which of these situations corresponds to n independent bernoulli trials having the same probability p of success?

Answer:

The number of hailstones striking the window per unit time is:

n = 580 hailstones / 41 s = 14.1463 hailstones/s

The mass of each hailstone is 7 g = 0.007 kg, and its speed is 6.7 m/s. The kinetic energy of each hailstone is:

K = (1/2) * m * v^2 = (1/2) * 0.007 kg * (6.7 m/s)^2 = 0.167 N*m

The angle of incidence is 31°, so the angle between the hailstones and the normal to the window is 59°. The average force on the window is the rate of change of momentum of the hailstones. The momentum of each hailstone before the collision is:

p1 = m * v * cos(59°) * (-i) + m * v * sin(59°) * j

where i and j are the unit vectors in the x- and y-directions, respectively. The negative sign in front of the i-vector indicates that the hailstone is moving to the left (in the negative x-direction).

The momentum of each hailstone after the collision is:

p2 = m * v * cos(59°) * i + m * v * sin(59°) * j

The change in momentum of each hailstone is:

Δp = p2 - p1 = 2 * m * v * cos(59°) * i

The rate of change of momentum (i.e., the force) is:

F = n * Δp / Δt

where Δt is the time for each hailstone to strike the window. This time is equal to the width of the window divided by the component of the velocity perpendicular to the window, which is:

Δt = 1.346 m / (v * sin(59°)) = 1.346 m / (6.7 m/s * sin(59°)) = 0.139 s

Substituting the values, we get:

F = 14.1463 hailstones/s * 2 * 0.007 kg * 6.7 m/s * cos(59°) * (-i) / 0.139 s

F = 28.051 N * i

Therefore, the average force on the window is 28.051 N, in the negative x-direction.

Explanation:

Answer:

Explanation:

??????????

A 0.842g sample of Hydrogen-3 decays to 0.0526g. Approximately 4.206 half-lives have occurred.

To determine the number of half-lives that have occurred, we can use the decay equation and the concept of exponential decay. The decay equation for radioactive decay is given by:

N(t) = N₀ * (1/2)^(t/T),\((1/2)^(^t^/^T^),\)

where N(t) is the remaining amount of the substance at time t, N₀ is the initial amount, t is the time elapsed, and T is the half-life of the substance.

In this case, we have an initial mass of 0.842g (N₀) and a remaining mass of 0.0526g (N(t)). We can set up the equation as follows:

0.0526g = 0.842g \(* (1/2)^(^t^/^1^2^.^3^2)\),

where t represents the number of half-lives that have occurred.

To solve for t, we can take the logarithm of both sides of the equation:

log(0.0526g/0.842g) = log\([(1/2)^(^t^/^1^2^.^3^2^)\)].

Using the logarithmic property log(\(a^b\)) = b*log(a), we can rewrite the equation as:

log(0.0526g/0.842g) = (t/12.32) * log(1/2).

Simplifying further:

log(0.0526g/0.842g) = (t/12.32) * (-log2),

where log2 is the logarithm base 2.

Now, we can solve for t:

t = (12.32 * log(0.0526g/0.842g)) / (-log2).

Using the given values and performing the calculation, we find:

t ≈ 4.206.

Therefore, approximately 4.206 half-lives have occurred.

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Answer:

1 km

Explanation:

displacement =velocity ×time

displacement =40m/s ×25s

displacement =1000m equivalent to 1km

The potential and kinetic energy of the system at the following time instances is zero and maximum.

From the given,

The displacement of the system is, x = A cos(3πt/T)

1) At t =0, the displacement of the system is given by, x = cos(3π×0/T)= cos(0) = 1. The displacement is maximum at t=0. Hence, the potential energy is maximum and kinetic energy is zero.

2) At t=T, the displacement, x = cos(3πT/T)= cos(3π) = -1. The displacement is minimum and hence, the potential energy is minimum and kinetic energy is maximum.

3) At t = T/6, the displacement x = cos(3πT/6T)=cos(π/2)=0, the displacement is zero, and hence, both the potential and kinetic energy is zero.

4) At t=T/3, the displacement, x= cos(3πt/T)=cos(3πT/3)= -1. The displacement is minimum and hence, the potential energy is minimum and kinetic energy is maximum.

5) At t=T/2, the displacemetn x = cos(3πt/T) = cos(3πT/2T) = cos (3π/2)=0. Hence, both the potential and kinetic energy is zero.

