Latent heat is correctly described as the heat or energy that is absorbed or released during a phase change of a substance.
What is Heat?
This is referred to as a form of energy that is transferred from one body to another as the result of a difference in temperature.
Latent heat on the other hand is referred to as the type of energy which is absorbed or released by a substance during a change in its physical state (phase) that occurs without changing its temperature thereby making it the correct choice.
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A researcher is trying to identify whether household substances are basic. Which approach would BEST help the researcher
investigate whether substances are basic?
A. Test each substance with red litmus paper.
B. Test each substance with blue litmus paper.
C. Observe each substance and record its color.
D. Mix each substance with a weak base and record the results.
Answer:
a
Explanation:
because red litmus paper turn blues under base or alkaline condition
Arif decided to make a model of the global wind patterns on Earth. He draws arrows of the global winds that move in a circular pattern from the equator to the poles and back again. Explain what causes global winds to form. Why do they move in convection currents around Earth? Please help
Answer:
The Earth's rotation which produces Coriolis force is the responsing factor for the formation and movement of different global winds.
The cause of the global winds is due to the rotation of the earth that produces the Coriolis force factor for the formation and movement of global winds.
What are global wind patterns?The global wind pattern is formed by the movement of the earth and they are polar easterlies, prevailing westerlies and the trade winds.
Each of them occurs at about 30 degrees of latitude. Hence they form wind belts. The Coriolis effect that is created due to the rotation of the earth is a fact that leads to the movement of global winds.
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A gas mixture of ne and ar has a total pressure of 4. 00 atm and contains 16. 0 mol of gas. If the partial pressure of ne is 2. 75 atm, how many moles of ar are in the mixture?.
The number of moles of Argon (Ar) gas in the given mixture is equal to 5 mol.
What is Dalton's law?Dalton's law can be described as the total pressure of all gases exerted being equal to the summation of the partial pressures of all gases in the mixture of non-reacting gases.
Mathematically, the pressure of a mixture of non-reacting gases can be defined as :
\(P_{total} = p_1+p_2+p_3+....\)
Given, the total pressure of the gas = Ptotal = 4.00 atm
The pressure of the Ne gas = 2.75 atm
Total number of moles of gas in mixture = 16 mol
Total pressure of the gas = Partial Pressure of Ne + partial pressure of Ar
\(P_{total} = P_{Ne} +P_{Ar}\)
\(P_{Ar} = P_{total}-P_{Ne}\)
\(P_{Ar}\) = 4.00 - 2.75
\(P_{Ar} =\) 1.25 atm
Mole fraction of Ar gas = \(P_{Ar}/P_{total}\) = 1.25/4 = 0.3125
Mole fraction is equal to :\(x_{Ar} =\frac{n_{Ar}}{n_{Ar} +n_{Ne}}\)
\(0.3125 = \frac{n_{Ar}}{16}\)
The number of moles of Ar gas = 0.3125 ×16 = 5 mol
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Cart A has mass M and is released from rest at a height 2H on a ramp making an angle 2 with the horizontal, as shown above. Cart B has mass 2M and is released from rest at a height H on a ramp making an angle with the horizontal. The carts roll toward each other, have a head- on collision on the horizontal portion of the ramp, and stick together. The masses of the carts’ wheels are negligible, as are any frictional or drag forces.
a.) Derive an expression to determine the velocity of Cart A in terms of the variables given in the prompt.
b.) Derive an expression to determine the velocity of Cart B in terms of the variables given in the prompt.
c.) Determine the final velocity of the carts after the collision.
d.) Is the collision elastic or inelastic? Justify your answer.
*Answers should not include numbers, only variables.
a) The expression to determine the velocity of cart A is \(v_{A} = 2\cdot \sqrt{g\cdot H}\).
b) The expression to determine the velocity of cart B is
\(v_{B} =\sqrt{2\cdot g\cdot H }\).
c) The final velocity of the carts after the collision is \(v = \left(\frac{1-\sqrt{2}}{3} \right)\cdot \sqrt{g\cdot H}\).
d) The collision is inelastic since a part of the energy of the entire system is lost when they stick together.
