20 drops of an essential oil have a mass of 407.7 mg (milligram) and a density of 0.875g/cm3. what is the volume occupied by the drops?

There are 2501.3m³ in 88,263 ft³ the Olympic swimming pool.

Along with arithmetic, geometry is one of the oldest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions. Geometer is the term used to describe a mathematician who specializes in geometry.

The area of mathematics known as geometry is concerned with the characteristics of the surrounding environment as well as the shapes of particular objects and their spatial relationships.

swimming pool is approximately 88,263 ft³

assume there are 3.28 ft in 1 meter.

Now ,

Given that :

3.28ft = 1m

1 ft = 1/(3.28)m

So,

1 ft = (1/3.28)³m³

88,263 ft³ = 88263/(3.28)³

                = 2501.3m³

There are 2501.3m³ in the Olympic swimming pool.

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The statement is True.  

Neurons have a net negative charge when it is at rest. This means that when they are well active, they must have a positive charge.

At rest, neurons have a net negative charge; the inside of neurons is approximately 70 millivolts more negative than the outside. When neurons are active, they must be positively charged in order to generate an action potential.

Neurons have a strong negative charge within them, as opposed to a positive charge outside. This is due to the presence of other molecules known as anions. They are negatively charged but far too large to escape through any available channel. They remain in place and give the cell a negative charge on the inside.

Because of an unequal distribution of positive ions across the membrane, the resting potential is negative; 3 Na+ is pumped out of the cell for every 2 K+ that enters, so the inside of the cell is less negative (less positive) than its surroundings.

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The electric potential at point p is 86.53 KV

We know that,

Electric potential V = kQ / r

where,

k = Coulomb's constant

Q = Point charge

r = Distance

Given that,

r = 24 cm = 0.24m

Q = 2.31 mC = 2.31 * [tex]10^{6}[/tex] C

k = 8.99 * [tex]10^{9}[/tex] N [tex]m^{2}[/tex] / [tex]C^{2}[/tex]

V = ( 8.99 * [tex]10^{9}[/tex] * 2.31 * [tex]10^{6}[/tex] ) / 0.24

V = 86.53 KV

Electric potential is the amount of work energy required to move a unit charge from a reference point to a specific point inside an electric field. It is a scalar quantity.

Therefore, the electric potential at point p is 86.53 KV

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a) Yes, there is one outlier (lower).

b) The boxplot can be seen with the image as attached below.

Looking at the distribution of the lower/smallest observation, we can see that there is a value in the lower/smallest that is very far from others. See the attached diagram of the boxplot to understand it better.

The median is the line in the middle of the boxplot.

The Lower fourth is the lower whisker line and upper fourth is the upper whisker line. The lower box (just below the median) line is the 1st quartile, and the upper box line (just above the median) is 3rd quartile.

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Complete Question

A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. consider the following partial sample information.

median = 202.1

lower fourth= 196.0

upper fourth= 216.8

three smallest observation 125.8 188.1 193.7

three largest observations 221.3 230.5 250.2

a. Are there any outliers in the sample? Any extreme outliers?

b. Construct a boxplot that shows outliers, and comment on any interesting features

The  empirical   formula  is KClO₃

Empirical formula - The simplest whole no. combination of element in that compound.

The  empirical  formula of the  compound is  calculated :

sample of compound (mass) ,M = 23.23g

potassium, k, = 7.41 g

 chlorine, cl,=  6.72

 oxygen, o, = ?

  [tex]M = k_{m} + Cl_{n} + o_{p}[/tex]

23.23g = 7.41g + 6.72g + o

o = 9.1g

the  moles  of  each  element,  (moles)  = mass/  molar  mass

moles of   K  =  7.41g/39 g/mol(molar  mass  of K)  =  0.18  moles

moles  of Cl = 6.72g/35.5 g/mol(molar  mass  of Cl) =  0.18 moles

moles of  O  =  9.1g/ 16g/mol(molar  mass of  O) = 0.57 moles

then  calculate e  mole ratio by  dividing  each  mole  by  the  smallest  number  of  moles  (  0.18 moles)

K= 0.18/0.18= 1

Cl=0.18/0.18=1

O=  0.56/0.18=3

Hence  the  empirical   formula  = KClO₃

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In the photoelectric effect, a beam of light impinges on metal, and it is observed that electrons are ejected from the metal in greater numbers as the intensity of light increases.

