Compound interest is more advantageous than simple interest because it allows for the accumulation of interest on both the principal amount and the interest earned over time. In simple interest, interest is only earned on the principal amount, while in compound interest, the interest earned is added to the principal amount and then interest is earned on the new, higher amount. This leads to a compounding effect where the interest earned increases over time, resulting in a larger total return on investment. Additionally, compound interest is commonly used for long-term investments such as retirement funds and savings accounts, where the power of compounding can significantly increase the final amount earned.
Four point masses 2kg, 4kg, 6kg and 8kg are placed at the corners of Square ABCD of 2cm long respectively. Find the Position of centre of mass of the system from the corner A.
The position of the center of mass of the system from corner A is 4.3692cm.
To find the position of the center of mass of the system, we need to use the formula:
C.M. = (m1r1 + m2r2 + m3r3 + m4r4)/(m1 + m2 + m3 + m4)
where m1, m2, m3, and m4 are the masses of the four-point masses, and r1, r2, r3, and r4 are the distances of the point masses from the reference point (in this case, corner A).
Let's first find the distances of the four-point masses from corner A. We can see that the distance of the 2kg mass from corner A is 2 cm. The distance of the 4kg mass from corner A is the diagonal of a square of side 2 cm, which is sqrt(22 + 22) = 2.828 cm. Similarly, the distances of the 6kg and 8kg masses from corner A are also 2.828 cm.
Now, let's substitute the values in the formula:
C.M. = (2kg2cm + 4kg2.828cm + 6kg2.828cm + 8kg2.828cm)/(2kg + 4kg + 6kg + 8kg)
C.M. = (4cm + 11.312cm + 16.968cm + 22.624cm)/20kg
C.M. = 1.824cm + 0.5656cm + 0.8484cm + 1.1312cm
C.M. = 4.3692cm
Therefore, the position of the center of mass of the system from corner A is 4.3692cm.
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Complete the following sentences:
Wave speed is NOT dependent on _________ or ____________. Instead, wave speed only changes when the ______________ changes. This means that if a sound wave is traveling in pure water and the frequency doubles, the wavelength must _________.
Mel adjusted, in a futile attempt to strengthen his pectoral muscles, stretches a spring exercise device 0.73 meters by exerting a force of 177N. What is the stiffness constant
In the case, Mel stretches a spring exercise device by 0.73 meters with a force of 177 N. We can use Hooke's law, which states that the force applied to a spring is directly proportional to the displacement of the spring from its equilibrium position, to calculate the stiffness constant.
Hooke's law is given by the equation:
F = kx, where F is the force applied to the spring, k is the stiffness constant, and x is the displacement of the spring from its equilibrium position.
Plugging in the given values:
Force (F) = 177 N Displacement (x) = 0.73 m
We can rearrange the equation to solve for the stiffness constant (k):
k = F / x
Plugging in the values:
k = 177 N / 0.73 m
k ≈ 242.47 N/m (rounded to two decimal places)
Therefore, the stiffness constant of the spring exercise device is approximately 242.47 N/m.
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[Rotational motion] Calculate the length L between the 40N weight and the pivot needed to balance the beam shown in Figure 10.9. (solution says it's 7 m but it's unclear how it was obtained)
Answer:
L = 7m
Explanation:
The beam is balanced (not moving), so the moments about the pivot have to sum to 0.
Let x = dist. from pivot to the 10N ↓ force
CCW rotation is +
CW rotation is -
(100 N)(3 m) - (10 N)(x) - (40 N)(L) = 0
300 N·m - (10 N)(x) - (40 N)(L) = 0 divide by 10 on both sides
30 - x - 4L = 0
x + 4L = 30
10N is the Weight of the beam, so it is at the midpoint of the beam.
x = 5 - 3 = 2 m substitute into the equation above:
2 + 4L = 30
4L = 30 - 2 = 28
L = 28/4 = 7 m
What is the natural period of oscillation of your leg when you march? Compute your velocity? Explain your answer; make comments. (Please use formula and explain with your words clearly)
Electric Electronics Engineering course - Vibrations and Titrations
The natural period of oscillation of a leg when marching is the time it takes for one complete cycle of oscillation. It can be calculated using the formula:
T = 2π √(L/g)
What is the oscillation about?Where T is the natural period of oscillation, L is the length of the leg, and g is the acceleration due to gravity (9.81 m/s^2).