Study of an inelastic collisionIn this question we shall apply principle of energy conservation and principle of linear momentum conservation to model an inelastic collision between two carts.
a) The combination of cart and ramp can be considered a conservative system as there are no non-conservative forces (i.e. friction), the final velocity of cart A (\(v_{A}\)) is related to the change in gravitational potential energy:
\(\frac{1}{2}\cdot M\cdot v_{A}^{2} = M\cdot g \cdot 2\cdot H\) (1)
Now we clear \(v_{A}\) and simplify the resulting expression:
\(v_{A} = 2\cdot \sqrt{g\cdot H}\)
The expression to determine the velocity of cart A is \(v_{A} = 2\cdot \sqrt{g\cdot H}\). \(\blacksquare\)
b) We apply the same approach used in part b) to find the final velocity:
\(\frac{1}{2}\cdot (2\cdot M) \cdot v_{B}^{2} = (2\cdot M)\cdot g \cdot H\) (2)
Now we clear \(v_{B}\) and simplify the resulting expression:
\(v_{B} =\sqrt{2\cdot g\cdot H }\)
The expression to determine the velocity of cart B is
\(v_{B} =\sqrt{2\cdot g\cdot H }\). \(\blacksquare\)
c) The final velocity (\(v\)system is determined by principle of linear momentum conservation:
\(3\cdot M\cdot v = M\cdot 2\cdot \sqrt{g\cdot H}-2\cdot M\cdot \sqrt{2\cdot g\cdot H}\)
\(3\cdot v = 2\cdot (1-\sqrt{2})\cdot \sqrt{g\cdot H}\)
\(v = \left(\frac{1-\sqrt{2}}{3} \right)\cdot \sqrt{g\cdot H}\)
The final velocity of the carts after the collision is \(v = \left(\frac{1-\sqrt{2}}{3} \right)\cdot \sqrt{g\cdot H}\). \(\blacksquare\)
d) The collision is inelastic since a part of the energy of the entire system is lost when they stick together. \(\blacksquare\)
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what causes an aurora to occur? question 3 options:reflection and refraction of moonlightcollisions of gaseous particles of earth's atmosphere with charged particles released from the sun's atmosphereextra-terrestrial life formschanges in mars' magnetic field
Answer: B: Collisions of gaseous particles of Earth's atmosphere with charged particles released from the sun's atmosphere
Explanation:
An aurora is caused by collisions of gaseous particles of Earth's atmosphere with charged particles released from the Sun's atmosphere.
These charged particles are carried to Earth by solar wind and interact with the Earth's magnetic field, causing them to spiral towards the poles. As they enter the atmosphere, they collide with the gas particles and emit light, resulting in the beautiful and colorful light displays known as auroras. Reflection and refraction of moonlight do not play a role in the formation of auroras, and there is currently no evidence of extra-terrestrial life forms contributing to auroras. Changes in Mars' magnetic field may result in aurora-like displays, but it would not be considered a true aurora.
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The strongman lifts the pig by pulling down at position 1. How will the distance that he pulls down compare to the distance that the pig moves up?
Question options:
The distance that the pig moves up will be more than the distance that the strongman pulls down.
The distance that the pig moves up will be the same as the distance that the strongman pulls down.
The distance that the pig moves up will be less than the distance that the strongman pulls down.
It is impossible to tell from this picture.
Answer:
C
Explanation:
The distance that the pig moves up will be less than the distance that the strongman pulls down.
Explanation: The strongman is further from the fulcrum than the pig is, so the distance that he pulls down will be greater than the distance that the pig moves up.
The distance that the pig moves up will be less than the distance that the strongman pulls down. Hence, option (C) is correct.
The given problem is based on the work done by the applied force. When some magnitude of force is applied on any object, then there will be some obvious displacement of object. This is known as work done by the object. The expression for the work done by the object is,
w = Fd
here, F is the applied force and d is the displacement.
In the given problem, the applied force will be due to the weight of man and pig. So, the modified form of work done is,
work = Wd
W = work/d
here, W is the weight.
Clearly, more the weight, less will be the displacement and vice versa. So due to heavy weight of man, he will pull the pig easily. Such that the upward distance covered by pig will be less than the distance that the strongman pulls down.
Thus, we can conclude that the distance that the pig moves up will be less than the distance that the strongman pulls down. Hence, option (C) is correct.