In physics, the photoelectric effect refers to a phenomenon in which the emission of charged particles takes place from a material or substance after absorbing electromagnetic radiation.

When light hits the surface of the material then electrons are released known as photoelectrons.

This phenomenon better explains the quantum nature of electrons and light.

Moreover, the study of the dual nature of wave particles has further expanded the scope, investigation, and understanding of the matter.

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sine wave or sinusoidal wave -

sine wave can be described as a geometric waveform that oscillates periodically.

It retains its wave shape when added to the another sine wave of the same frequency.

It is a continuous wave.

the general form of sine wave is

y = asin(bx)

where

amplitude is the maximum displacement from its mean position to extreme position.

Periodicity is a repeating continuous pattern which determine its wavelength and frequency.

Frequency of sine wave.

1kHz that is sine wave goes through thousand complete cycle in one second.

Speed of sine wave.

Speed = frequency x wavelength

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3000 N of friction exists between the bear and the tree.

How does friction force work?

Between solid surfaces, there are three basic types of friction:

Explanation:

The bear goes down at a constant speed, thus there is no acceleration. The forces add up to zero. As a result, upward friction and downward weight result in zero  

i.e.,

F-mg=0

F = mg

F = (300 kg)/10 [tex]m/s^{2}[/tex] (gravitational acceleration)

3000 N frictional force equals F.

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Pressure above the left beaker the pressure outcome of the current experimental circumstances.

Either the action of pressing or the state of pressing. A strain or force exerted against resistance in any direction. Force per unit of area is a measure of force exerted uniformly over a surface.

Pressure is the ratio of the force applied perpendicularly to an object's surface to its area. Its abbreviation is "p" or "P."

The force applied by one region of a gas, liquid, or solid to another, expressed as a function of area. A substance is said to have negative pressure if another substance exerts greater force per unit area on it than it does on it. Pressure is commonly measured in Pascal units, atmospheres, or pounds per square inch. Its value is just the opposite of the pressure the other substance is exerting.

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The density of galena is 7.56 g/cm³.

We need to know about the density to solve this problem. Density can be described as how much the mass is in a volume unit. It can be written

ρ = m / V

where ρ is density, m is mass and V volume

From the question above, we know that

m = 12.4 g

V = 1.64 cm³

By substituting the given parameter, we can calculate the density

ρ = m / V

ρ = 12.4 / 1.64

ρ = 7.56 g/cm³

Hence, the density of galena is 7.56 g/cm³.

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Left of z = 0.49 and right of z = 2.05, the area underneath the standard normal curve is equal to 0.7081.

The horizontal axis is approached by the standard normal bend as it extends indefinitely both in directions without ever being touched by it. The center of the bell-shaped, z=0 standard normal curve. Between z=3 and z=3, almost the entire area underneath the standard normal curve is located.

Use the normal distribution's standard form to calculate probability. Since the standard normal distribution is indeed a probability distribution, the probability that a variable will take on a range of values is indicated by area of the curve between two points. 100% or 1 is the total area beneath the curve.

the region to the left of the standard normal curve,

z=0.49

To the right of,

z = 2.05

So,

The area will be:

= P[z < 0.49] + P[ z >2.05]

= P[z < 0.49] + 1 -  P[ z < 2.05]

= .6879 + 1 - .9798

= 0.7081

Left of z = 0.49 and right of z = 2.05, the area underneath the standard normal curve is equal to 0.7081.

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I understand that the question you are looking for is:

Find the area under the standard normal curve to the left of z = 0.49 and to the right of z = 2.05. Round your answer to four decimal places, if necessary.

(a) Duration of the ball's flight is 2.5S

(b) Angle of its velocity is 16.1

(c) Speed of the ball is 22.53 m/s

(a). To determine the duration of the ball's flight in

We calculate the whole time when the ball touches the ground, thus we enter y=0 and all other specified values in the equation.

