Find the range, mean, median, and mode of the following data set. 4, 24, 9, 19, 23, 21, 9, 20 a. Range 20 Mean 15.1 Median 20 Mode 9 c. Range 20 Mean 16.1 Median 19.5 Mode 9 b. Range 22 Mean 15.1 Median 20 Mode 4 d. Range 20 Mean 16.1 Median 20 Mode 19

Answer:

The acceleration of \(25\ m/s^2\) is produced in the person.

Explanation:

We have,

Mass of a person is 80 kg

Force acting on the person is 2000 N

It is required to find the acceleration produced in the person due to force.

The force acting on the person is given by :

\(F=ma\\\\a=\dfrac{F}{m}\\\\a=\dfrac{2000}{80}\\\\a=25\ m/s^2\)

So, the acceleration of \(25\ m/s^2\) is produced in the person.

Its P path describes the change of state i.e from solid to liquid.

"A solid is that state of matter which has a fixed shape, mass, and volume. It suffers very small changes in volume by changing the temperature. It can not be compressed, e.g. — Sand, Wood, Copper, Ice, etc."

"A liquid is a sample of matter that conforms to the shape of a container in which it is held, and which acquires a defined surface in the presence of gravity. The term liquid is also used in reference to the state, or condition, of matter having this property."

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a) Live wire

b) It has gained extra electrons.

c) Part of circuit can be turned off while other parts remain on.

d) \( R=\frac{V}{I}=60 \Omega\)

Answer:

smaller and further from

Explanation:

Pass light through something clear and light, you'll most likely be able to see all of it's rays spread out, the "normal." Now, pass it through something dense, the amount of light will shrink, therefore be further from the "normal."

As a result, there is no net charge inside the conductor. A conductor's net charge is always zero under electrostatic conditions.

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Answer:

\(0.361\ \text{m}\)

Explanation:

\(f_s\) = Frequency of source = 375 Hz

\(\Delta f\) = Difference between the maximum and minimum sound frequencies = 2.75 Hz

v = Speed of sound in air = 343 m/s

T = Time period = 1.8 s

\(v_m\) = Maximum speed of the microphone

We have the relation

\(\Delta f=2f_s\dfrac{v_m}{v}\\\Rightarrow v_m=\dfrac{\Delta fv}{2f_s}\\\Rightarrow v_m=\dfrac{2.75\times 343}{2\times 375}\\\Rightarrow v_m=1.26\ \text{m/s}\)

Amplitude is given by

\(A=\dfrac{v_mT}{2\pi}\\\Rightarrow A=\dfrac{1.26\times 1.8}{2\pi}\\\Rightarrow A=0.361\ \text{m}\)

The amplitude of the simple harmonic motion is \(0.361\ \text{m}\).

The time the two locomotives will take to reach each other is 1.07 minutes.The speed of both the locomotives is 155 km/hr with respect to the ground.The distance between both the trains at initial point is 8.5 km

We have to calculate the time it will take for them to meet:Distance is equal to speed multiplied by time, so the distance between them (8.5 km) is equal to the relative speed between them multiplied by the time it takes them to meet.Let's calculate the relative speed:Relative speed = Speed of locomotive 1 + Speed of locomotive 2= 155 km/hr + 155 km/hr= 310 km/hrNow we can use the formula:Distance = Relative Speed × Time

We know the distance and the relative speed. Therefore,Time taken to meet = Distance / Relative speed= 8.5 km / 310 km/hr= 0.0274 hoursConvert hours to minutes:1 hour = 60 minutes0.0274 hours = 0.0274 × 60 minutes = 1.07 minutesSo, the time the two locomotives will take to reach each other is 1.07 minutes.

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Equation of motion: To find the equation of motion and the oscillation frequency of a mass-spring system, we'll use Newton's second law of motion.

Force (F) = mass (m) × acceleration

F = ma

The force acting on a spring is given by Hooke's law:

F = -k x

where k is the spring constant and x is the displacement from the equilibrium position.

