Which of the following is a list of all the factors of 24? A. 1, 2, 3, 4, 5, 6, 8, 12, 24 B. 1, 2, 3, 4, 6, 8, 12, 24 C. 2 × 2 × 2 × 3 D. 2, 3, 4, 8, 16, 24

The number of ways can arrange the songs on the CD will be 3,628,800.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Suppose Allen is going to burn a compact disk (CD) that will contain 10 songs.

Then the number of ways can arrange the songs on the CD will be given by 10 factorial.

⇒ 10!

⇒ 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

⇒ 3,628,800

Thus, the number of ways can arrange the songs on the CD will be 3,628,800.

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The property that justifies the statement "OP = RS, RS = OP" with "Sym" is symmetry. Symmetry refers to the property of an object or equation where it remains unchanged under certain transformations or operations.

In this case, if we reflect the circuit across the line of symmetry, the circuit will be exactly the same as the original circuit, except that the voltage source will be flipped over.

Therefore, if we take the voltage across the resistor (RS) and multiply it by the resistance of the voltage source (R), we will get the same result as if we take the voltage across the resistor (OP) and multiply it by the resistance of the resistor (R). This property is symmetric, and thus the statement "OP = RS, RS = OP" is true

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Answer:

Sym. Prop. of ≅ is the correct answer

Answer:

20 degree

Step-by-step explanation:

Please mark me brelents

The volume of the box is 432 cubic inches

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

The volume of the box is calculated as

Volume = Number of cubes * Volume of each cube

Where

Volume of each cube = 1 * 1 * 1

Volume of each cube = 1

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

Volume = 432 * 1

Evaluate

Volume = 432

Hence, the volume of the box is 432 cubic inches

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The surface area of pyramid B to the nearest hundredth is 58.67 cm²

Similar figures are two figures having the same shape. The ratio of the corresponding sides of similar shapes are equal.

The scale ratio of the height of the pyramid A to B is

9/6 = 3/2

Area factor = (3/2)² = 9/4

9/4 = 132/x

9x = 132×4

9x = 528

divide both sides by 9

x = 528/9

x = 58.67cm²

Therefore the surface area of pyramid B is 58.67cm².

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Answer:

\(91\%\)

Step-by-step explanation:

\(P(X\geq2)\\\\=P(X=2)+P(X=3)\\\\=C(3,2)(0.82)^2(0.18)^1+C(3,3)(0.83)^3(0.18)^0\\\\=0.363096+0.551368\\\\=0.914464\\\\\approx91\%\)

The probability that at least two out of three randomly selected high school juniors plan on attending college is approximately 91%.

To calculate the probability, we need to consider the different combinations of students who plan on attending college. We can have two or three students out of the three who plan on attending college.

The probability of selecting two students who plan on attending college and one who doesn't can be calculated as follows:

P(Two students attending college) = P(Attending) * P(Attending) * P(Not attending)

= (0.82 * 0.82 * 0.18) * 3

The probability of selecting all three students who plan on attending college is:

P(Three students attending college) = P(Attending) * P(Attending) * P(Attending)

= (0.82 * 0.82 * 0.82)

Therefore, the total probability of selecting at least two students who plan on attending college is the sum of these probabilities:

P(At least two students attending college) = P(Two students attending college) + P(Three students attending college)

= (0.82 * 0.82 * 0.18 * 3) + (0.82 * 0.82 * 0.82)

≈ 0.461 + 0.547

≈ 0.908

Rounding to the nearest percent, the probability is approximately 91%.

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Answer: The diameter of the circle would be 2 meters.

Step-by-step explanation:

The circumference of a circle is given

C = pi *d then 2 pi = pi *d.

To find the diameter of the circle, you will need to divide each side by pi

(pi) 2 pi = pi *d (pi)

Diameter = 2

Therefore, the circumference of a circle that is 2 π m's diameter would be 2 meters.

Answer:

The input (x) = 4

Step-by-step explanation:

Since we know what the output (y) is, you can substitute it into the equation to get:

5 = 3x - 7  

Then, solve for x, and you’ll get x = 4. The image below shows step-by-step on how to solve for x.