[tex]25sin30t-1/210t^{2} = 0[/tex]

[tex]t = 2.5 s[/tex]

(b) After it has been in the air for one-fourth of this period, determine the angle of its velocity with respect to the ground.

t1=1/4 t = 2.5/4 = 0.625 s

[tex]v_{x} = 25\sqrt{3} /2 m/s[/tex]

[tex]v_{y} = 25/2 - 2.5/2 = 12.5/2 m/s[/tex]

∅= 16.1

(c) To determine speed of the ball for time [tex]t_{1} ,t_{2} , t_{3}[/tex]

[tex]v=\sqrt{v} ^{2}{x} + \sqrt{v} ^{2} y_{}[/tex]

vt1 = 22.53 m/s

vt2 = 21.65 m/s

vt3 = 22.53 m/s

The turning point on the corresponding parabolic curve is where the speed is at its lowest in the xx direction. Physically speaking, the shift in speed does make sense. The ball's initial motion against gravity causes its speed to decrease, but after it reaches the turning point, its speed begins to increase as it descends.

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​

An ethical dilemma​ describes a conflict between two morally correct courses of action.

Being able to reason effectively and logically about what to believe or do is known as critical thinking. It comprises the capacity for independent and thoughtful thought. These are some examples of what someone with critical thinking abilities can do:

The ability to think clearly and rationally is crucial whatever we choose to undertake. It should go without saying that critical thinking is crucial if you work in the fields of education, research, business, law, or management.

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You could double the charge to 2Q in order to double the size of the field at P.

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The reason why voltage across the inductor and capacitor can have higher magnitudes than that of input source voltage is because of electrical energy's oscillation between magnetic and electric field.

When current passes through an inductor a magnetic field is produced and the collapsing magnetic field produced by the inductor charges the capacitor. This process repeats itself causing the electrical energy to oscillate between magnetic and electric field. Because of this oscillation, at resonance, voltage across the inductor and capacitor can be greater than the input voltage.

For a RLC circuit,

[tex]V_{s}[/tex] = [tex]\sqrt[]{V_{R}^{2} + (V_{L} - V_{C})^{2} }[/tex]

where,

[tex]V_{R}[/tex] = Voltage across the Resistor

[tex]V_{L}[/tex] = Voltage across the inductor

[tex]V_{C}[/tex] = Voltage across the capacitor

At resonance,

[tex]V_{L}[/tex] = [tex]V_{C}[/tex]

Therefore, the reason why voltage across the inductor and capacitor can have higher magnitudes than that of input source voltage is because of electrical energy's oscillation between magnetic and electric field.

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This system's potential energy changed by 40 J.

Energy = charge * potential difference

=> Energy = (8v)*5

=> Energy = 40 J

Hence the answer is 40 J.

Potential difference, often known as voltage, is equal to the amount of current times the resistance. One Joule, or one Volt, of energy is required for one Coulomb of charge to flow from one place in a circuit to the another.

V=U q, The change in the potential energy of a charge q transported from point A to point B, divided by the charge, is what is used to determine the electric potential difference between points A and B, or VBVA. The joules per coulomb unit of the potential difference is called the volt (V).

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A and B are orthogonal vectors, so projab=0 and projab = b

If the vectors a and b are present in, then b is projected onto an as

[tex]proj_{a} b[/tex] = [tex]\frac{a.b}{a^{2} }[/tex]a.

​Suppose a and b are orthogonal vectors. Then  and

[tex]proj_{a} b[/tex][tex]=\frac{a.b}{a^{2} }=0[/tex]

Suppose a and b are parallel vectors. Then a scaler c exists such that b=cx and

[tex]proj_{a} b=[/tex][tex]=\frac{a.b}{a^{2} }=c\frac{a.b}{a^{2} } a=ca=b[/tex]

[tex]proj_{a} b=0\\proj_{a} b=b[/tex]

The term "orthogonal unit vectors" refers to a collection of vectors that are mutually perpendicular to one another, that is, they intersect at an angle of 90° with a magnitude of one unit. Since Cos90 is zero, the dot product of an orthogonal vector is always zero.

Two orthogonal vectors have a zero dot product. The zero dot product of the two column matrices that represent them. It only matters in relation to orientation. In the case of orthogonal vectors, the dot product is zero.

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A person travelled a distance of 0.32m in coming to a complete stop.

Acceleration - Acceleration is the rate of change of velocity with respect to time.

The distance travelled is calculated as  

Time t = 33ms = 33/1000 = 0.033s

Acceleration a = 60g

g = 9.8 m/s²

a = 60g = 60 × 9.8 = 588 m/s²

The person must be moving at a certain initial velocity.