Assuming an average leg length of 1 meter, the natural period of oscillation of a leg is:
T = 2π √(1/9.81) ≈ 0.64 seconds
To compute the velocity of the leg during the march, we can use the formula:
v = 2πL/T
where v is the velocity, L is the length of the leg, and T is the natural period of oscillation.
Substituting the values, we get:
v = 2π(1)/(0.64) ≈ 9.8 m/s
Therefore, This means that during the march, the leg moves back and forth with a velocity of approximately 9.8 meters per second. It's important to note that this calculation assumes a simple harmonic motion, which may not be the case in reality due to the complex motion of various joints and muscles involved in marching.
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are physical quantities and fundamental quantities same
Answer:
The physical quantities are the quantities that are the base quantities of the measurement. They are known as the fundamental quantities. The units of those units are known as the fundamental units. The derived physical quantities are dependent on the fundamental quantities.
How did earth change about 2.5 billion years ago when many organisms began using photosynthesis to make food
A. The amount of oxygen in the atmosphere increased
B. Mass extinctions occurred
C. The oceans became larger
D. Rainfall increased
A 5.0 kg block and a 4.0 kg block are connected by a 0.6 kg rod. The links between the blocks and the rod are denoted by A and B. A force F is applied to the upper block.
In Figure 4.2, the blocks and rod assembly move downward at constant velocity. The applied force F is closest to:
a)88 N
b)90 N
c)92 N
d)94 N
e)96 N
Answer::
D) 94 N
F = M a = (5.0 + 4.0 + .6) a
a = 9.80 m/s^2 since only acceleration is gravitational
F = 9.6 * 9.8 = 94 N
4 A student notices that she gets a shock when she touches a metal door handle she has been charged by walking across a carpet. Would she get a shock if the handle was made of plastic?
Answer:
Not likely
Explanation:
She might feel a slight shock if she touches a plastic door handle after walking across a carpet, but not nearly as much as when she touches a metal handle. This is because plastic is an insulator, which means it does not conduct electricity very well. Metal is an excellent conductor. When the student drags her feet across a carpet, she builds up a negative electric charge on her body. Free electrons are released from the carpet due to friction between the carpet and her shoes, and the electrons collect on the surface of her body. If she touches a metal object like a door handle, the electrons flow from her body to the metal, resulting in a static discharge--a shock. However, if she touches a plastic object, the charge will not flow as easily and she is less likely to feel a shock. The electrons on her body repel the electrons in the metal door knob, leaving the surface of the metal doorknob positively charged, so the electrons jump across a short air gap to the metal door and she feels an electrical shock. This won't happen so dramatically with a plastic handle because the electrons in plastic won't be as easily repelled as in a metal handle.
What is the inertia of motion?
Answer:
The ability of a body to resist changes to its uniform motion condition is known as inertia of motion.
___________________
Hope this helps!
13. List the general strengths and weaknesses of epidemiology for providing an answer to Mary Beth’s question.
14. List the specific strengths and weaknesses of this study.
15. List the general strengths and weaknesses of toxicology for providing an answer to Mary Beth’s question.
The general strengths of epidemiology for providing an answer to Mary Beth’s question.
epidemiology can study a large populationepidemiology can identify patterns and trends in health and diseaseepidemiology can be used to study different diseases and health conditionsThe general weaknesses of epidemiology for providing an answer to Mary Beth’s question:
epidemiology may not provide a definitive answer or explanationepidemiology results may be affected by biases and confounding variablesThe Specific strengths of a study:
Big sample sizeLengthy follow-up periodThe specific weaknesses of a study are :
Use of self-recorded data, which may be inaccurate or biasedBiased selection due to non-random samplingWhat is epidemiology?Epidemiology is described as the study and analysis of the distribution, patterns and determinants of health and disease conditions in a defined population.
The main objective of epidemiology has been said is to find out what causes different health outcomes in different groups of people.