Thus, combining these two equations gives us the following equation of motion for a mass-spring system:

ma = -k x

Rearranging this, we get:

m(d²x/dt²) + k x = 0

This is the differential equation of motion of the mass-spring system.

Oscillation frequency:

The oscillation frequency can be calculated using the equation:

f = (1/2π) √(k/m)

where f is the frequency, k is the spring constant, and m is the mass.

Lagrange function:

The Lagrange function for a mass-spring system can be written as:

L = T - VL

is the difference between the kinetic energy (T) and potential energy (V) of the system.

The kinetic energy of the system is given by:

T = (1/2) mv²where m is the mass and v is the velocity.

The potential energy of the system is given by:

V = (1/2) kx²

where k is the spring constant and x is the displacement from the equilibrium position.

L = (1/2) mv² - (1/2) kx²

Equation of motion:

Using the Euler-Lagrange equation, the equation of motion for a mass-spring system can be derived.

It is given by:

d/dt (∂ L/∂v) - ∂L/∂x = 0

Substituting the values from the Lagrange function:

L = (1/2) mv² - (1/2) kx²∂L/∂v = m v ∂L /∂x = -k x.

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Answer:

they will align themselves with a magnetic field

Explanation:

Answer:

Explanation:

To find the distance covered by the dolphin , we use the formula

From the question

velocity = 17 m/s

time = 3600 s

We have

distance = 17 × 3600

We have the final answer as

Hope this helps you

(a)The tension in the cable is (M + m)(0.391)g.

(b)The tension in the cable is (0.391)mg.

(a) When the helicopter and the truck are moving downward together:

Let T be the tension in the cable.

The net force acting on the system is given by:

F_net = T - (M + m)g = (M + m)a

We are given that the downward speed is decreasing at a rate of 0.609g, which means the acceleration (a) is -0.609g (negative because it's in the opposite direction of the positive upward direction).

Substituting the values into the equation, we have:

T - (M + m)g = (M + m)(-0.609g)

Simplifying the equation:

T - (M + m)g = -0.609(M + m)g

T = -0.609(M + m)g + (M + m)g

T = (M + m)(1 - 0.609)g

T = (M + m)(0.391)g

(b) When the helicopter hovers and the truck is still moving downward:

In this case, the net force acting on the system is given by:

F_net = T - mg = ma

Since the helicopter is at rest, its acceleration (a) is zero.

The truck's downward speed is decreasing at a rate of 0.609g, which means the acceleration (a) is -0.609g (negative because it's in the opposite direction of the positive upward direction).

Substituting the values into the equation, we have:

T - mg = m(-0.609g)

Simplifying the equation:

T - mg = -0.609mg

T = -0.609mg + mg

T = (1 - 0.609)mg

T = (0.391)mg

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Answer:

THIS IS SUPER EASY!!!!!!

BOLD = ANSWER

Explanation:

REMEMBER: force = mass x acceleration

4. 6.0kg x 4.0m/s2 = 24N

5. 7.5kg x 8.3m/s2 = 62.25N

6. 2,000kg x 8.3m/s2 = 16,000N

REMEMBER: mass = force / acceleration

7. 6.0N / 3.0m/s2 = 2kg

8. 6.0N / 12.0m/s2 = 0.5kg

9. 20.0N / 5.0m/s2 = 4kg

10. 20.0N / 2.0m/s2 = 10kg

11. 4.0N / 7.3m/s2 = 0.55kg

12. 4.6N / 16.3 m/s2 = 0.28kg

I hope this helps u! :D

Answer:

15.76N

Explanation:

horizontal component =Fcos¢ = 20cos38 = 15.76N

horizontal component = Fx = F cos α

vertical component = Fy = F sin α

the horizontal component of the force on the box:

\(\tt =20\times cos~38^o\\\\=\boxed{\bold{15.76~N}}\)

Answer:

Sedimentary rocks.