Since the person is going to stop, V = 0

using equation of motion we get

V = U - at

0 = U - 588 × 0.033

0 = U - 19.404

U = 19.404 m/s

The distance travelled is

using equation of motion

V² = U² - 2aS

0 = (19.404)² - 2 × 588S

1176S = 376.51

S = 376.51 / 1176

S = 0.32 m

the distance is 0.32m

The person travelled a distance of 0.32m in coming to a complete stop.

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Using the Newton's second law the net force of the runner is 131.25 N

To solve this exercise the formula for net force and the formula for uniformly varied rectilinear motion (UVRM) to be applied are:

Where:

Information about the problem:

Applying the formula for UVRM we can calculate the acceleration of the runner:

a = (vf - vi) /t

a = (7 m/s - 0 m/s) / 4s

a = 7 m/s / 4s

a = 1.75 m/s²

With the acceleration we can apply the net force formula and get:

F = m * a

F = 75 kg * 1.75 m/s²

F = 131.25 N

It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.

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Answer:

Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches.

MECHANICS :

Mechanics is the branch of physics that deals with the motion of an object without or with the reference of force. Mechanics can be further divided into two branches, namely quantum mechanics and classical mechanics. Quantum mechanics deals with the behaviour of the smallest particles like neutrons, protons, and electrons, while classical mechanics is the branch that deals with laws of motion of forces and physical objects.

OPTICS :

This branch of physics deals with the behaviour, propagation, and properties of light. Optics can be simply described as the study of the behaviour of infrared light, visible light, and ultraviolet.

THERMODYNAMICS:

Thermodynamics deals with the study of heat and its relation with work and energy. Thermodynamics also deals with the transmission of heat energy by means of convection, conduction, and radiation.

ELECTROMAGNETISM:

Electromagnetism deals with the study of electromagnetic force like electric fields, light, magnetic fields, etc. There are two aspects of electromagnetism which are “electricity” and “magnetism”.

RELATIVITY:

This branch of physics deals with the theorem that was formulated by Albert Einstein. The theory of relativity states that space and time are relative and all the motion must be relative to a frame of reference.

ACOUSTICS :

Acoustics deals with the study of sound and its transmission, production, and effects. Acoustics mainly involves the mechanical waves in gases, liquids, and solids, which include vibration, sound, ultrasound, and infrasound.

The acceleration of this item will remain constant if I double the force and double the mass.

The rate at which a moving object's speed and direction change over time. When something moves faster or slower, it is considered to be accelerating. Motion on a circle accelerates even while the speed is constant because the direction is always changing.

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More iron could be found from the cores of the other terrestrial planets. Option A

Iron is one of the elements that could be found on earth. This element is present in abundant amounts in the earth's core and ranks as the fourth most abundant element in the core of the earth.

The earth has a lot more deposit of iron in it. We know that earth lies at the center of the solar system for the sole reason that it is habitable. No other planet in the solar system is habitable though efforts are underway to make the other planets equally habitable.

Iron can also be found in the cores of other terrestrial planets but the amounts may be less than the amount of iron that is found on earth. As such, If earth experienced an iron shortage, astronomers could direct cosmic mining equipment to the  cores of the other terrestrial planets find more.

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Gold foil experiment

Ernst Rutherford conducted the Gold Foil Experiment in which α particles (doubly charged Helium Atoms) were bombarded on a thin gold foil. This experiment led to the discovery of the nucleus.

1) Most of the particles passed through undeflected

⇒ this meant that most of an atom is empty space

2) Some Alpha particles were deflected by some small angles

⇒ Since alpha particles are positively charged species , they can only be deflected if there are some positively charged atoms present that would repulse these particles.

3) A few ( about 1/20000 particles) bounced back

⇒There is a heavy mass of positively charged species in the atom , and since the alpha particles bounced back , this mass of positively charged species must have been highly dense.

Therefore, from these observations and inferences Rutherford concluded that most of an atom is empty space and there is a mass of positively charged particles in the center of the atom called the nucleus which contains protons. The electrons revolve around this nucleus at high speeds.

The mass of the atom is concentrated in the nucleus and is very small in size , making it highly dense.

The strength of this electric field is 10.64×10⁸ N/C.

Electric field strength is a quantitative expression of the intensity at a particular location of a electric field.

It is a vector quantity.

Electrostatic force on the  charge :

[tex]F_{e} = mg[/tex]          (equation1).

m = mass

g = gravity

electrostatic force of a charge on an electric field :

[tex]F_{e} = Eq[/tex]           (equation2).