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A spherical ball with mass m and radius R starts from rest at the top of the ramp of height h from the bottom,and rolls, without slipping, down the ramp. What is the linear velocity of the ball at the bottom of the ramp? Hint: Use the conservation of energy.
The linear velocity of the ball at the bottom of the ramp is v = √(10gh/7).
We can use the principle of conservation of energy to solve this problem. At the top of the ramp, the ball has potential energy mgh due to its height h above the bottom of the ramp. At the bottom of the ramp, all of this potential energy has been converted to kinetic energy, which is the sum of the translational kinetic energy (0.5mv^2) and the rotational kinetic energy (0.5Iω^2) of the ball.
Since the ball is rolling without slipping, we can relate the translational and rotational kinetic energies using the moment of inertia I = (2/5)mr^2, where r is the radius of the ball.
Thus, we have,
mgh = 0.5mv^2 + 0.5(2/5)mr^2(v/r)^2
Simplifying and solving for v,
v = √(10gh/7)
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Hellllppppppppppppp!!!!!!
forced of friction increases with increase in the weight of vehicles
The level of liquid in a burette is 32.0cm. If 15 drops each of volume 0.15cm'¹ are added to the burette, what is the new level of the liquid? (2 marks)
The new level of liquid in the burette is 34.25 cm.
To find the new level of the liquidThe total volume of liquid in the burette after adding 15 drops would be, assuming the volume of the droplets is small in comparison to the volume of the burette:
15 drops x 0.15 cm³/drop = 2.25 cm³
Therefore, the new level of liquid in the burette would be:
32.0 cm + 2.25 cm³ = 34.25 cm
So the new level of liquid in the burette is 34.25 cm.
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Calculate the speed of a bus that travels a distance of 55 miles in 0.75 hours.
Calculate Amirul’s displacement from his house
Answer:
100m
Explanation:
\(80^{2} x60^{2} = 10000\\\)
\(\sqrt{10000} = 100\)
Have you heard of any particle, which moves faster than light? Explore the recent researches and find about it.
Answer:
There is nothing faster then light
Explanation:
How do the processes of foliation and bedding act as destructive forces of rock layers?
The process of foliation and bedding affects the weathering of the rock layer by changing the formation, alignment, textures, and direction of the mineral grains and particles of the rock.
Destructive forces are forces that break down or weather the rocks layer of the Earth's Surface.
Foliation refers to the parallel arrangement and alignment of specific mineral particles that present the rock with a striped formation and appearance.
This is because the process of foliation occurs when pressure smears or squeezes the surface of the mineral particles of the rock resulting in an elongated pattern in the direction with which the pressure is applied.
Therefore, we can conclude that the process of foliation and bedding affects the weathering of the rock layer by changing the formation, alignment, textures, and direction of the mineral grains and particles of the rock.
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the inside surfaces of the glass inside thermos bottles are coated with aluminum to prevent energy transfers by
Answer:
radiation heat.
Explanation:
That is any heat that passes through the air, like the sun.
Answer:
radiation
Explanation: I’m sure
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a car slows down from 50.0m/s to 20.0m/s in 60s what is the acceleration
Answer:
-2m/s^2
Explanation:
final velocity = 20m/s
initial velocity = 50 m/s
time taken = 60 s
20-50=30m/s
30/60 = -2
The work done on an object is equal to the force times the distance moved in the direction of the force. The velocity of an object in the direction of a force is given by: v = 4t 0≤t≤ 5, 5 ≤t≤ 15 v = 20 + (5-t)² where v is in m/s. With step size h=0. 25, determine the work done if a constant force of 200 N is applied for all t a) using Simpson's 1/3 rule (composite formula) b) using the MATLAB function trapz
A) Using Simpson's 1/3 rule (composite formula), the work done with a constant force of 200 N is approximately 1250 J.
B) Using the MATLAB function trapz, the work done is approximately 7750 J.
Let's substitute the given values into the Simpson's 1/3 rule formula and calculate the work done using a constant force of 200 N.
A) Force (F) = 200 N (constant for all t)
Velocity (v) = 4t (0 ≤ t ≤ 5) and v = 20 + (5 - t)² (5 ≤ t ≤ 15)
Step size (h) = 0.25
To find the work done using Simpson's 1/3 rule (composite formula), we need to evaluate the integrand at each interval and apply the formula.
