write the principal of the conservative of energy​

(a) The probability that we roll the die n times is (5/6) n−1 = (1/6)

(b) The expected number of times we roll the die is 6

We would have to roll (n – 1) numbers that are not 6 followed by a 6. In other words, other five numbers are expected to be rolled each, and since there are five other numbers aside 6, so the probability is

(5/6) n−1 = (1/6)

The expected number of dies to be rolled is given by the relation:

E(N) = ∑_(n=1)^∞▒n

= (5/6) n−1* (1/6)

= (1/6) (1/(1-(5/6)))2

= 6

This is the correct answer since after 6 rolls we would expect to have rolled exactly one 6 while other numbers appear once per time.

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Answer:

Approximately [tex]4.9\; {\rm m\cdot s^{-1}}[/tex] backward, assuming that the canoe was initially stationary.

Explanation:

When an object of mass [tex]m[/tex] is moving at a velocity of [tex]v[/tex], the momentum [tex]p[/tex] of that object would be [tex]p = m\, v[/tex].

With a mass of [tex]m = 67\; {\rm kg}[/tex] and a velocity of [tex]v = 3.3\; {\rm m\cdot s^{-1}}[/tex] forward, the momentum of Fred would be [tex]p = m\, v = 67\; {\rm kg} \times 3.3\; {\rm m\cdot s^{-1}} = 22.11\; {\rm kg \cdot m \cdot s^{-1}}[/tex] (forward.)

Before the jump, the velocity of the boat and Fred were both [tex]0\; {\rm m \cdot s^{-1}}[/tex]. Hence, the momentum of both Fred and the boat would initially be [tex]0\; {\rm kg \cdot m \cdot s^{-1}}[/tex].

Momentum is preserved immediately after the jump. Thus, the momentum of Fred plus the momentum of the boat would still be [tex]0\; {\rm kg \cdot m \cdot s^{-1}}[/tex] after the jump.

Since the momentum of Fred was [tex]22.11\; {\rm kg \cdot m \cdot s^{-1}}[/tex], the momentum of the boat would be [tex](-22.11\; {\rm kg \cdot m \cdot s^{-1}})[/tex] (backward, as the negative sign indicates.)

Rearrange [tex]p = m\, v[/tex] to find velocity in terms of mass [tex]m[/tex] and momentum [tex]p[/tex]:

[tex]\begin{aligned} v &= \frac{p}{m} \\ &= \frac{-22.11\; {\rm kg \cdot m \cdot s^{-1}}}{67\; {\rm kg}} \\ &\approx (-4.9)\; {\rm m \cdot s^{-1}}\end{aligned}[/tex].

In other words, the velocity of the boat would be approximate [tex]4.9\; {\rm m\cdot s^{-1}}[/tex] backwards.

The heat developed per hour is 2896740 J/h.

The electric potential of the electric iron is V.

V = 121 v

The current drawn by the electric rod is I.

I = 6.65 A

The heat developed is,

Power = Electric potential × Current

P = V × I

= 121 × 6.65

= 804.65 watts

Heat developed developer in watts is 804.65 watts.

The heat developed in joules per second is,

= 804.65 J/s

The heat developed in joules per second is 804.65 Joules per second.

The heat developed per hour is,

[tex] = \frac{804.65}{ \frac{1}{3600}hour } [/tex]

= 2896740 J/h

Therefore, the heat developed per hour is 2896740 joules per hour.

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According to the  given statement  these option are apply for strong hypothesis:

B-A good hypothesis results in a test with quantifiable outcomes.

C-A good hypothesis leads to a test with measurable results.

E-A good hypothesis provides a possible explanation to answer a scientific question.

A few examples of simple hypotheses: "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast." Complex hypothesis: "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."

Simple hypothesis is one example of a hypothesis. complex hypothesis direction-hypothesis

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Which statement describes the best reason for having a strong hypothesis ?  Check all that apply.

A-A good hypothesis is based on one's personal opinion.

B-A good hypothesis can be tested.

C-A good hypothesis results in a test with quantifiable outcomes.

D-A good hypothesis does not always have to be based on prior knowledge or research.

E-A good hypothesis provides a possible explanation to answer a scientific question.

The wavelength is 1.87 m of these radio waves round your answer to 2 significant digits.

