The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50 + 10 log x. Suppose each of the x objects increases its sound power by 10 decibels, so that the new total sound power, in decibels, is given by the function g(x) = f(x) + 10.

The correct answer is option 4: A1, B2, C2

A1: The force of friction acting on the ladder is given by:

f_friction = µ * N

where µ is the coefficient of static friction and N is the normal force acting on the ladder, which is equal to the gravitational force acting on the ladder.

B2: The gravitational force acting on the ladder can be expressed as:

f_gravity = m * g

where m is the mass of the ladder and g is the acceleration due to gravity.

C2: The component of the gravitational force acting parallel to the wall can be expressed as:

f_parallel = f_gravity * sin(θ)

where θ is the angle between the ladder and the wall.

The ladder will remain stationary as long as the force of friction acting on it is equal to or greater than the component of the gravitational force acting parallel to the wall. Setting these two forces equal to each other, we get:

f_friction = f_parallel

µ * N = m * g * sin(θ)

The smallest angle θ for which the ladder remains stationary is given by:

sin(θ) = µ * N / (m * g)

θ = sin^-1 (µ * N / (m * g))

Note that the value of µ * N / (m * g) must be less than or equal to 1 for the ladder to remain stationary.

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Answer:

Below

Explanation:

Hz is   cycles per second....each cycle is 2 pi

  so multiply Hz * 2 pi to get R/s

example

12 Hz          12 * 2pi = 24 pi  rad/s  = 75.4 Rad/s

The EROI system of evaluating energy exploitation from various sources is based upon the ratio of energy output to energy input in the extraction process

The EROI system evaluates the efficiency of energy exploitation by comparing the amount of energy obtained from a given source to the amount of energy required to extract it. In mathematical terms, the EROI ratio can be expressed as follows:

EROI = Energy output / Energy input

The energy output refers to the amount of energy obtained from a particular source, such as oil or wind.

The higher the EROI ratio, the more efficient the energy source is, as it means that more energy is being produced for every unit of energy input.

In conclusion, the Energy Return on Investment (EROI) system provides a useful tool for evaluating the efficiency of different energy sources by comparing the amount of energy obtained to the amount of energy required to extract it.

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Answer: A gravitational pull is keeping the ball in place and not letting it go flying into the air. so simple answer is gravity

The time period is 0.3 s and frequency is 3 Hz

Step 1 :

Given:

No. of cycles N = 24

Total time take t = 8 s

Step 1 : Calculating the frequency:

The frequency of a wave or oscillation is defined as the number of cycles or completed alternations per unit time.

f = N/t

f = 24/8

f = 3 Hz

Step 2: Calculating the time period:

Frequency and time period are inversely proportional.

The amount of time it takes for something to complete one oscillation is called its time period.

Time period = 1/Frequency

Time period = 1/3 = 0.3 s

So, the time period is 0.3 s and frequency is 3 Hz.

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A 25-foot ladder is set against the side of a house so that it reaches up to 15 feet. If Damian grabs the ladder at its base and pulls it 3 feet farther from the house, the distance from the side of the house to which the ladder reaches now is 9.8m.

The total length of the ladder is 25m. The distance the ladder is set up against the side of the house is 15m.

According to the image, apply Pythagoras' theorem, we get,

(25)² = (15)²+(a)²

a²=(25)²-(15)²

a²=625-225 =400

a=[tex]\sqrt{400}[/tex]

a= 20m.

Now, if Damian grabs the ladder at its base and pulls it 3 feet farther from the house, so the total base is (20+3) = 23m.

Applying Pythagoras' theorem again, we get

(25)² = (23)²+(a)²

a²=(25)²-(23)²

a²=625-529 =96

a=[tex]\sqrt{96}[/tex]

a= 9.8m.

The length to which the ladder reaches now is 9.8m.

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Answer:

5.3 x 10^13 N.