Explanation:

A rock cycle can be defined as a concept used to describe the continuous process that leads to a rock's creation, formation, transformation from one form to another, destruction and reformation over a specific period of time. The natural phenomenons that influences the rock cycle are weathering, plate tectonic activity, erosion, etc.

A fossil can be defined as the mineral impression or remains of living organisms such as plants and animals that are prehistoric in nature.

Basically, the three (3) main types of rocks are; igneous rock, sedimentary rock and metamorphic rock.

Sediments come from living organisms such as plants to form organic sedimentary rocks and they are usually formed at pressure and temperature that doesn't destroy the fossils contained therein. Organic sedimentary rocks includes chalk, fossiliferous, coal, diatomite, etc. Also, some examples of inorganic land-derived sedimentary rocks are conglomerate, brescia and sandstone.

Hence, an organic sedimentary rock is a type of rock that contains or comprises of fossils.

Alec put 4 fins on each rocket.

Alec has a total of 14 fins to put on 3 rockets. To find out how many fins he puts on each rocket, we can divide the total number of fins by the number of rockets:

14 fins ÷ 3 rockets = 4 with 2 left over

Since he uses as many fins as he can on each rocket, he must put 4 fins on each of two rockets and 6 fins on the third rocket (for a total of 4+4+6 = 14 fins).

Thus, Alec puts 4 fins on each rocket.

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The correct answer is B) real, inverted, and magnification less than one.

When an object is placed closer to a concave mirror than its focal point distance, the image formed is real, inverted, and magnified. This is a result of the reflective properties of a concave mirror and the rules of ray optics. A real image is formed when the reflected light rays actually converge at a point. In this case, the real image is formed in front of the concave mirror. The image formed is also inverted, meaning it is upside down relative to the object. This occurs because the rays of light coming from the object converge after reflection at the mirror's surface. Furthermore, the magnification of the image is less than one. This means that the image appears smaller than the object. The magnification can be calculated as the ratio of the image height to the object height.

In summary, when the object's distance from a concave mirror is less than the focal point distance, the resulting image is real, inverted, and has a magnification less than one.

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Answer:False static friction helps us from not sliding it hold us.

Explanation:

The phenomenon you are describing is called habituation.

Once the cupcake has been on your desk for a while, your brain becomes accustomed to its presence and it no longer registers as noteworthy or interesting.

Habituation is defined as a behavioral response decrement that results from repeated stimulation and that does not involve sensory adaptation/sensory fatigue or motor fatigue.

Habituation is the reduction of a behavioral response to a stimulus after repeated presentations of that stimulus  Habituation can occur to stimuli detected by any of your senses. You may become habituated to loud sounds, bright lights, strong odors, or physical touch.

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The rock will take 3.61 seconds to hit the surface of the water.

The equations of motion can be described as the equation that described the relationship between the velocity (v & u), acceleration, time, and displacement (S) of a moving body.

The mathematical  expression of the equations of motion:

\(v = u +at\\S = ut +(1/2)at^2\\v^2-u^2 = 2aS\)

Given, the height of the bridge from the ground, h = 64.0 m

The gravitational acceleration on the rock, g = 9.8 m/s²

The initial speed of the rock, u = 0

From the 2nd equation of motion, calculate the time rock takes to hit the surface of the water:

h = ut + (1/2)gt²

64.0 = 0×t + (1/2)× 9.8×t²

t² = 64 ×2/9.8

t = 3.61 s

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The statement that does not explain why the apple speeds up as it falls is "The momentum of earth -apple system is conserved." The correct answer is Option A.

Momentum is the measurement of an object’s motion in relation to its mass and velocity. The formula for momentum is P = m x v where P stands for momentum, m stands for mass, and v stands for velocity.

Newtons Second Law states that force is equal to the change in momentum per change in time. The formula for Newton's Second Law is F = m x a where F stands for force, m stands for mass, and a stands for acceleration.