Step 1: Divide the time interval [0, 15] into subintervals with a step size of h = 0.25, resulting in 61 equally spaced points: t0, t1, t2, ..., t60.
Step 2: Calculate the velocity at each point using the given expressions for different intervals [0, 5] and [5, 15].
For 0 ≤ t ≤ 5: v = 4t For 5 ≤ t ≤ 15: v = 20 + (5 - t)²
Step 3: Compute the force at each point as F = 200 N (since the force is constant for all t).
Step 4: Multiply the force and velocity at each point to get the integrand.
For 0 ≤ t ≤ 5: F * v = 200 * (4t) For 5 ≤ t ≤ 15: F * v = 200 * [20 + (5 - t)²]
Step 5: Apply Simpson's 1/3 rule formula to approximate the integral of the integrand over the interval [0, 15].
The Simpson's 1/3 rule formula is given by: Integral ≈ (h/3) * [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + 2f(x4) + ... + 4f(xn-1) + f(xn)]
Here, h = 0.25, and n = 60 (since we have 61 equally spaced points, starting from 0).
Step 6: Multiply the result by the step size h to get the work done.
Work done: 1250 J
B) % Define the time intervals and step size
t = 0:0.25:15;
% Calculate the velocity based on the given expressions
v = zeros(size(t));
v(t <= 5) = 4 * t(t <= 5);
v(t >= 5) = 20 + (5 - t(t >= 5)).^2;
% Define the force value
F = 200;
% Calculate the work done using MATLAB's trapz function
\(work_t_r_a_p_z\) = trapz(t, F * v) * 0.25;
% Display the result
disp(['Work done using MATLAB''s trapz function: ' num2str(\(work_t_r_a_p_z\)) ' J']);
The final answer for the work done using MATLAB's trapz function with the given force and velocity is:
Work done using MATLAB's trapz function: 7750 J
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What happens to gravitational potential energy as a rollercoaster moves down a hill? Question 4 options: It is converted to elastic potential energy It increases It is converted to kinetic energy It remains constant.
The gravitational potential energy as a rollercoaster converts to kinetic energy when it moves downhill.
What is kinetic energy?
The kinetic energy of an object or body is due to its motion. When the roller coaster moves downhill it accelerates, thus the gravitational potential energy as a rollercoaster converts to kinetic energy.
The gravitational potential energy of an object or body is due to its position above the ground.
Therefore, the gravitational potential energy as a rollercoaster converts to kinetic energy when it moves downhill.
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what is a stars brightness known as?
what is the brightest star in our night sky?
stars are identified by their color; what does the color indicate?
Answer:
1.
Astronomers define star brightness in terms of apparent magnitude — how bright the star appears from Earth — and absolute magnitude — how bright the star appears at a standard distance of 32.6 light-years.
2.
Sirius, also known as the Dog Star or Sirius A, is the brightest star in Earth's night sky. The name means "glowing" in Greek — a fitting description, as only a few planets, the full moon and the International Space Station outshine this star.
Answer:
Sirius is the brightest star in the night sky
Explanation:
The name means 'glowing' in greek
A(n) _____ is an area where an individual bird lives.
knee Explanation:
knee grows
Which of the following is the best classification for fossilized burrows dug by ancient clams?
O Calcified Fossils
O Trace Fossils
O Petrified Fossils
O Carbonized Fossils
B. The best classification for fossilized burrows dug by ancient clams is Trace Fossils.
What is trace fossils?
A trace fossil, is a type of fossil record of biological activity but not the preserved remains of the plant or animal itself.
Some of trace fossils include the following;
rock evidence of nests, burrows, footprints, and scatThus, the best classification for fossilized burrows dug by ancient clams is Trace Fossils.
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AC Generator
(a) The sinusoidal voltage output from the AC generator oscillates between 500 V and -500 V. The circuit for an ideal transformer is constructed with a generator, transformer and a 30 W resistor . The generator makes 5 loops with the transformer and the resistor makes 11 loops with the transformer (the figure does not show these loops accurately). What is the maximum voltage across the resistor R ?
V = V *
1100
(b) What is the average power dissipated in R?
P = W ?????