Explanation:

The force of gravity between two objects can be calculated using the equation:

F = G * (m1 * m2) / d^2

where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects, and d is the distance between their centers.

To calculate the average force of gravity between Pluto and the Sun, we need to know their masses and the average distance between them.

Pluto has a mass of approximately 1.309 x 10^22 kg, and the average distance between Pluto and the Sun is about 5.9 x 10^9 m.

Plugging these values into the equation, we get:

F = 6.67 x 10^-11 N m^2/kg^2 * (1.309 x 10^22 kg * 1.989 x 10^30 kg) / (5.9 x 10^9 m)^2

F = 5.3 x 10^13 N

So the average force of gravity between Pluto and the Sun is approximately 5.3 x 10^13 N.

Answer:

Uniform Circular Motion:

When a car goes around a circular curve, the velocity of the car definitely changes because of the change in the direction of the car. However, the speed of the car does not necessarily change and circular motion can be sustained by a constant speed. Explanation: i don't know dawg :)

A millimeter (mm) is made up of 1,000 micrometers (µm). That is, one millimeter equals 1,000 micrometers or [tex]10^{-3}[/tex] meters.

Micrometers are typically used to measure very tiny distances, notably in microscopy, whereas millimeters are commonly used to measure greater distances, such as an object's length or breadth.

It is crucial to note that the micrometer is also known as a micron, therefore the conversion may be represented as 1,000 microns in a millimeter at times. Regardless matter whether you use micrometers or microns, the conversion is the same: a millimeter has 1,000 of them.

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The force exerted on a can that is whirled overhead by a string in a circular path is a centripetal force, and its direction is toward the center of the circle.

What is the force exerted and the direction of center of circle?

When you whirl a can overhead by a string in a circular path, the direction of the force exerted on the can is toward the center of the circle. This force is known as the centripetal force and is required to keep the object moving in a circular path.

The centripetal force is given by the equation:

F = m * a

where F is the centripetal force, m is the mass of the object (the can), and a is the centripetal acceleration, which is given by:

a = v^2 / r

where v is the velocity of the object and r is the radius of the circular path.

In this case, the force exerted on the can is the tension in the string pulling the can toward the center of the circle. The direction of the force is always towards the center of the circle, regardless of the direction of motion of the object.

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.

Answer: Towards the center of the circle

Explanation: Whirling a can overhead makes it go towards the center.

True, A frequency distribution usually has equal bin widths.

What is frequency distribution?

In frequency tables or charts, frequency distributions are displayed. The exact number of observations that fall into each range may be seen in frequency distributions, as well as the proportion of observations that do. The distribution in the latter case is known as a relative frequency distribution.

What is frequency distribution formula?

The formula for the square root of the frequency distribution is expressed as: C = n, where n is the total number of observations of the data that has been distributed. C (number of classes) = 1 + 3.3 logn, where (log is base 10)

Hence True is a correct answer.

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The number of mutations that will occur in the S.aureus population in foot wounds is 0.0336.

The natural habitat of S. aureus in humans is in the area of ​​the skin, nose, mouth, and large intestine, where under normal immune system conditions, S. aureus is not pathogenic (normal human microflora).

Bacterial genes can mutate quickly. These mutations can make bacteria reproduce faster, become stronger, and kill. The mutation can also be accelerated by the excessive use of antibiotics. As a result, bacteria also become more resistant to antibiotics.

Generations are produced in 12 hours:

12*60/30 = 24 generations.

Mutations in 1 generation are 0.0028.

Then the mutation after 12 hours is 12* 0.0028 = 0.0336

Your question is incomplete but most probably your full question was:

Staphylococcus aureus is a bacterium that can cause infections in broken skin. A single S. aureus cell gets into a wound on someone's foot. An S. aureus cell divides by binary fission approximately every 30 minutes. S. aureus has 2.8 x 106 base pairs in its genome. Mutations occur at a rate of 1 per 1010 base pairs per generation. Therefore, approximately 0.0028 mutations will occur per cell in the population. At the end of 12 hours, how many mutations will be present in the population of S. aureus in the wound on the foot?