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Economics NCS Topic Test No 5. Perfect Market 1.3. Give ONE term for each of the following descriptions. Write uonly the term next to the question numbers (1.3.1 to 1.3.5) in the ANSWER BOOK. Abbreviations, acronyms and examples will NOT be accepted. 1.3.1 Actual expenditure of business such as wages and interest 1.3.2 The cost that changes as more or less outputs are produced 1.3.3 An institution that can make final decisions by reviewing the decisions of the competition commission and Tribunal. 1.3.4 A word that describe the characteristics of differentiated product in oligopoly or monopolistic competition. 1.3.5 A period when inputs or factors of production are fixed. (5x1) (5) TOTAL SECTION A: [201
1.3.1 - Operating costs
1.3.2 - Variable costs
1.3.3 - Competition Appeal Court
1.3.4 - Product differentiation
1.3.5 - Short run
What is inertia of motion explain one example?
THE INABILITY OF A BODY TO CHANGE ITS STATE OF MOTION BY ITSELF
example : a passenger tends to fall forward when breaks are applied in a busThe tendency of an item to resist a change in its state of motion is referred to as inertia. It specifically refers to an object's resistance to any change in velocity, whether that change be in speed or direction.
What is Inertia ?When you are riding in a car and the driver abruptly stops, you are experiencing inertia of motion. Because of inertia, your body wants to continue going forward at the same pace and in the same direction as before the brakes were applied. You will lean forward as a result, and if you are not wearing a seatbelt, you may be flung forward. Similarly, while the automobile speeds, your body tries to remain at rest owing to inertia, causing you to be motionless. Despite being widely accepted, Aristotle's theory of motion was challenged by prominent philosophers multiple times over the course of roughly two thousand years. For instance, Lucretius claimed that mobility rather than stasis (stagnation) was the "default state" of the matter (following, presumably, Epicurus).
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Which model of the universe is the most widely accepted, and what does it
predict?
A. An open universe, in which the universe never stops expanding
B. A flat universe, in which the universe stops expanding but does not
contract
C. A closed universe, in which the universe stops expanding but does
not contract
OD. A closed universe, in which the universe never stops expanding
Which step of the PRICES method is represented by the letter S?
A.
Raise the injured area above the heart.
B.
Stop the activity until the injury is evaluated.
C.
Wrap the injured site to decrease swelling.
D.
Apply a brace or a splint to the area.
Two whistles emit sounds of wavelength 3.2 m and 2.9 m which produce a beat frequency of about? a) 2 hertz b) 3 hertz c) 4 hertz d) 7 hertz e) 11 hertz
Two whistles emitting sound of wavelength 3.2 m and 2.9 m would produce a beat of frequency 11 Hertz, hence option e.
The beat frequency (f_beat) is given by the difference in frequency (f) between the two whistles,
f_beat = |f₁ - f₂ |, frequencies of the two whistles are f₁ and f₂ . The frequencies can be calculated from the wavelengths (λ) using the formula,
f = c/λ, speed of sound in air is c, which is approximately 343 m/s at room temperature and atmospheric pressure. For the first whistle with a wavelength of 3.2 m,
f₁ = c/λ₁
= 343/3.2
= 107.1875 Hz
For the second whistle with a wavelength of 2.9 m,
f₂ = c/λ₂
= 343/2.9
= 118.2759 Hz
The difference in frequency is,
f_beat = |f_1 - f_2|
= |107.1875 - 118.2759| ≈ 11.1 Hz
Therefore, the beat frequency is approximately 11 hertz.
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A boy of mass 60 kg and a girl of mass 40 kg are together and at rest on a frozen pond and push each other apart. The girl moves in a negative direction with a speed of 3 m/s. What must be the total final momentum of the boy and girl combined?
A. 0 kgm/s
B. -120 kgm/s
C. 120 kgm/s
D. -100 kgm/s
Answer:
Explanation:
The total initial momentum of the system is zero since the boy and girl are at rest initially. According to the law of conservation of momentum, the total final momentum of the system must also be zero.
If the girl moves in a negative direction with a speed of 3 m/s, then she gains a momentum of -3 x 40 = -120 kgm/s in the negative direction. To conserve momentum, the boy must gain a momentum of +120 kgm/s in the positive direction, so that the total momentum of the system remains zero.