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Answer:

quizlet

Explanation:

they help

If all of the resistors in the diagram below are equivalent, then the voltage across the resistor R2 is 2.5 V.

The value of resistor is not give take the value of resistor 5Ω

R2 and R3 are in series hence its equivalent resistor Rs is R2 + R3 = 10Ω

R1 = 5Ω and Rs = 10Ω both this resistors are in parallel hence,

I()s = V/Rs = 5/10 = 0.5 A

I(1) = V/R1 = 5 / 5 = 1 A

In order to get voltage across R2 we have to apply voltage devider rule,

voltage across R2 is

V(R2) = R2 ÷ (R1 + R2) V

Putting all the values

V(R2) = 5/10 × 5

V(R2) = 5/10 × 5 = 2.5 V

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Answer:

Explanation:

if he is moving at a constant velocity, the work changes the potential energy

W = PE = mgh = 80(9.8)(5) = 3,920 J

Power is the rate of doing work

P = W/t = 3920/10 = 392 W(atts)

Approximately 0.123 kg of liquid water at 26 degrees Celsius would be needed to melt 41 grams of ice.

To calculate the minimum amount of liquid water required to melt 41 grams of ice at 0°C, we need to consider the energy required for the phase change from solid to liquid, which is known as the specific heat of fusion of ice.

The energy required to melt 1 kg of ice is 3.33×105 J/kg.

Therefore, the energy required to melt 41 grams of ice is (3.33×105 J/kg) × (41/1000) kg = 13653 J.

To calculate the amount of liquid water required, we use the specific heat capacity of water, which is 4180 J/kg/°C.

Assuming the initial temperature of water is 26°C, the amount of water needed can be calculated as (13653 J) ÷ (4180 J/kg/°C) ÷ (26°C) = 0.123 kg or approximately 123 ml of water.

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The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².

To calculate the average acceleration of the motorcycle, we can use the formula:

Average acceleration = (final velocity - initial velocity) / time

First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.

Converting the final velocity:

Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s

Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:

Average acceleration = (21.67 m/s - 0 m/s) / time

To find the time taken to reach this velocity, we need to use the formula for average speed:

Average speed = total distance/time

Rearranging the formula:

time = total distance / average speed

Plugging in the values:

time = 50 m / 21.67 m/s ≈ 2.31 seconds

Now we can calculate the average acceleration:

Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²

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The specific heat capacity of the metal, given that 27.777 g of water at 22.1 °C was mixed with the metal is 9.7×10⁻² Cal/gºC

Step 1: Obtain the heat absorbed by the water. This is shown below:

Q = MCΔT

= 27.777 × 1 × 7.2

= 199.9944 Cal

Step 2: Determine the specific heat capacity of the metal using the heat absorbed by the water. Details below:

Q = MCΔT

-199.9944 = 29.292 × C × -70.6

-199.9944 = -2068.0152 × C

Divide both sides by -2068.0152

C = -199.9944 / -2068.0152

= 9.7×10⁻² Cal/gºC

Thus, the specific heat capacity of the metal is 9.7×10⁻² Cal/gºC. None of the options are correct.

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According to the statement, on the assumption of requesting help from a statistical software consultant, the given case that P(A) + P(B) = 1 is not true, since A and B are not mutually exclusive events.

It is possible for the next request to be related to both SPSS and SAS, in which case it would be included in both A and B.  Therefore, we cannot simply add their probabilities to get the total probability of either event.

B. P(A') represents the probability that the next request is NOT related to the SPSS package. We can find this by subtracting P(A) from 1, since the sum of the probabilities of an event and its complement is always equal to 1:

P(A') = 1 - P(A) = 1 - 0.30 = 0.70

Therefore, the probability that the next request is NOT related to SPSS is 0.70.

C. P(A ∪ B) represents the probability that the next request is related to either SPSS or SAS or both. We can find this by using the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Where P(A ∩ B) represents the probability that the next request is related to both SPSS and SAS. Since we don't have information about the probability of this intersection, we cannot calculate P(A ∪ B) exactly. However, we know that the probability of the intersection must be between 0 and the minimum of P(A) and P(B), which in this case is 0.30. Therefore, we can say:

0 ≤ P(A ∩ B) ≤ 0.30

and use this range to get a lower and upper bound for P(A ∪ B):

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) ≤ 0.30 + 0.50 - 0 = 0.80

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) ≥ 0.30 + 0.50 - 0.30 = 0.50

Therefore, the probability that the next request is related to either SPSS or SAS (or both) is between 0.50 and 0.80.