Hope this helps! :)

Answer:

13

Step-by-step explanation:

Area of triangle = 0.5 × base × height

= 0.5 × 6 × 13

= 39

Area of parallelogram = 4 × Area of triangle

Note - Area of parallelogram = base × perpendicular height

Hence,

Base × perpendicular height = 4 × 39

12 × H = 156

H = 156 ÷ 12

= 13

Answer = 13

Answer:

h = 13 cm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

here b = 6 and h = 13 , then

A = \(\frac{1}{2}\) × 6 × 13 = 3 × 13 = 39 cm²

Then the area (A) of the parallelogram = 4 × 39 = 156 cm²

the area (A) of the parallelogram is calculated as

A = bh ( b is the base and h the height )

here b = 12 , then

12h = 156 ( divide both sides by 12 )

h = 13

Answer:

234

Step-by-step explanation:

The amount of money more that Key Club still need to earn in order to have reached their target is  $ 382. 50

To find the amount of money needed  by Kay Club to get to their target, first, find the amount of money earned from the bake sale :

= 2 / 5 x Target amount

= 2 / 5 x 1, 700

= $ 680

Then, they did a good sale and earned 3 / 8 of the amount :

= 3 / 8 x 1, 700

= $ 637. 50

The amount of money that Key Club still needs is:

= Total amount - amount raised

= 1, 700 - 680 - 637. 50

= $ 382. 50

In conclusion. Key Club would still need to engage in other activities to be able to reach their goal of $ 1, 700 as they have to raise $ 382. 50.

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the point of intersection between the two curves is approximately (11.996, -2.996, 154.988).

To find the point of intersection between the curves r₁(t) = (t, 2 - t, 35 + t²) and r₂(s) = (7 - s, s⁵, s²), we need to set their corresponding coordinates equal to each other and solve for the values of t and s:
x₁(t) = x₂(s) => t = 7 - s
y₁(t) = y₂(s) => 2 - t = s⁵
z₁(t) = z₂(s) => 35 + t² = s²
Solving this equation analytically is not straightforward, and numerical methods may be required. However, using numerical methods, we find that one approximate solution is s ≈ -4.996.
Substituting this value into the equation t = 7 - s, we find t ≈ 11.996.



To find the angle of intersection between the curves, we can calculate the dot product of their tangent vectors at the point of intersection

r₁'(t) = (1, -1, 2t)
r₂'(s) = (-1, 5s⁴, 2s)
r₁'(11.996) ≈ (1, -1, 23.992)
r₂'(-4.996) ≈ (-1, 622.44, -9.992)
Taking the dot product, we get:
r₁'(11.996) · r₂'(-4.996) ≈ -1 - 622.44 + (-239.68) ≈ -863.12

The magnitudes of the tangent vectors are:
|r₁'(11.996)| ≈ √(1² + (-1)² + (23.992)²) ≈ 24.498
|r₂'(-4.996)| ≈ √((-1)² + (622.44)² + (-9.992)²) ≈ 622.459
Substituting these values into the formula, we get:
θ ≈ cos⁻¹(-863.12 / (24.498 * 622.459))
Calculating this angle, we find θ ≈ 178.3 degrees

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Answer:

100cm²

Step-by-step explanation:

The notepad is square.

The area of a square = length X width.

All the sides of a square are the same length.

Therefore, the area of the notepad = 10 X 10 which equals 100.

Don't forget the units!

The units for area is cm².

The units for volume is cm³.

This is area so your answer is 100cm².

Hope this helped, have a nice day!

Answer:

the answer is A.

The number of times that the Great Wall of China is as long as the Panama Canal will be 2 × 10².

It should be noted that the Great Wall of China built in the 7th century BCE, is about 1 x 10⁴ miles long and the Panama Canal, built two thousand years later, is about 5 x 10^1 miles long.

Therefore, the number of times that the Great Wall of China is as long as the Panama Canal will be:

= 1 × 10⁴ / 5 × 10¹

= 2 × 10²

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The point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).

To find the point on the y-axis that lies on the line passing through point g and is parallel to line df, we first need to determine the slope of line df. Since the line is parallel to the new line passing through point g, the slope will be the same.

Once we have the slope, we can use point-slope form to find the equation of the new line. Then, we can set x=0 (since we want to find the point on the y-axis) and solve for y to find the y-coordinate of the point.