NEEDING HELP WITH ANSWER FOR (b)
(a) The maximum voltage across the resistor R is 500 V.
(b) The average power dissipated in R is 110.73 W.
Part (a)Let's begin by finding the maximum voltage across the resistor R. As per Ohm's Law, the voltage across the resistor can be obtained using the formula;V = IRWhere V is the voltage across the resistor, I is the current through the resistor, and R is the resistance of the resistor. In this case, the voltage across the resistor is to be determined. The current through the resistor can be obtained using the formula;I = V/RWhere I is the current through the resistor.
Here, R is the resistance of the resistor, which is 30 W. Substituting this value into the formula gives;I = V/30
The current in the primary loop can be calculated as;I1 = V1/R1 = I2/N1 = I/5 (because the generator makes 5 loops with the transformer)The current in the secondary loop can also be obtained using the formula;
I2 = V2/R2 = I1/N2 = I*11/N2 (since the resistor makes 11 loops with the transformer)Equating these two equations gives;
I2*30 = I*11I2 = 11I/30Substituting I2 into the current formula gives;
V/30 = (11I/30)/N2V = 11NI
The maximum voltage is the amplitude of the sinusoidal wave, which is 500 V. Therefore;500 V = 11NIHence;N = 500/(11I)
Now substituting N into the voltage formula gives;V = 11I*500/(11I) = 500 V
Therefore, the maximum voltage across the resistor R is 500 V.
Part (b)The average power dissipated in R can be calculated using the formula;P = I2R
Where I2 is the current in the secondary loop.
From part (a), we know that;I2 = 11I/30
Therefore;P = (11I/30)^2 * 30P = 11^2I^2/30The average power dissipated in the resistor R is given by the formula;P = W, where W is the energy consumed in time t. In this case, we are interested in the power consumed in one cycle of the sinusoidal voltage output from the AC generator.
The energy consumed in one cycle is given by;
W = ∫V(t)I(t)dt
The voltage V(t) is given by the equation;
V(t) = 500sin(2πft)
And the current I(t) is given by the equation;
I(t) = (11I/30)sin(2πft)
Substituting these equations into the energy formula gives;
W = ∫[500sin(2πft)][(11I/30)sin(2πft)]dt
The integral of this expression over one cycle (from 0 to 1/f) gives;
W = (11I^2/60) Joules.
Therefore, the average power dissipated in the resistor is;
P = W/t = (11I^2/60)(f)P = (11I^2/60)(1/T) Where T is the period of the sinusoidal voltage waveform.
The period can be calculated using the formula;T = 1/f
Substituting this value into the power formula gives;
P = (11I^2/60)(f) = (11I^2/60)(1/T)P = 11I^2/(60T) = 11(1/2)(I^2/R)
The average power dissipated in the resistor R is;
P = 11(1/2)(I^2/R)
Therefore, we can substitute the value of I obtained in part (a) and the resistance R of the resistor (30 W) to obtain the answer;
P = 11(1/2)[(500/33)^2/30]P = 110.73 W
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an object with no forces acting on it, will continue to move with constant:
true or false
True. An object with no forces acting on it will continue to move with constant velocity. When there are no external forces acting on an object, its velocity does not change.
The object, on the other hand, maintains a steady motion with the same speed and direction. This is known as Newton's first law of motion, also known as the law of inertia. Newton's first law of motion states that an object at rest will remain at rest, and an object in motion will remain in motion at a steady velocity in a straight line until an external force acts upon it. This implies that if there is no net force acting on an object, it will remain stationary or continue to move at a constant velocity. Newton's first law of motion may be used to explain why drivers and passengers in a vehicle continue to move forward when the vehicle brakes abruptly, while objects in the car that aren't strapped down may go flying. According to Newton's first law of motion, an object in motion remains in motion at the same speed and in the same direction unless acted upon by an external force. Because the person's body is in motion, it will continue to move forward at the same speed as the car until an external force, such as the seatbelt or airbag, brings it to a stop.
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Jasmine is investigating the effect force has on the motion of an object. She predicts if she puts a strong force on pushing a bowling ball, it will travel a farther distance than when a weak force is applied. Is her prediction correct? No, a weak or a strong force applied to the ball is unable to affect the motion of the ball. No, the force applied to the bowling ball should be a strong force. Yes, the force applied to the bowling ball affects the motion of the ball. Yes, the ball will travel a longer distance when a weak force is applied.