Therefore, the total final momentum of the boy and girl combined is 120 kgm/s in the positive direction. The answer is C. 120 kgm/s.
Answer:
The girl acquires a velocity of -3 x 40 = -120 kgm/s in the negative direction if she goes with a speed of 3 m/s in the opposite direction. The boy must acquire a momentum of +120 kgm/s in the positive direction to preserve and keep the system's overall momentum at zero.
Explanation:
The answer is option D
Brainliest please :)
How does the frequency of a string affect its wavelength?
Answer:
As the frequency goes down, the speed goes down by the same factor, and so the wavelength doesn't change
Explanation:
A 100-volt electromotive force is applied to an RC-series circuit in which the resistance is 400 ohms and the capacitance is 10−4 farad. Find the charge q(t) on the capacitor if q(0) = 0
And also the current in I(t)
The charge q(t) on the capacitor would be, [tex]q(t)= 0.25c(1-e^{-t/0.04s})[/tex]
And the current I(t) in the circuit will be,[tex]I(t)= 0.25mA(1-e^{-t/0.04s})[/tex]
To find the charge q(t) on the capacitor at any time t, we can use the equation for the charge on a capacitor in an RC circuit:
[tex]q(t)= Q_{max} (1-e^{-t/RC})[/tex]
where Qmax is the maximum charge on the capacitor, R is the resistance, C is the capacitance, and t is time.
To find Qmax, we can use the equation for the maximum charge on a capacitor in an RC circuit:
Qmax = E × C
where E is the electromotive force.
So, we have:
Qmax = 100 V × 10⁻⁴F = 0.01 C
Using the given values of R and C, we have:
R*C = 400 ohms × 10⁻⁴F = 0.04 s
Substituting these values into the equation for q(t), we get:
[tex]q(t)= Q_0.01(1-e^{-t/0.04C})[/tex]
To find the current I(t), we can use Ohm's law and the equation for the charge on a capacitor:
I(t) = (1/R) × d(q(t))/dt
where d(q(t))/dt is the derivative of q(t) with respect to time.
Taking the derivative of q(t), we get:
[tex]dq(t)/dt= 0.01C (1-e^{-t/0.04C})[/tex]
Substituting this into the equation for I(t), we get:
[tex]I(t)= (1/400ohm)(0.01/0.04s) (1-e^{-t/0.04C})[/tex]I
Simplifying, we get:
[tex]I(t)= 0.25mA(1-e^{-t/0.04C})[/tex]
Therefore, the charge q(t) on the capacitor is:
[tex]q(t)= 0.25c(1-e^{-t/0.04s})[/tex]
And the current I(t) in the circuit is:
[tex]I(t)= 0.25mA(1-e^{-t/0.04s})[/tex]
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What is the force of gravity between two 70.0kg masses that are separated by 2.50m?
Answer:
F = 5.2324 x 10⁻⁸ N
Explanation:
F = G(m₁ · m₂) / r²
where F is the gravitational force, G is the gravitational constant (6.674 x 10⁻¹¹ N·m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between them.
Plugging in the given values m1 = m2 = 70.0 kg, r = 2.5 m:
F = (6.674 x 10⁻¹¹)(70.0 kg)² / (2.50 m)²
F = 5.2324 x 10⁻⁸ N
Therefore, the gravitational force between the two 70.0 kg masses separated by 2.50 m is approximately 5.2324 x 10⁻⁸ N.
3. You may have seen this question previously but now you will approach it using energy
concepts.
A pair of sleds weighs 25 kg and experience a frictional force of 25 N. If a dog team applies a
175 N force pulling it 12 m find:
a) the work done by friction.
b) the work done by the dog team.
c) the net work done (using the net force). How does then net work compare to the answers
from the previous two parts of the question?
d) What form of energy does the frictional force represent? What form of energy does the net
force produce?
a) Work done by friction is 300 J.
b) Work done by the dog team is 2100 J
c) Net work done 1800 J.
d) loss of mechanical energy.
How to determine work done?a) The work done by friction can be calculated using the formula
W = Fd, where F = frictional force and d = distance moved.
Therefore, W = 25 N × 12 m = 300 J.
b) The work done by the dog team can be calculated using the same formula, where F = force applied by the dog team.