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The answer to this equation is not possible to calculate without knowing the value of x and y.

An equation is a mathematical statement that expresses the equality of two expressions. Equations are used to find unknown values, such as the number of solutions to a problem, and to describe the relationship between two or more variables. An equation is composed of two expressions connected by an equal sign (=). The two expressions must be the same, meaning that whatever value is on one side of the equation must be the same value on the other side. Equations can be used to describe a wide variety of real-world situations, such as the speed of a car, the cost of a house, or the force of a magnet.

This equation contains two variables, x and y. In order to calculate the answer, we would need to know the value of each variable.

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The slopes that are formed by angular, ragged stones are more stable because they have the largest angle of repose.

1. In physics, the angle formed by the plane de contact between both bodies and the horizontal so when upper body is just about to slide: the angle whose tangent represents the frictional resistance of the two bodies.

One aspect of inter particulate friction, or the resistance to particle movement, is angle of repose. The USP describes it as the consistent, three-dimensional angle (relative to the horizontal base) acquired by a cone-shaped pile of material created using any of a number of different techniques.

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Answer:

d. the orthogonal force.

Explanation:

The other three forces, the tension force, the normal force, and the thrust force, are commonly discussed in introductory physics courses.

B is correct option. Mechanical waves and electromagnetic waves both transfer energy through space, but they differ in fundamental ways.

Mechanical waves require a medium for their transmission, whereas electromagnetic waves can travel through a vacuum. This is a fundamental difference between the two types of waves that affects their behavior and properties.

In a mechanical wave, energy is transferred through the vibration of particles in a medium, such as air, water, or a solid material. The motion of the particles in the medium creates regions of compression and rarefaction, which propagate as the wave moves through the medium. This means that mechanical waves cannot exist in a vacuum or in a medium that is not capable of transmitting the wave.

In contrast, electromagnetic waves are self-propagating and do not require a medium for their transmission. They consist of oscillating electric and magnetic fields that can travel through a vacuum or any other medium capable of transmitting them.

While the other characteristics listed in the options (crests and troughs, clearly defined wavelengths, and limited speed) are also properties of mechanical waves, they are not as fundamental as the requirement for a medium. The requirement for a medium is what separates mechanical waves from electromagnetic waves at the most fundamental level.

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Complete question: Which of the following characteristics separates mechanical waves from electromagnetic waves the most fundamentally? A. There are crests and troughs on mechanical waves. B. A medium is necessary for the transmission of mechanical waves. C. The wavelengths of mechanical waves are clearly defined. D. The speed of mechanical waves is limited.

The new pressure is 4 atm.

Pressure is the amount of force applied over a given area it is typically measured in unit of Pascal's PA or pounds per square in each PSI pressure can be caused by a variety of factors including the weight of the atmosphere the weight of liquid and the weight of objects is that is important in many physical phenomena including the flow of liquids the transfer of energy and the propagation of sound in general when pressure is increase the volume of the material decrease.

The ideal gas law states that the pressure of an ideal gas is directly proportional to its temperature and inversely proportional to its volume. Thus, when the temperature is doubled and the volume is halved, the pressure is quadruple. Therefore, the new pressure is 4 atm.

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The molarity of the aqueous ammonia solution is 0.0165 mol/mL.

The concentration of ammonia in aqueous ammonia solution can be expressed as a mass percentage or as a molarity. The molarity of a solution is defined as the number of moles of solute per liter of solution.

To find the molarity of the aqueous ammonia solution, we first need to find the mass of ammonia in a given volume of solution, and then convert that mass to moles.