According to Newton's Second Law, an object's speed and direction can be altered by forces acting on it. Therefore, the fact that "The momentum of earth -apple system is conserved" does not affect the speed of the apple as it falls. So, option (a) is correct.

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you a 8 years oodn

Explanation:

The magnitude of current flowing through the conductance is:
(a) 0.2 A.

(b) 100 A.

(c) 10 e^(-2t) A.

(d) 0.5 sin(5t) A.

(e) 0 A.

To determine the magnitude of the current flowing through a conductance, we need to use Ohm's Law, which states that the current (I) flowing through a conductor is equal to the voltage (V) across it divided by its conductance (G).

Ohm's Law equation: I = V / G

Given the voltage across the conductance in each case, we can calculate the current magnitude using the given conductance values.

(a) Voltage = 2 mV, Conductance = 10 mS (10 ms)

I = (2 mV) / (10 mS)

I = 0.2 A

The magnitude of the current flowing through the conductance is 0.2 A.

(b) Voltage = -1 V, Conductance = 10 mS (10 ms)

I = (-1 V) / (10 mS)

I = -100 A

The magnitude of the current flowing through the conductance is 100 A.

(c) Voltage = 100 e^(-2t) V, Conductance = 10 mS (10 ms)

I = (100 e^(-2t)) / (10 mS)

I = 10 e^(-2t) A

The magnitude of the current flowing through the conductance is 10 e^(-2t) A.

(d) Voltage = 5 sin(5t) V, Conductance = 10 mS (10 ms)

I = (5 sin(5t)) / (10 mS)

I = 0.5 sin(5t) A

The magnitude of the current flowing through the conductance is 0.5 sin(5t) A.

(e) Voltage = 0 V, Conductance = 10 mS (10 ms)

I = (0 V) / (10 mS)

I = 0 A

The magnitude of the current flowing through the conductance is 0 A.

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The function of sleep theory supported by the illustration is sleep conserves and protects.

From the first sentence, bats sleep a lot because they face little danger from predators and as such, they have a high-calorie diet of insects.

From the second sentence, cows sleep less, because they face more danger from predators and as such, they have a low-calorie diet of insects.

We can conclude that sleep helps to keep animal safe. Therefore, the correct option will be, "Sleep conserves and protects".

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Measurement means weight, size, length, or capacity of something.

Answer:

Measurement is the length, weight, size, quantity, value, or amount of something.

A. The initial speed in which the ball should be thrown is 27.65 m/s

B. The total time spent by the ball in the air is 5.64 s.

A. Determination of the initial velocity

v² = u² – 2gh (since the ball is going against gravity)

0² = u² – (2 × 9.8 × 39)

0 = u² – 764.4

Collect like terms

u² = 0 + 764.4

u² = 764.4

Take the square root of both side

u = √764.4

u = 27.65 m/s

B. Determination of the total time spent by the ball in the air.

We'll begin by calculating the time taken to reach the maximum height.

s = ½(u + v)t

39 = ½(27.65 + 0)t

39 = ½ × 27.6 × t

39 = 13.825 × t

Divide both side by 13.825

t = 39 / 13.825

t = 2.82 s

Finally, we shall determine the total time.

T = 2t

T = 2 × 2.82

T = 5.64 s

Therefore, the total time spent by the ball in the air is 5.64 s

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The two example plots of potential energy as a function of position will be Simple Harmonic Oscillator Potential and Potential Well.

Potentials of the following kind can limit a particle to a certain region of space:

1) Simple Harmonic Oscillator Potential: This potential restricts the motion of an attached mass on a spring and restricts the vibration of a heterogeneous molecule about its mean location.

Consequently, an upward parabola will represent the plot for this function. The weak force that this potential energy represents is that. (In this case, the Restoring Force is in charge of changing the particle's potential energy.)