Therefore, W = 175 N × 12 m = 2100 J.
c) The net work done is the sum of the work done by the dog team and the work done by friction.
Therefore, the net work done is
2100 J - 300 J = 1800 J.
The net work done is positive, which means that the sleds have gained energy.
d) The frictional force represents the loss of mechanical energy due to the interaction between the sleds and the ground. This energy is converted into thermal energy or heat. The net force produced by the dog team produces kinetic energy, which is the energy of motion of the sleds.
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11 When you stand on scales you see your mass in kg. Explain whether
it is your mass or your weight that makes the scales work.
When yоu stаnd оn а scаle, thе reаding thаt yоu sее is аctuаlly а meаsurement оf thе forсe thаt yоur bоdy is еxеrting оn thе scаle.
What makes the scale workThis forсe rеsults frоm thе grаvitаtiоnаl аttrаctiоn between yоur bоdy аnd thе eаrt. Тhe scаle meаsures thе forсe with а sрring or а string gаuge, cоnverts thе reаding tо а morе рrecise meаsurement in kilogrаms, аnd finаlly reсords thе rеsult.
Thus, thе scаles operаte bаsed оn thе forсe еxеrtеd by yоur bоdy, whiсh is dirеctly proportiоnаl tо yоur wеight. Тhe forсe оf grаvity аcting оn аn оbject is cаlled wеight, аnd it vаries bаsed оn thе mаss оf thе оbject аnd thе strength оf thе grаvitаtiоnаl field. On thе othеr hаnd, mаss is а meаsurement оf thе quаntity оf mаtter present in аn оbject аnd is cоnstаnt аcross time.
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Eli is a 9-year-old and his friend has asked him to share his test answers. Eli refuses to let his friend cheat off his paper because he does not want to get in trouble with the teacher Given Eli’s age and response, which stage of moral development did he demonstrate:
Group of answer choices
Preoperational
Conventional
Preconventional
Postconventional
The stage of moral development Eli demonstrated is Preconventional.
The early stage of moral development can be seen in preconventional morality. Up until about age nine, it persists. Children's decisions at this age are mostly influenced by what adults expect of them and the repercussions of disobeying them.
Morality is externally regulated at the preconventional level. In order to avoid punishment or gain rewards, people abide by the rules that are set forth by authority figures. According to this viewpoint, what is morally correct depends on one's ability to get away with it or what will make them feel good about themselves.
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A 0.1 kg toy train car moving at 1.0 m/s runs into a stationary car with a mass of 0.15 kg. At what speed do they move off together?
We can use the conservation of momentum principle to solve this problem. According to this principle, the total momentum of a system of objects remains constant if there are no external forces acting on the system. In this case, we can assume that there are no external forces acting on the two cars after they collide, so the total momentum of the system before the collision must be equal to the total momentum of the system after the collision.
The momentum of an object is defined as its mass multiplied by its velocity:
momentum = mass * velocity
Before the collision, the momentum of the first car (m1) is:
p1 = m1 * v1 = (0.1 kg) * (1.0 m/s) = 0.1 kg⋅m/s
Since the second car is stationary, its momentum before the collision is zero:
p2 = m2 * v2 = (0.15 kg) * (0 m/s) = 0 kg⋅m/s
The total momentum of the system before the collision is:
p1 + p2 = 0.1 kg⋅m/s + 0 kg⋅m/s = 0.1 kg⋅m/s
After the collision, the two cars move together with a common velocity (v), so the momentum of the system is:
p = (m1 + m2) * v
We can set the total momentum before the collision equal to the total momentum after the collision:
p1 + p2 = p
0.1 kg⋅m/s + 0 kg⋅m/s = (0.1 kg + 0.15 kg) * v
0.1 kg⋅m/s = 0.25 kg * v
v = 0.1 kg⋅m/s ÷ 0.25 kg
v = 0.4 m/s
Therefore, the two cars move off together at a speed of 0.4 m/s after the collision.
What type of circuit is shown
=When three resistors are connected in parallel, they form a parallel circuit. In a parallel circuit, each resistor is connected across the same two points, with the current split between the resistors.