Given that the concentration of ammonia is 28% by mass and the density of the solution is 0.90 g/mL, we can calculate the mass of ammonia in a volume of 1 mL of solution:

Mass of ammonia in 1 mL is

=> (28 g/100 mL) * (1 mL)

=> 0.28 g

Now that we know the mass of ammonia, we can convert it to moles using the formula:

Moles = Mass / Molecular weight

The molecular weight of ammonia (NH3) is 17 g/mol, so we have:

Moles = 0.28 g / 17 g/mol

=> 0.0165 mol/mL.

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Over time, the molecules will undergo various processes, such as diffusion, collision, and chemical reactions. These processes can cause the molecules to change their physical and chemical properties, as well as their spatial arrangement.

For example, diffusion can cause molecules to spread out and move from areas of high concentration to areas of low concentration. Collision can cause molecules to bounce off each other and change their direction of movement. Chemical reactions can cause molecules to form new substances with different properties.

Overall, the behavior of molecules over time is determined by the laws of physics and chemistry, and can be observed and studied using various experimental techniques.

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Answer:

166 meters. Displacement is the movement of something from one place/position to another. Unless the type of displacement you're talking about is “the occupation by a SUBMERGED body or part of a body of a volume which would not otherwise be occupied by a fluid”.

Explanation:

33 + 71 + 62 = 166

The distance you traveled does not depend upon where, is about how much.

This equation assumes that the eyeball is a simple harmonic oscillator and that the musculature acts as a linear spring. The frequency of the vibration (f) is equal to the natural frequency of the eyeball's oscillation and the mass (m) is the mass of the eyeball.

The frequency is the rate or number of occurrences of a particular event or phenomenon with respect to its occurrence within a given period of time. It is typically measured in cycles per second (hertz), or the number of times an event occurs in a given period of time. Frequency can also refer to the rate at which something is repeated, such as the number of times a sound is repeated in a given span of time. Frequency can also refer to the number of times a certain action is performed, such as the number of times a person visits a store in a given month.

The effective spring constant of the musculature attached to the eyeball is equal to the frequency squared (f^2) multiplied by the mass (m) divided by 4pi^2:

k = f^2 m / 4pi^2

k = (29 Hz)^2 (7.5 g) / (4(3.14)^2)

k = 0.395 N/m (2 sig figs)

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Equation [tex]\\k = 0.395 N/m (2 sig figs)[/tex] assumes that the eyeball is a simple harmonic oscillator and that the musculature acts as a linear spring.

The frequency of the vibration (f) is equal to the natural frequency of the eyeball's oscillation and the mass (m) is the mass of the eyeball.

The frequency is the rate or number of occurrences of a particular event or phenomenon with respect to its occurrence within a given period of time. It is typically measured in cycles per second (hertz), or the number of times an event occurs in a given period of time. Frequency can also refer to the rate at which something is repeated, such as the number of times a sound is repeated in a given span of time. Frequency can also refer to the number of times a certain action is performed, such as the number of times a person visits a store in a given month.

The effective spring constant of the musculature attached to the eyeball is equal to the frequency squared (f^2) multiplied by the mass (m) divided by 4pi^2:

[tex]k = f^2 m / 4\pi^2\\k = (29 Hz)^2 (7.5 g) / (4(3.14)^2)\\k = 0.395 N/m (2 sig figs)[/tex]

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Based on the provided chemical and physical properties, the unknown substance would be most useful as a fuel.

The substance is an easily combustible organic compound that is in liquid form at room temperature, and it contains a lot of volatile, high-energy bonds.

These properties make it an ideal fuel for a range of applications. The high energy content of the bonds means that the fuel can be used to power engines and generate heat, while the liquid form makes it easily transportable.

The combustible nature of the substance also makes it a suitable fuel for cooking and other activities that require a flame. The fact that it is in liquid form at room temperature also makes it easier to store and use.

The unknown substance is a versatile fuel that can be used for a variety of applications.

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Answer:

a

Explanation:

the chemical change in the physical change

The stars must be so distant that their parallaxes are too small for the ancient Greeks to have been able to measure with their technology.