Radio waves are part of the electromagnetic spectrum, any radiation of that electromagnetic spectrum has a speed of 3.00x10⁸ m/s in vacuum.

Consequently, the following equation can be used to determine the wavelength:

c =  λ.ν --------- (1)

Where c is the speed of light, λ is the wavelength and  is the frequency.  

Then, λ can be isolated from equation 1

λ = c / ν --------- (2)

Keep in mind that Hz units must be used to express frequency.

ν = 160 MHz x (1000000Hz/1 MHz)

  = 160000000 Hz

λ = 3 x 10⁸ m/s / 160000000 Hz

But 1 Hz = s⁻¹

λ = 3 x 10⁸ m/s / 160000000 s⁻¹

λ = 1.87 m

Hence, the wavelength is 1.87 m

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In the electromagnetic spectrum, the type of radiation that has less energy than visible light is microwave.

The electromagnetic spectrum is the arrangement of all types of electromagnetic radiation in order of decreasing frequencies and increasing wavelength. In the electromagnetic spectrum, the frequencies of the electromagnetic radiation can range from as low as 1 hertz to as high as 100 million hertz.

Frequency is directly proportional to energy. In other words, the more frequency an electromagnetic wave has, the more energy it will also have. The electromagnetic wave with the highest frequency and energy is gamma ray. Visible light falls somewhere in the middle of the spectrum, and the frequency of microwaves is less than that of visible light. Hence, microwaves have less energy than visible light.

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The transformer secondary turns should be 83 turns.

We need to know about the transformer to solve this problem. Transformer is a device that can increase or reduce the voltage. The changed voltage depends on the current and number of coil turns. It can be written as

Vi / Vs = Ni / Ns = Is / Ii

where Vi is input voltage, Vs is output voltage, Ni is primary turn, Ns is secondary turn, Is i output current and Ii is input current.

From the question above, we know that

Vi = 120 V

Ni = 1000 turns

Vs = 10V

By substituting the following parameters, we can calculate the secondary turns

Vi / Vs = Ni / Ns

120 / 10 = 1000 / Ns

Ns = 1000 / 12

Ns = 83 turns

Hence, the transformer secondary turns should be 83 turns.

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Answer: acting, lying, or being across : set crosswise. 2 : made at right angles to the long axis of the body a transverse section.

Explanation:

An energy unit known as a kilowatt-hour is one kilowatt of power for one hour. It is 3.6 megajoules, or in conventional units.

The Formula for Calculating Watts Into Kilowatt-Hours:

kWh = (watts × hrs) ÷ 1,000

[tex]= ( 16*6)/1000[/tex]

=0.096 kwh

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The density of wood is 118.095 gram/liter.

We need to know about the density to solve this problem. Density is a unit that measures how dense an object is. Density can be measured by dividing mass by volume. It can be written as

ρ = m / V

where ρ is density, m is mass and V is volume

From the question above, we know that

m = 62 grams

V = 0.525 liter

By substituting the following parameters, we can calculate the density

ρ = m / V

ρ = 62 / 0.525

ρ = 118.095 gram/liter

Hence, the density of wood is 118.095 gram/liter.

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The ball's acceleration during its entire motion is  -9.6 m/s^2

The ball's total displacement after 2.00 s is 0 m

From the statements, we have got 2 cases, first we have to find acc and then find the distance, we will kinematics equation to solve this

we have given,

u=19.6 m/s

v=0

t=2 second

a=v-u/t

a= -19.6/2

a= -9.6 m/s^2

the ball's acceleration  is  -9.6 m/s^2

now, we need to find the ball's total displacement after 2.00 s

s=u+gt^2÷2

s= -19.6+9.8×2

s= -19.6+19.6

s= 0 m

the ball's total displacement after 2.00 s is 0 m

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The total displacement of the ball in 2 seconds is o meter.

Displacement is defined as the change in position of an item. it's far a vector amount and has a course and magnitude. it's miles represented as an arrow that points from the beginning role to the final function. as an example- If an object moves from A role to B, then the object's position modifications.