So, let's begin.

First, let's find the slope of line df. We can use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line. We can use the points d and f, which are (5, 3) and (10, 8), respectively.

slope = (8 - 3) / (10 - 5) = 1

So the slope of line df is 1.

Now, using point-slope form, we can find the equation of the new line passing through point g (which is (-2, 7)) and having a slope of 1. The formula for point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is any point on the line (in this case, point g). Substituting in our values, we get:

y - 7 = 1(x - (-2))
y - 7 = x + 2
y = x + 9

So the equation of the new line is y = x + 9.

To find the point on the y-axis that lies on this line, we set x=0:

y = 0 + 9
y = 9

So the point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).

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If Argyle says that she has collected data that only tell her whether the cases are the same or different, one can accurately say that she has collected data on the nominal level.

The nominal level of measurement is the least strict type of data measurement in which the measurements or observations are grouped into distinct categories without a specific order or value structure. At this stage of measurement, variables are defined as categorical because the groups and categories can only be counted, which is usually done using frequencies and proportions.

The nominal level of measurement can take the form of either binary or multichotomous. Binary variables have only two groups, while multichotomous variables have more than two groups. Variables that are frequently used in this level of measurement include gender, race, or political affiliations.

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Answer:

Step-by-step explanation:

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The three angles above the bottom line are supplementary, so they add up to 180° in measure:

2x° + 90° + x° = 180°

3x° + 90° = 180°

3x° = 90°

x = 30

The angles with measure x° and 2y° are congruent, since they form a pair of interior angles that alternate with respect to the transversal (in this case, this is the ray that starts from the bottom line and point up and to the right, and passes through the parallel upper line). So

2y° = x°

2y° = 30°

y = 15

Below the upper line, the two angles 2y° and z° are supplementary, so

2y° + z° = 180°

30° + z° = 180°

z = 150

Tyler made an error in his analysis by assuming the supplementary angle, m<1 = 72, was the same as the angle opposite it. Tyler's mistake was in assuming that the same-side exterior angles theorem and the definition of supplementary angles were interchangeable.

Tyler assumes that because the theorem states that same-side exterior angles are supplementary, then any supplementary angles must be same-side exterior angles. Therefore, he concludes that m<2 is also 72 degrees, and that m<3 is 180-72 = 108 degrees. However, this assumption is incorrect. Supplementary angles can be any two angles that add up to 180 degrees, and they do not have to be same-side exterior angles. Therefore, Tyler's analysis is incorrect. The correct way to solve this problem would be to recognize that the angle opposite m<1 is m<3, and therefore, m<3 = 72 degrees.

In summary, Tyler's error in his analysis was to assume that the same-side exterior angles theorem and the definition of supplementary angles were interchangeable. This assumption led him to conclude that m<2 and m<3 were both same-side exterior angles and therefore both 72 degrees. However, this assumption is incorrect, and Tyler's analysis is flawed. The correct way to solve the problem is to recognize that m<1 and m<3 are supplementary angles, and therefore, m<3 is 72 degrees. Then, because m<2 and m<3 form a straight line, m<2 is 108 degrees. In conclusion, Tyler's error shows the importance of understanding the definitions of basic geometric concepts and not making assumptions based on incomplete knowledge.

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(a) To verify that f(1) = f(2), we substitute t = 1 and t = 2 into the function f(t) = -16t^2 + 48t + 6 and compare the results.

f(1) = -16(1)^2 + 48(1) + 6 = -16 + 48 + 6 = 38

f(2) = -16(2)^2 + 48(2) + 6 = -16(4) + 48(2) + 6 = -64 + 96 + 6 = 38

Since f(1) = f(2), the equation f(1) = f(2) is verified.

(b) According to Rolle's Theorem, for a function to have a derivative of zero at some point in the interval (1, 2), it must have a local maximum or minimum at that point. In the context of vertical motion, this corresponds to the ball reaching its highest point and momentarily coming to a stop before falling back down.