Option C.

Parallax is the apparent shift in the position of an object when viewed from different locations. In the case of measuring stellar parallax, astronomers look at the apparent shift in the position of a star against the background of more distant stars as the Earth orbits the Sun.

However, the amount of parallax observed is related to the distance to the star, with more distant stars showing smaller amounts of parallax. The ancient Greeks did not have the technology to measure small angles accurately, and so they were unable to measure the small parallaxes of the distant stars.

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Energy is transported by mechanical waves perpendicular to wave motion. Energy is carried parallel to the wave motion by electromagnetic waves.

Whether or not the waves require a medium for propagation determines one of their characteristics. This characteristic is also the basis for the main distinction between magnetic and electric waves. While electromagnetic waves can travel without a medium, mechanical waves can not.

In contrast to mechanical waves, electromagnetic waves can travel without a medium. This implies that microwaves can pass not only through solid objects like air and rock but also through empty space.

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A constant force is exerted on a cart (initially at rest) on an air track. Neglect friction. The force acts for a short time and gives the cart a certain final speed. To reach the same final speed with a force that is only half as big, the force must be exerted on the cart for a time interval twice as long as the time interval for the stronger force.

Assuming that the force acts in the same direction as the motion of the cart, we can use the impulse-momentum theorem to relate the force, the time interval it acts for, and the resulting change in momentum of the cart.

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The speed of light in the solid is 1.88 × 10⁸m/s

What are the light's wavelength and frequency?

The distance between equivalent places in two consecutive light cycles is known as the wavelength of light, and the frequency of light is the number of light cycles that pass a specific spot in a second.

The ratio of the speed of light in a vacuum to that in a second medium with a higher density is used to compute the refractive index (also known as the index of refraction). If the solid's wavelength is 420/670, or 0.627 times that of air, then the solid's light speed is also 0.627 times that of air. Bonus: The reciprocal of speed is proportional to refractive index. Given that the refractive index of air is 1, the clear solid's refractive index is 670/420, or 1.60.

The refractive index of a material is,

[tex]n = \dfrac{\lambda_v}{\lambda_m}[/tex]

[tex]n = \dfrac{670 }{420 }[/tex]

n = 1.59

Now,

The speed of light in the solid is,

[tex]\mathrm{v = \dfrac{c}{n} }[/tex]

Here, c is speed of light = 3 × 10⁸ m/s

So,

[tex]\mathrm{v = \dfrac{3 \times 10^8}{1.59} }[/tex]

v = 1.88 × 10⁸ m/s

Thus, The speed of light in the solid is 1.88 × 10⁸m/s

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Complete question:

A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420nm.

What is the speed of light in this solid?

Magnetic field lines are closest together in areas where the magnetic field is strongest. Magnetic field lines represent the direction of the magnetic force and the closer the lines are together, the stronger the magnetic field.

What are magnetic field lines?

In a magnetic field, the direction of the magnetic force experienced by a moving charged particle is perpendicular to both the direction of motion of the particle and the direction of the magnetic field. The magnetic field lines provide a visual representation of the direction of the magnetic force at any given point in space, and the closer the lines are together, the stronger the magnetic field and the greater the force experienced by a moving charged particle.

It is important to note that magnetic field lines never intersect, as the magnetic force at a given point in space has a unique direction. The number of magnetic field lines passing through a given area is proportional to the strength of the magnetic field in that area.

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The sled's runners experience kinetic frictional force from the snow, which causes the sled to slow down and eventually stop. The amount of kinetic friction is 0.050.

Writing - When writing, the pen's tip comes into touch with the paper, causing rolling friction for ballpoint pens or sliding friction for pencils. During skating.

The force that opposes motion when the surfaces of two objects come into contact is known as friction. Friction lessens a machine's mechanical advantage, or, to put it another way, reduces the output to input ratio.