Acceleration is the price of alternate of the rate of an object with admire to time. Accelerations are vector portions. The orientation of an item's acceleration is given via the orientation of the internet force performing on that object.

u=19.6 m/s

v=0

t=2 second

a=v-u/t

a= -19.6/2

a= -9.6 m/s²

The acceleration of the ball is  -9.6 m/s²

To find the ball's total displacement after 2.00 s

s=u+gt²÷2

s= -19.6+9.8×2

s= -19.6 +19.6

s= 0 m

Hence, the total displacement of the ball after 2 s is 0 m.

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The net force is zero due to the direction.

We need to know about force resultant to solve this problem. The force resultant is the total net force applied to the object according to the direction. It can be written as

R = F1 + F2 + ... + Fn

where R is force resultant (net force)

From the question above, we know that

F1 = F2 = F N

Because the direction is the same, the force will be minus each other.

R = F1 - F2

R = F - F

R = 0 N

Hence, the net force is 0 N

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The answer is correct, the magnet will start rotating and the magnet on the left side will start rotating in a clockwise direction.

Something that can produce magnetic fields, pull similar poles apart, and attract opposing poles.

Basic characteristics of magnets include:

If two magnets are permitted to approach one another, their opposite poles will attract. If they are also given free rotation, their opposite poles will eventually come close to one another. The north poles of two magnets repel one another, and vice versa for the south poles.

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Answer: Ask the rest of the question.

Explanation:

Answer: Acceleration is 2m/s^2

Explanation:

The slope of a velocity graph is the acceleration

Acceleration = (Final Velocity - Initial Velocity) / Total Time

A = (12 - 2) / 5

A = 10/5

A = 2

Therefore the acceleration is 2m/s^2

The amplitude of the electric field in a plane electromagnetic wave is 100  v/m then the amplitude of the magnetic field is 3.34×[tex]10^{-7}[/tex].

Electromagnetic waves, or EM waves, are produced by the oscillations of an electric field and a magnetic field. In other words, electromagnetic (EM) waves are created when magnetic and electric fields oscillate.

Electromagnetic waves are produced when an electric field and a magnetic field interact. They are referred to as "electromagnetic" waves as a result. The electric field and magnetic field of an electromagnetic wave are perpendicular to one another (at right angles). They are also parallel to the direction of the EM wave.

According to the question,

Electric Field, E₀= 100 v/m and,

B₀/E₀=1/c

The amplitude of the magnetic field  will be :

B₀=E₀/c

=100/(3×[tex]10^{8}[/tex])

B₀=3.34×[tex]10^{-7}[/tex]

Hence, the amplitude of the magnetic field is 3.34×[tex]10^{-7}[/tex].

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The rocket is still moving at 30 Km/s after 60 seconds

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

The follwing data were obtained from the question:

From the data given, we were told that the rocket experience no forces.

This simply implies that the rocket was still moving at the said speed (i.e 30 Km/s)

Thus, we can conclude that the speed of the rocket after 60 seconds is 30 Km/s since it experience no forces.

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The liquid density is 1.25 g/ml.

We need to know about the density to solve this problem. Density is a unit that measures how dense an object is. Density can be measured by dividing mass by volume. It can be written as

ρ = m / V

where ρ is density, m is mass and V is volume

From the question above, we know that

m = 10.47 lb

V = 1 gal

Convert mass to grams

m = 10.47 lb

m = 10.47 x 453.592 grams

m = 4749.11 grams

Convert volume to milliliters

V = 1 gal

V = 1 x 3785.41 ml

V = 3785.41 ml

By substituting mass and volume, we can determine the density

ρ = m / V

ρ = 4749.11 / 3785.41

ρ = 1.25 g/ml

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If 4.71 l of nitrogen gas and 24.96 l of hydrogen gas were allowed to react, in total 16.616 L of ammonia could form.

The balanced reaction for this would be:

N2(g) + 3H2(g) → 2NH3(g)

assuming STP:

∴ V N2(g) = 4.71 L

∴ V H2(g) = 24.96 L

The ideal gas equation is stated as:

PV = RTn

∴ moles N2(g) = PV/RT

⇒ mol N2(g) = (1 atm) (4.71L)/ (0.082 atm.L/K.mol)(298 K)

⇒ mol N2(g) = 0.007 mol

∴ moles H2(g) = PV/RT

⇒ mol H2(g) = (1) (24.96) / (0.082) (298) = 1.021 mol (limit reagent)

∴ moles NH3(g) = (1.021 moles H2(g)) (2 moles NH3 / 3 mol H2) = 0.680 mol

∴ V NH3(g) = RTn/P

⇒ V NH3(g) = ((0.082 atm.L/K.mol)(298 K) (0.680 mol))/(1 atm)

⇒ V NH3(g) = 16.616 L

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Answer:

If the gas is ideal while volume and temperature stay unchanged, there would be a five-fold increase in the pressure of this gas.