E = magnitude of electric field

q = charge

using equation 1 and 2 we get

Eq = mg

m = 1.67×10⁻²⁷ kg

g = 10.2 m/s²

q = 1.6 ×10⁻¹⁹

E = mg/q

     =  1.67×10⁻²⁷ kg ×10.2 m/s² /  1.6 ×10⁻¹⁹ C

     E= 10.64×10⁸ N/C

The strength of this electric field is 10.64×10⁸ N/C.

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The correct answer is 369.2765m

Speed of tortoise = v_t= 16.3cm/s=0.163m/s

Speed of hare= v_h=220.2cm/s=2.202m/s

Rest time of hare is t_r=1.6min

Tortoise wins by distance of x = 108cm=1.08m

Consider that S is the length of a racetrack.

At the conclusion of the race, calculate the tortoise's distance travelled.

S=v_t×t

S=0.163m/s×t ______(1)

Here, t is the race's actual time.

Find out how long the hare spent racing.

t_h=t-t_r

t_h=t-1.6min×(60s/1min)

t_h=(t-2160)s

At the conclusion of the race, determine the hare's distance travelled.

S-x=v_h×t_h

S-1.08m=2.2×(t-2160)s

S=2.2×(t-2160)s+1.08m_____(2)

To determine the race time, substitute equation (1) for equation (2).

0.163m/s×t=S=2.2×(t-2160)s+1.08m

0.163t=2.26t-4752+1.08

4752-1.08=2.26t-0.163t

4750.92=2.097t

4750.92/2.097=t

2265.5=t

To determine the length of the race or the track, substitute the amount of time in equation (1).

S=0.163m/s×t

S=0.163×2265.5

S=369.2765m

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Mass of substance is 0.6324 kg

Given:

volume = V = 680ml = 0.68 L

density = D = 0.930

To Find:

mass in kg

Solution: mass, in physics, quantitative measure of inertia, a fundamental property of all matter. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force.

Density = mass/volume

mass = Density x Volume = 0.93 x 680

Mass = 0.6324 kg

Hence, the mass of substance is 0.6324 kg

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The work done in the isothermal process is 10 joule.

We need to know about the isotherm process to solve this problem. The isotherm process can be described as a process where the initial temperature system will be the same as the final temperature. Hence, the internal energy change will be zero.

ΔU = 0

Hence,

ΔU = Q - W

0 = Q - W

Q = W

It means that the heat transferred is the same as the work done.

From the question above, we know that the heat transferred is 10 joule. Thus, the work done in the isothermal process is 10 joule.

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Answer:

Fail-close

Explanation:

A failed open switch is a switching device (be it mechanical, relay, semiconductor) that has lost it's switching capabilities (it's defective) and the switched contacts are now constantly open (disconnected) regardless of the control signal to the switch.

Similarly a failed closed switch is the same just with the contacts connected through.

A robot at that distance sees the light flash at time = 2500sec

Given,

A robot sees the flash light from distance = 5 astronomical unit (AU)

A robot at that distance sees the light flash at time = ?

Solution,  

An Astronomical Unit can be defined as , the mean distance of the center of the Sun from the center of the Earth.

1 Astronomical Unit (AU) = 1.496 × 10¹¹m

Time for the light reach to the earth T = 8min 20 sec

speed of light c= 3 ×10¹¹m/s

T = distance/speed

Distance = 5AU

Speed = c

therefore ,

T time = 5 AU/C

AU/C=  5Time= 5 ( 8×60 + 20 )sec

Time = 2500 sec

A robot at that distance sees the light flash in 2500 seconds.

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The minimum diameter of a steel wire is 1.41mm

STRESS : The restoring force per unit area. unit of stress is N/m²

     It is denoted by σ

      σ = F/ A

Where σ = stress

F = force

A = area

force = ma

Area of a steel wire is πr²

2r = d

so area becomes

π(d/2)² =πd²/4

here , mass = 80kg

elastic limit = 5.0×10⁸kg

using these values

σ = mg/ πr²

5×10⁸ = 80×10³ × 9.8/ π*d²/4

π *d²/4 = 784 ×10³ /  5×10⁸

           = 156.8 ×10⁻⁵

   d² = 19.9×10⁻⁵

   d = 1.41 mm

The minimum diameter of a steel wire is 1.41mm

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