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The speed us the swimmer should have relative to the water is 7.07 km/hr.

The speed is the rate at which an object or person moves from one place to another. It can be measured in terms of velocity, which is the rate of change of position over time. Speed can also be measured in terms of acceleration, which is the rate of change of velocity over time. Speed is typically measured in units such as miles per hour (mph), kilometers per hour (kph), or meters per second (m/s).

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The speed, Us of the swimmer relative to the water, is, Us = 4.02km/hour.

If the swimmer reported their pace in kilometers per hour, we must calculate our speed relative to the water.

Consequently, the swimmer's speed in relation to the water is

Us equals 4.02 km/h

It is possible to separate the swimmer's speed Us into its vertical and horizontal components.

Thus, Usx = -(Us Cos45°) is the formula for the horizontal component of speed, Us.

Because the speed, Us, is located on the negative x-axis, the above symbol is negative.

Additionally, Usy = Us Sin45° represents the vertical component of speed.

Additionally, the river's horizontal component of speed Vr is,

Cos0° + Vrx = Vr + 5km/h

Additionally, the river's vertical component of speed Vr is,

Sin0° = 0km/h, where Vry = Vr

This is true because the speed VR forms a horizontal angle of 0°.

As a result, V'x and V'y represent the total speed in the horizontal and vertical directions, respectively, at (5-UsCos45) and (UsSin45).

As a result, the amount of time needed to go from point A to point C is,

Ty = d1/(UsSin45) (UsSin45).

Furthermore, the time Tx needed to go from point C to point B is,

Tx = d2/(5 - UsCos45) (5 - UsCos45)

Though Tx = Ty.

Therefore,

UsSin45 d1/ = d2 (5 - UsCos45).

i.e 159 / (0.7071Us) = 121 / (5 - 0.7071Us) (5 - 0.7071Us).

the cross-product

85.56Us = 795 - 112.43Us

85.56Us + 112.43Us = 795

197.99Us = 795

Us = 795 / 197.99 for the speed.

Usual swimming speed in relation to water is,

Us equals 4.02 km/h.

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Complete question -

The months of the year, in order, are:

January, February, March, April, May, June, July, August, September, October, November, December.

January: This is the first month of the year and is named after the Roman god Janus, who had two faces and was believed to look back on the old year and forward to the new one.

February: This is the shortest month of the year, with 28 days in a regular year and 29 days in a leap year. It is named after Februa, a Roman festival of purification.

March: This is the third month of the year and is named after Mars, the Roman god of war. It is associated with the beginning of spring in the Northern Hemisphere.

April: This is the fourth month of the year and is believed to be named after the Latin word "aperire," which means "to open," as this is the time of year when trees and flowers begin to bloom.

May: This is the fifth month of the year and is named after the Greek goddess Maia, who was associated with growth and fertility.

June: This is the sixth month of the year and is named after the Roman goddess Juno, who was the queen of the gods and the patroness of marriage and childbirth.

July: This is the seventh month of the year and is named after Julius Caesar, the Roman general and statesman who reformed the calendar and was born in this month.

August: This is the eighth month of the year and is named after Augustus Caesar, the first Roman emperor and the successor of Julius Caesar.

September: This is the ninth month of the year and is derived from the Latin word "septem," which means "seven," as it was originally the seventh month in the Roman calendar.

October: This is the tenth month of the year and is derived from the Latin word "octo," which means "eight," as it was originally the eighth month in the Roman calendar.

November: This is the eleventh month of the year and is derived from the Latin word "novem," which means "nine," as it was originally the ninth month in the Roman calendar.

December: This is the twelfth and final month of the year and is derived from the Latin word "decem," which means "ten," as it was originally the tenth month in the Roman calendar.

Each month has a varying number of days, ranging from 28 to 31. The months with 31 days are January, March, May, July, August, October, and December. The months with 30 days are April, June, September, and November. February has 28 days in a regular year and 29 days in a leap year.

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