Explanation:

Let [tex]V[/tex] denote the volume of this gas, let [tex]P[/tex] denote the pressure of the gas, let [tex]n[/tex] denote the number of particles in this gas, let [tex]T[/tex] denote the temperature of this gas, and let [tex]R[/tex] denote the ideal gas constant.

If this gas is an ideal gas, it would satisfy the ideal gas law:
[tex]P\, V = n\, R\, T[/tex].

Assuming that this gas is uniform. The mass of this gas will be directly proportional to the number of particles [tex]n[/tex] in this gas. Hence, a five-fold increase in the mass of this will increase the number of particles in this gas by five folds.

Rearrange this equation to separate pressure [tex]P[/tex] from the number of particles in this gas [tex]n[/tex]:

[tex]\begin{aligned} P &= \left(\frac{R\, T}{V}\right) \, n\end{aligned}[/tex].

In other words, if the temperature and volume of this gas stays the same, the pressure [tex]P[/tex] of this gas will be proportional to the number of particles [tex]n[/tex] in this gas. Thus, the five-fold increase in the number of particles (from a five-fold increase in mass) will increase the pressure of this gas by five folds.

Increase in wavelength of light leads to decrease in the radiation energy.

Radiation energy is inversely proportional to the wavelength of light. Thus, an increase in the wavelength of light will decrease the radiation energy and a decrease in the wavelength of light will increase the radiation energy.

Radiation energy is calculated by the formula:

E = hυ

where,

E is the radiation energy

h is the Planck’s constant

υ is the frequency

But,

υ = c / λ

where,

c is the speed light travels at in vacuum

λ is the wavelength of light

Therefore,

E = hc/λ

And thus, radiation energy and wavelength of light are inversely proportional.

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The power does the razor consume as it is ruined 160 watt.

From joules law of heating, current flows through a resistor, converts a part of electric energy into heat energy.

The rate at which the power dissipated through a resistor is,

[tex]P = V^2/R[/tex]

Here,V is the applied voltage or voltage from source Ris the resistance of the resistor, Resistance of the device Ac razor)is,

[tex]R = V^2/P[/tex]

[tex]= (120)^2/ 40[/tex]

= 14400/40

= 360 ohm

NOW, the input voltage is change to V1, new power consumed by the razor is

[tex]P_1 = V_1^2/R[/tex]

[tex]= (240)^2/360[/tex]

= 57,600/360

=160 watt

Joule's law is the e rate at which heat is produced in a conductor is directly proportional to the square f the current provided is resistance is constant.

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You are done with you vacation and you are about to go back to the u.s. then The local bank of 0.72 gdp is used.

The market worth of all the final goods and services produced and sold (not resold) in a certain time period by countries is measured in dollars using the term "gross domestic product" (GDP).

This measure is frequently amended before being regarded as a trustworthy indication due to its subjective and complex character.

To compare living standards between countries, using a basis of GDP per capita at purchasing power parity (PPP) may be more useful, whereas nominal GDP is more useful for comparing national economies on the global market. GDP (nominal) per capita does not, however, reflect differences in the cost of living and the inflation rates of the countries.

Therefore, You are done with you vacation and you are about to go back to the u.s. then The local bank of 0.72 gdp is used.

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The fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s is 256 Hz.

The fundamental frequency is the lowest frequency that any given instrument can produce. The instrument's first harmonic is another name for the fundamental frequency.

Given,

Length of the tube = 0.672-m

Speed of sound = 344 m/s

Tube open at both the ends

Solution:

Since the tube is open at both ends,

[tex]f_{n}[/tex] = n ([tex]V_{w/2L}[/tex])

n = 1, 2, 3, 4,...