In this configuration, the voltage across each resistor is the same, but the current through each resistor can be different. The total resistance of the circuit is calculated using the equation:
1/R_total = 1/R1 + 1/R2 + 1/R3
where R1, R2, and R3 are the resistance values of the individual resistors.
The total current in the circuit is equal to the sum of the currents through each resistor:
I_total = I1 + I2 + I3
where I1, I2, and I3 are the currents through each resistor.
The total power dissipated in the circuit can be calculated using the equation:
P_total = V² / R_total
where V is the voltage across the resistors.
In summary, when three resistors are connected in parallel, they form a parallel circuit, with each resistor connected across the same two points, and the current split between them. The total resistance, current, and power dissipated in the circuit can be calculated using the equations provided.
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How long will the light take in travelling a distance of 500 m in water refractive index of water is 1.33 and velocity of light in vacuum is 3 × 108 m/s. [2] Ans: 2.2 x 10 s
The light will take 2.2 μs in travelling a distance of 500 m in water refractive index of water is 1.33 and velocity of light in vacuum is 3 × 10⁸ m/s.
When a light is going from medium 1 to medium 2. The refractive index is defined as a ratio of velocity of light in medium 1 to velocity of light in medium 2. Refractive index is the factor which deals with the amount of bending of light. More refractive index means more it will bend in the medium 2. When it is 1 we can say that light has not been bent.
refractive idex of the medium is given by,
μ = velocity of light in vacuum/ velocity of light in medium
velocity of light in water = velocity of light in vacuum/ μ
velocity of light in water = 3 × 10⁸ m/s. / 1.33
velocity of light in water = 2.25 × 10⁸ m/s
Time = distance/velocity
Time = 500 m / 2.25 × 10⁸ m/s
time = 222 × 10⁸ s
time = 2.2 μs
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The figure below shows electrons moving along an electric current towards and away from the light bulb.
Electrons traveling along an electric current. Arrow under electrons points right and left both towards and away from the light bulb.
Does this figure show a direct or alternating current? Explain your response.
Based on the information provided, it is likely that the figure shows an alternating current (AC). The arrows under the electrons pointing right and left, both towards and away from the light bulb, indicate that the direction of the electron flow is changing periodically. This is a characteristic of alternating current, where the flow of electric charge reverses direction periodically, typically in a sinusoidal manner.
In an AC circuit, the voltage also changes direction periodically, which is consistent with the changing direction of the electron flow shown in the figure.
In an alternating current, the flow of electrons periodically reverses direction, causing the current to switch between positive and negative values. This is different from direct current (DC), where electrons flow in a single, constant direction.
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Which of the rays drawn above would be correct as the light goes from the air into the water? (5 points)
A
B
C
Answer:
First option A
Explanation:
Since the light is passing from air (less dense) into water (more dense), it is bends downwards.
The answer above is wrong because like I mentioned light bends when it goes through a medium and option B doesn't match that, so please don't use that answer.
Hope I helped and have a great day ahead.
6.
Sonography uses infrasonic waves to create images of objects found inside other objects.
True
False
Sonography uses infrasonic waves to create images of objects found inside other objects.-False
Sonography, commonly known as ultrasound imaging, creates pictures of structures and organs inside the body using high-frequency sound waves (rather than infrared rays). These sound waves are emitted by a transducer, a portable device put on the skin and deliver sound waves through the body. The waves reverberate off internal organs and structures and are picked up by the transducer, which generates a visual representation on a computer screen. Ultrasonic imaging is widely used in obstetrics to monitor fetal development and in other medical specialties to diagnose and treat various disorders.
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6.3 A probability found through quantum mechanics. In the test of Bells
theorem, experiment 6.2, what is the probability given by quantum
mechanics that, if the orientation settings are different, the two
detectors will flash different colors?
According to the given information, regardless of the orientation settings, the two detectors will flash different colors with probability . This prediction is based on quantum mechanics.
How to explain the experimentIn the experiment described, a pair of atoms are produced from a central source and detected by two detectors that are separated by a distance of nearly seven miles.
Each detector has the possibility of being oriented as A, B, or C, and is mounted with two colored lamps, a red lamp, and a green lamp.
According to the predictions of quantum mechanics, if the orientation settings of the two detectors are the same, then the two detectors always flash different colors.
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