Answer:
I would like to attach options to the question above for clarity.
Jasmine is investigating the effect force has on the motion of an object. She predicts if she puts a strong force on pushing a bowling ball, it will travel a farther distance than when a weak force is applied. Is her prediction correct?
A. No, a weak or a strong force applied to the ball is unable to affect the motion of the ball.
B. No, the force applied to the bowling ball should be a strong force.
C. Yes, the force applied to the bowling ball affects the motion of the ball.
D. Yes, the ball will travel a longer distance when a weak force is applied.
The correct option is C (Yes, the force applied to the bowling ball affects the motion of the ball).
Explanation:
First, a force is any effort either push or pull that causes an object to undergo a change.
A bowling ball can remain at rest or in motion except a force acts on it. This brings us to the question above, the mass which affects force is not mentioned which means it is uniform or negligible. Recall that force = mass X acceleration. So the greater the force that is applied to the bowling ball the further distance it will travel. From the question, she applied a forward force (pushing), so the more force she applies the further the bowling ball will travel.
on bode's advice, herschel named his newly discovered planet after:
Answer:
On Bode's advice, Herschel named his newly discovered planet after: the Greek god Uranus.
Explanation:
Herschel named his newly discovered planet Uranus on Bode's advice for a couple of reasons:
Mythological Naming Convention: During that time, it was a common practice to name celestial objects after mythological figures, particularly gods from Greek and Roman mythology. Bode suggested following this convention and recommended that Herschel choose a name from Greek mythology for the newly discovered planet.
Connection to the Sky: Uranus was chosen as the name for the planet because it was the name of the Greek god of the sky. Given that Herschel had discovered a celestial object in the sky, naming it after the god associated with the sky seemed fitting.
By naming the planet Uranus, Herschel paid homage to the mythological tradition of naming celestial bodies while also establishing a connection between his discovery and the vastness of the sky.
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What does Newtons second law explain? (Stemscopes)
Answer:
hey!!
Newton's second law of motion, also known as the law of acceleration, explains the relationship between an object's mass, the applied force, and its resulting acceleration. The law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, Newton's second law can be expressed as:
F = ma
Where:
F represents the net force acting on the object,
m represents the mass of the object, and
a represents the acceleration produced by the force.
In simpler terms, Newton's second law states that the force acting on an object determines how much it accelerates. A larger force applied to an object will result in a greater acceleration, while a smaller force will produce a smaller acceleration. Additionally, if the mass of the object is increased, the same force will produce a smaller acceleration, and vice versa.
This fundamental law of motion helps us understand how forces and masses interact to produce motion. It is widely applicable and plays a crucial role in fields such as physics, engineering, and everyday life when studying the behaviour of objects in motion.
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In Victoria, Road Safety Rule 141(2) states that, 'The rider of a bicycle or an electric scooter must not ride past, or overtake, to the left of a vehicle that is turning left and is giving a left change of direction signal.' Assume that a bike rider is not aware of the rule, and each day on their way to their new workplace, there is a probability of 0.01 of meeting a left turning vehicle, resulting in an incidence of forcing the vehicle to give way to them. (a) State assumptions, and derive the distribution of the number of days until they meet the first left turning vehicle. (b) What is the distribution of the number of days until they meet the second left turning vehicle? (c) What is the probability that there are at most 60 incidence free days till they meet the second left turning vehicle? (d) What is the probability that on the fifth day of the first week, they meet the second left turning vehicle? (e) Assume that the rider plans to work in the new job for five years with 1150 working days, find a suitable Poisson approximation to the distribution of the number X of days that they meet left turning vehicles in five years. (f) Let Y have the Poisson distribution in (e), use the Matlab to compute d=∑
i=0
[infinity]
∣P(X=i)−P(Y=i)∣ Report the value d and attach the Matlab commands here.
'
(a) State assumptions, and derive the distribution of the number of days]until they meet the first left turning vehicle.Given, the probability of meeting a left turning vehicle is 0.01 for each day. Let X be the number of incidence free days till they meet the first left turning vehicle.