[tex]f_{1}[/tex] = 1(344/2*0.672)

   = 256 Hz

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The fact that voyager 1 continues to speed out of the solar system even though its rockets have no fuel is an example of Newton's first law of motion.                                                                                                                                                  

Newton's first law of motion states that "an object will continue to be in a state of rest, or will continue to move at constant speed, unless it is acted upon by a force". In other words, if an object is already moving, it won't slow down or speed up on its own, unless it collides with another object, or a force acts on it.

Voyager 1 was launched in 1977 in an attempt to study the outer solar system. While it was being launched, rockets were used in order to break free from the gravitational pull of the earth. After that, the rockets continued to propel voyager 1 away from the earth, until it eventually ran out of fuel.

Even though its rocket is out of fuel, the satellite will continue to speed out of the solar system. This is because, according to Newton's first law of motion, voyager 1 will still continue in uniform motion out to space, unless it collides with an asteroid, or it enters the gravitational field of another planet, but for now, it will just continue to move.

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Answer: The total distance walked is about 59 meters more than the student’s displacement.

Explanation:

The student walked 58.57 meters more than compared to its total displacement from its starting point.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or an estimate based on other factors in common usage.

The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes. Displacement is the term used to describe this shift in an object's position.

According to the question :

A student walked 100 meters north and then walks 100 meters west then its displacement will be, according to the Pythagoras theorem

h² = p²+b²

h² = 100² + 100²

h² = 20,000

h = 141.42 meters

This means the total displacement is 141.42 meters, but the student has traveled 200 meters.

200 - 141.42 = 58.57 meters

Hence, the student walks 58.57 meters more than the total displacement.

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When using parallax, astronomers calculate distance from the sun and not earth to improve on the accuracy of their measurement, since parallax angle decreases as star distance increases.

Parallax enables astronomers to measure the distances of far away stars by using trigonometry.

As the distance of star increases, the parallax angle decreases, and great degree of accuracy is required for its measurement.

So taking a refence from the earth instead of the sun will impact the accuracy of their measurement.

Thus, when using parallax, astronomers calculate distance from the sun and not earth to improve on the accuracy of their measurement, since parallax angle decreases as star distance increases.

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Brand equity is a measure of the brand's ability to capture consumer preference and loyalty.

When compared to a generic equivalent, brand equity is the value premium that a firm raises from a product with a successful brand. Companies can build brand equity for their merchandise by making them easily recognizable,  memorable, and superior in terms of quality and dependability.

Customers graciously pay a premium for a company's products when it has good brand equity, even if they could purchase the exact thing from a rival for less. Customers effectively pay a high price to do business with a company they know and respect. Because the business with brand equity does not encounter a higher cost than its competitors to create and distribute the product, the price difference goes to their margin.

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Therefore, the calculated volume is 1000 cm³

The density of a place refers to the quantity of things—which may include people, animals, plants, or objects—there are in it. Divide the number of objects by the area's measurement to determine density. A country's population density is calculated by dividing its total population by its area, expressed in square kilometers or miles. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb).

Volume of fish tank = mass/ density

mass=1.0 kg=1000 g

density=1.0 g/cm³

volume=1000 cm³

Therefore, the calculated volume is 1000 cm³

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The acceleration of the following given forces and masses are Mass = 50 kg, Force = 150N, Acceleration = 3m/s², Mass = 50 kg, Force = 200N, Acceleration = 4m/s², Mass = 50 kg, Force = 250N, Acceleration = 5m/s², Mass = 50 kg, Force = 300N, Acceleration = 6m/s².

According to Newton's second law of motion, the rate of change of momentum is directly proportional to the force.

F = ma                                ----(1)

where,

m is the mass of the body

a is the acceleration by which body move

F is the force

From 1 equation,

a = F/ m

By substituting all the values, we get

For (1),

a = 150/ 50

a = 3m/s²

For (2),

a = 200/50

a = 4 m/s²

For (3),

a = 250/50

a = 5m/s²

For (4),

a = 300/50

a = 6 m/s²

Thus, we concluded that the acceleration of the following given forces and masses are

Mass = 50 kg, Force = 150N, Acceleration = 3m/s²

Mass = 50 kg, Force = 200N, Acceleration = 4m/s²

Mass = 50 kg, Force = 250N, Acceleration = 5m/s²

Mass = 50 kg, Force = 300N, Acceleration = 6m/s²

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