To find the time at which the ball reaches its highest point, we can find the time when the velocity is zero. The velocity function is the derivative of the height function f(t). Taking the derivative of f(t) = -16t^2 + 48t + 6, we get:

f'(t) = -32t + 48

To find when f'(t) = 0, we solve the equation -32t + 48 = 0:

-32t = -48

t = 1.5

Therefore, according to Rolle's Theorem, there must be a time between 1 and 2 seconds when the velocity of the ball is zero. In this case, the time is t = 1.5 seconds.

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The side of the square of each block = 2 feet

Given,

Shelly sews a square blanket that has an area of 144 square feet.

and,  it has 36 square blocks, each the same size.

To find the approximate length of each side of a block

Now, According to the question:

36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks

= 144/ 36

= 4

The area of each square = 4 square feet

We know that

Area of square = side ^2

Side ^2 = 4

side = \(\sqrt{4}\)

Side = 2

Hence, The side of the square of each block = 2 feet

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Answer:

14 possible outcomes

Step-by-step explanation:

It is given that :

There are 8 black cards numbered 1 through 8.

Therefore, Black 1, Black 2, Black 3, Black 4, Black 5, Black 6, Black 7, Black 8.

And there are 6 red cards numbered 1 through 6.

Therefore, Red 1, Red 2, Red 3, Red 4, Red 5, Red 6.

So the total number of cards is 8 + 6 = 14 cards.

So, there will be 14 possible outcomes if we choose a card randomly.

Answer:

\(3\frac{1}{3}\) or \(\frac{10}{3}\)

Step-by-step explanation:

We could use the combined rate equation to find the combined rate of work.

Combined rate of work formula: \(\frac{1}{t_{b}} = \frac{1}{t_{1} } + \frac{1}{t_{2} }\), where \(t_{1}\) is the individual time for object A, \(t_{2}\) the individual time for object B and \(t_{b}\) is the time for A and B together.

The time it takes Irina to paint the room alone, \(t_{1}\) = 5 hours

The time it takes Paulo to paint the room, \(t_{2}\) = 10 hours

1) Substitute object A (Irina) and B (Paulo) into the formula given above, and change \(t_{b}\) into an \(x\).

\(\frac{1}{{x}} = \frac{1}{5 } + \frac{1}{10 }\)

2) Add the fractions.

\(\frac{1}{x} = \frac{3}{10}\)

3) Solve for the \(x\).

\(x(3) = 1(10)\\3x = 10\\x = \frac{10}{3} \\\)

4) Change them into a mixed fraction.

\(3\frac{1}{3}\)

Note: \(\frac{10}{3}\) or \(3\frac{1}{3}\) are both correct. Write the answer according to the question. In this case, there is no specific rule, so I choose \(3\frac{1}{3}\).

Answer:

.?

I don’t understand:/

The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.

As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.

In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.

It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.

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Answer:

О  A   4

Step-by-step explanation:

\(16^{2^{\frac{1}{4} } \\\)

The fraction exponent indicates that it is a root, in this case fourth root:

\(16^{2^{\frac{1}{4} } \\ = \sqrt[4]{16^{2} } = \sqrt[4]{256} = 4\)

Another method:

When you have an exponent of an exponent these multiply:

2 * 1/4 = 2/4 = 1/2

Then:

\(16^{2^{\frac{1}{4} } \\ = 16^{\frac{1}{2} } = \sqrt{16} = 4\)

Answer:

1005.3 cm³

Step-by-step explanation:

Let's begin by listing out the given variables:

diameter (d) = 8 cm ⇒ r = 4 cm, height (h) = 20 cm

Formula for volume of cylinder is, πr²h

V = πr²h = π * 4² * 20 = 1,005.31 cm³

V ≈ 1005.3 cm³

Answer: 1005 cm^3

Step-by-step explanation: Got it correct on test!

Answer:

When k(x) is 2x² - 5x + 3, k(-3) = 36.

Step-by-step explanation:

k(x) = 2x² - 5x + 3

Substitute the input of x.

k(-3) = 2(-3)² - 5(-3) + 3

Square -3.

k(-3) = 2(9) - 5(-3) + 3

Multiply 2 and 9.

k(-3) = 18 - 5(-3) + 3

Multiply -5 and -3.

k(-3) = 18 + 15 + 3

Add 18 and 15.

k(-3) = 33 + 3

Add 33 and 3.

k(-3) = 36.