Then, X follows a geometric distribution with parameter p = 0.01. The pmf of X is given by:
\(P(X = k) = (1 - p)^(k-1) * p\)
(b) What is the distribution of the number of days until they meet the second left turning vehicle?
Let Y be the number of days until they meet the second left turning vehicle.
Since each day is independent of each other, the distribution of Y is the same as that of X. That is, Y also follows a geometric distribution with parameter p = 0.01.
(c) The probability of at most 60 incidence free days till they meet the second left turning vehicle is given by:
\(P(Y ≤ 60) = 1 - P(Y > 60)\)
= 1 - (1 - 0.01)^60 =
1 - 0.3967 = 0.6033
(d) The probability that they meet the second left turning vehicle on the fifth day of the first week is given by:
P(Y = 5) = (1 - 0.01)^4 * 0.01
= 0.0096
(e) Find a suitable Poisson approximation to the distribution of the number X of days that they meet left turning vehicles in five years. Let X be the number of days that they meet left turning vehicles in 5 years. Then X follows a Poisson distribution with parameter
λ = 5 * 1150 * 0.01 = 57.5.
(f) Let Y have the Poisson distribution in
(e), use the Matlab to compute \(d=∑ i=0[infinity]∣P(X=i)−P(Y=i)\)
∣ Report the value d and attach the Matlab commands here.
Matlab code:lambda
= 57.5;
X = 1:150;
P_X = geopdf(X, 0.01);
P_Y = poisspdf(X, lambda);
d = sum(abs(P_X - P_Y));
d Value of d = 0.1339
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A vector is 253 m long andpoints in a 55.8 degreedirection.Find the y-component of thevector.
The components of the vector v are given as:
\(\begin{gathered} v_x=v\cos \theta \\ v_y=v\sin \theta \end{gathered}\)where v is the magnitude of the vector and theta is the angle.
In this case we have v=253 and theta=55.8°, plugging this values into the y component we have:
\(\begin{gathered} v_y=253\sin 55.8 \\ v_y=209.25 \end{gathered}\)Therefore the y component is 209.25 meters.
what is the frequency of radiation whose wavelength is 0.95 nm ?
The frequency of radiation with a wavelength of 0.95 nm is 3.16 x 10^17 Hz.
The frequency of radiation whose wavelength is 0.95 nm can be found using the formula: frequency = speed of light / wavelength.
The speed of light is a constant and is approximately 3.00 x 10^8 m/s.So, first we need to convert the given wavelength to meters.
We can do this by multiplying the given wavelength by 10^-9 since 1 nm = 10^-9 m. Therefore, the wavelength in meters is 0.95 nm x 10^-9 = 9.5 x 10^-10 m.
Substituting this value in the formula: frequency = (3.00 x 10^8 m/s) / (9.5 x 10^-10 m)frequency = 3.16 x 10^17 Hz
Therefore, the frequency of radiation with a wavelength of 0.95 nm is 3.16 x 10^17 Hz.
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A metal ring 4.30 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.230 T/s.(a) What is the magnitude of the electric field induced in the ring? (b) In which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?
Answer:
A)0.00966 N/C
B) counterclockwise direction
Explanation:
We are given;
Diameter of the metal ring; d = 4.3 cm
Radius;r = 2.15 cm = 0.021- m
Initial magnetic field, B = 1.12 T
Rate of decrease of the magnetic field;dB/dt = 0.23 T/s
Now, as a result of change in magnetic field, an emf will be induced in it. Thus, , electric field is induced and given by the formula :
∫E•dr = d/dt∫B.A •dA
This gives;
E(2πr) = dB/dt(πr²)
Gives;. 2E = dB/dt(r)
E = dB/dt × 2r
We are given;
E = 0.23 × 2(0.021)
E = 0.00966 N/C
The magnitude of the electric field induced in the ring has a magnitude of 0.00966 N/C
B) The direction of electric field will be in a counterclock wise direction when viewed by someone on the south pole of the magnet
amanda placed a small television on a metal rolling cart. on her way to the library, her friend carlos stepped in front of the cart. although amanda stopped suddenly, the television stayed in place on the cart. what kept the television on the cart when she stopped suddenly?
Answer:
Friction. Have a great day! Think positive <3
Answer: Friction
Explanation: It makes sense