

[tex]8C31 = 8! / (31! \times (8-31)!)[/tex]

[tex]= 8! / (31! \times (-23)!)[/tex]

= 87654321 / (313029...9(-23)(-24)(-25)...(-52))

= 12620256

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Therefore, the length of EG is 54 in parallelogram EFGH that is option (1).

A parallelogram is a four-sided flat shape with opposite sides parallel to each other. This means that the opposite sides of a parallelogram are always equal in length, and the opposite angles are also equal.

Here,

If EJ is equal to JG, then we can set their expressions equal to each other:

5x - 3 = 3x + 9

Solving for x, we get:

2x = 12

x = 6

Now that we know the value of x, we can find the length of EJ:

EJ = 5x - 3

= 5(6) - 3

= 27

Since EJ = JG and opposite sides of a parallelogram are equal in length, we know that:

HG = EJ

= 27

Similarly, we can find the length of EF:

EF = JG

= 3x + 9

= 3(6) + 9

= 27

And we know that:

EG = EF + HG

= 27 + 27

= 54

Therefore, the length of EG is 54.

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The correct answer to the given problem is choice B - No.

Jace's earnings are not proportional to the number of hours that he works  because if he worked twice as many hours, he would earn twice as much but he is not earning twice the amount.

Jace's earnings are not proportional to the number of hours that he works. Proportional means that one quantity is a constant multiple of the other. In this case, if Jace's earnings were proportional to the number of hours he works, we would expect that if he worked twice as many hours, he would earn twice as much. However, we can see from the table that this is not the case.

For example, when Jace works 1 hour, he earns $20, but when he works 2 hours, he earns $30, which is not double his earnings for 1 hour of work.

Therefore, Jace's earnings are not proportional to the number of hours that he works.

Hence, the correct option is "B".

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The radius of the circle with a circumference of 15 ft is approximately

7.5 ft.

We have,

The circumference of a circle is the distance around its boundary. It is calculated by multiplying the diameter of the circle by π (pi), which is approximately 3.14159.

The formula for the circumference of a circle is:

Circumference = 2 π radius

To find the radius of a circle, we can rearrange the formula and solve for the radius:

Radius = Circumference / (2 π)

In this case, the given circumference is 15 ft.

Plugging this value into the formula:

Radius = 15 ft / (2 π)

Simplifying further:

Radius ≈ 7.5 ft

Therefore,

The radius of the circle with a circumference of 15 ft is approximately

7.5 ft.

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There are 15 different possibilities for the three whole numbers whose product is 120.

To find the different possibilities for the three whole numbers, we need to find all the ways we can multiply three whole numbers together to get 120, which is the product.

We can start by listing out the factors of 120:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

From this list, we can start trying out combinations of three numbers that multiply to 120. For example:

1 x 1 x 120 = 120
1 x 2 x 60 = 120
1 x 3 x 40 = 120
1 x 4 x 30 = 120
1 x 5 x 24 = 120
1 x 6 x 20 = 120
1 x 8 x 15 = 120
2 x 3 x 20 = 120
2 x 4 x 15 = 120
2 x 5 x 12 = 120
2 x 6 x 10 = 120
3 x 4 x 10 = 120
3 x 5 x 8 = 120
4 x 5 x 6 = 120

So there are 15 different possibilities for the three whole numbers that multiply to 120.
To find the different possibilities for the three whole numbers whose product is 120, we need to find the combinations of factors of 120.

Step 1: Find the prime factorization of 120.
[tex]120 = 2*2*2*3*5 (2^3 * 3 * 5)[/tex]

Step 2: Identify the possible factors.
Using the prime factors, we can generate the different whole number factors for 120:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Step 3: Find the possible combinations of three whole numbers.
1. 1 × 1 × 120
2. 1 × 2 × 60
3. 1 × 3 × 40
4. 1 × 4 × 30
5. 1 × 5 × 24
6. 1 × 6 × 20
7. 1 × 8 × 15
8. 1 × 10 × 12
9. 2 × 2 × 30
10. 2 × 3 × 20
11. 2 × 4 × 15
12. 2 × 5 × 12
13. 2 × 6 × 10
14. 3 × 4 × 10
15. 3 × 5 × 8

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Set of factors can be rearranged in six different ways, there are actually 60 possible ways to arrange the factors into three numbers.

The possible combinations of three whole numbers that result in a product of 120.

One way to approach this is to list all the factors of 120 and then group them into sets of three.

Another method is to use prime factorization.

120 as a product of its prime factors: 2 x 2 x 2 x 3 x 5.

The possible combinations of three factors, we can use a combination formula.
The formula for the number of combinations of n items taken r at a time is:

[tex]nCr = n! / (r! \times (n-r)!)[/tex]
In our case, n = 5 (the number of prime factors), and r = 3 (the number of factors we want to choose).

So, the number of possible combinations is:
[tex]5C3 = 5! / (3! \times 2!) = (5 \times 4 \times 3) / (3 \times 2) = 10[/tex]
There are 10 different possibilities for the three whole numbers that multiply to 120.

These are:
[tex][tex]2 \times 2  \times 30, 2  \times 3  \times 20, 2  \times 4 \times 15, 2  \times 5  \times 12, 2  \times 6  \times 10, 3  \times 4  \times 10, 3  \times 5  \times 8, 4  \times 5  \times 6, 3  \times 2  \times 20, and  5  \times 2  \times 12.[/tex][/tex]
The order of the factors does not matter, so[tex]2 \times 3 \times 20[/tex] is the same as[tex]3 \times 2 \times 20[/tex].

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