2) Potential Well: Particles are imprisoned in an area with less energy than the potential energy surrounding it, and as a result, they require energy to leave the system. Consequently, a particle Outside of this area of high potential, no assistance is possible.

Protons and neutrons are held within the boundaries of the nucleus by the Strong Nuclear Force, which has an exceptionally high potential. These subatomic particles are imprisoned inside this potential and are therefore unable to leave without assistance.

Potential will be in the form of

V(x)=0   for -L<x<L

V(x)=V   for x<-L and x>L

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Answer:

J = 500 kg-m/s

Explanation:

Given that,

Initial speed of the motor, u = 5 m/s

Final speed of the motor, v = 7 m/s

Mass of the boat, m = 250 kg

We need to find the impulse applied by the motor. We know that impulse is equal to the change in momentum. It is represented by letter J.

J = m(v-u)

J = 250 (7-5)

J = 500 kg-m/s

Hence, the impulse applied by the motor is 500 kg-m/s.

The magnitude of the velocity of the car after undergoing this acceleration is 14.14 m/s.

The final velocity of the car is calculated by applying the third kinematic equation as shown below.

Mathematically, the third kinematic equation for the final velocity of the car is given as;

v² = u² + 2as

where;

When the car starts from rest, the initial velocity = 0

v² = 0² + 2as

v² = 2as

v = √ ( 2as )

The final velocity of the car is calculated as follows;

v = √ ( 2 x 2 x 50 )

v = 14.14 m/s

Thus, the final velocity of the car is a function of the acceleration and the distance covered by the car.

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Answer:

Conditions under which the belt and pulleys are operating – The friction between the belt and pulley may decrease substantially if the belt happens to be muddy or wet, as it may act as a lubricant between the surfaces.

Explanation:

I hope that this would be helpful

Assemblies that are mandated to possess a minimum fire resistance rating from an independent testing agency, based on the occupancy they serve, are referred to as fire-rated assemblies.

These assemblies are vital for maintaining the safety of building occupants, as they provide crucial fire protection by limiting the spread of fire and smoke, allowing for safe evacuation, and facilitating effective firefighting operations.

Building codes and regulations are established to safeguard the lives of individuals and protect property in the event of a fire. As a part of these regulations, certain types of assemblies within a building must be designed and constructed to withstand the effects of fire for a specified duration. This requirement ensures that occupants have adequate time to evacuate safely, while also facilitating effective fire suppression and containment.

The assemblies that are subject to these fire resistance requirements are typically walls, floors, columns, and roofs. The specific assemblies and their fire resistance ratings depend on various factors, including the occupancy type, building height, size, and use. The fire resistance rating represents the amount of time the assembly can endure exposure to fire before it fails to perform its intended function.

To determine the fire resistance rating of an assembly, independent testing agencies, such as Underwriters Laboratories (UL) or the American Society for Testing and Materials (ASTM), conduct rigorous tests according to standardized procedures. These tests subject the assembly to controlled heating conditions that simulate a real fire scenario. The assembly's performance during the test, including factors like structural integrity, insulation, and smoke containment, is closely monitored and evaluated.

Once an assembly successfully passes the testing procedure, it is assigned a fire resistance rating based on the duration it withstood the fire conditions. Common fire resistance ratings include 30 minutes, 1 hour, 2 hours, and 3 hours, although other durations may be specified depending on the building code and regulations in a particular jurisdiction.

The purpose of these fire-rated assemblies is to compartmentalize a building, creating barriers that slow down the spread of fire and smoke. By having these rated assemblies, the progression of fire is impeded, allowing occupants more time to escape and giving firefighters an opportunity to control and extinguish the fire. Additionally, fire-rated assemblies also prevent fire from spreading to adjacent structures, minimizing the potential for significant property damage and loss.

It is important to note that the specific term used to refer to these assemblies can vary based on the building codes and regulations in different regions. Some common terms for these assemblies include fire-rated assemblies, fire-resistive assemblies, or simply fire-rated walls, floors, columns, or roofs.

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