D. P(A' ∩ B') represents the probability that the next request is NOT related to either SPSS or SAS. We can find this using the formula:

P(A' ∩ B') = P((A ∪ B)')

Where (A ∪ B)' represents the complement of the event that the next request is related to either SPSS or SAS (or both). We can find (A ∪ B)' using the formula:

(A ∪ B)' = A' ∩ B'

Which represents the event that the next request is NOT related to either SPSS or SAS. Therefore:

P(A' ∩ B') = P((A ∪ B)') = 1 - P(A ∪ B)

From part c, we know that 0.50 ≤ P(A ∪ B) ≤ 0.80, so:

P(A' ∩ B') = 1 - P(A ∪ B) ≤ 1 - 0.50 = 0.50

P(A' ∩ B') = 1 - P(A ∪ B) ≥ 1 - 0.80 = 0.20

Therefore, the probability that the next request is NOT related to either SPSS or SAS is between 0.20 and 0.50.

Complete question:

Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS. Suppose that P(A) =. 30 and P(B) = .50.

a. Why is it not the case that P(A) + (B) = 1?

b. Calculate P(A ′).

c. Calculate P(A ∪B).

d. Calculate P(A′ ∩B′).

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The quantity of heat energy that must be transferred to 2.25 kg of brass to raise its temperature from 20 °C to 240 °C is 195030 J

First, we shall list out the given parameters from the question. This is shown below:

The quantity of heat energy that must be transferred can be obtained as follow:

Q = MCΔT

= 2.25 × 394 × 220

= 195030 J

Thus, we can conclude quantity of heat energy that must be transferred is 195030 J

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ANSWER

EXPLANATION

First, let us sketch a diagram to represent the problem:

From the diagram:

The circle represents the tightrope walker with a mass of 60kg

W represents the weight of the tightrope walker

T represents the tension on the rope

θ is the angle the sagged rope makes with the horizontal.

The vertical forces acting on the sagged rope are the tension and weight of the tightrope walker.

Notice that there are two tension forces acting on the rope, so, the vertical forces are:

According to Newton's second law, the total vertical force must be equal to 0, so:

Make T subject of formula:

where m = mass; g = acceleration due to gravity

Applying trigonometric ratios, we have that:

From the question:

mass, m = 60kg

This means that the tension on the rope is:

That is the answer.

AnswerHM???

Explanation:

I dONT KNOW

Hence the maximum pressure exerted by the brick is 2450 dyne/cm²

Given the mass of the brick=5kg

Dimension of  the brick=20cm*10cm*2cm.

So weight of the brick= F= mg

Where f= force on the body due to gravity

where m= mass, g= gravity.

So F= 5000*9.8

by doing the multiplication we get the result as

F= 49000 dyne where dyne is unit of force

Where surface area is 10cm*2cm is in contact with the ground then

Area= (10*2)= 20cm²

Applying pressure formula = F/Area= 49000/20

By dividing we get the answer as= 2450 dyne/cm²

When surface area is 20cm*2cm is in contact then

Area= 20cm*2cm= 40cm²

Applying pressure formula = F/Area= 49000/40 dyne/cm²=  1225 dyne/cm²

When the surface area is 20cm*10cm in contact then

Area= 20cm*10cm= 200cm²

By applying the pressure formula= F/Area= 49000/200=245 dyne/cm²

Hence the maximum pressure exerted by the brick is 2450 dyne/cm²

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Energy is directly proportional to the amplitude.

Thus, the amplitude of the wave increases as the energy of the wave increases.

The car is moving at approximately 12.5 meters per second.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = 1/2 * m * \(v^2\)

where

KE = kinetic energy,

m =Mass of the object, and

v = velocity.

In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .

Substituting the  values , we have:

125,000 J = 1/2 * 1600 kg *\(v^2\)

Now, we can solve for v by rearranging the equation:

\(v^2\) = (2 * 125,000 J) / 1600 kg

\(v^2\) = 156.25 \(m^2/s^2\)

Taking the square root, we find:

v = √156.25\(m^2/s^2\)

v ≈ 12.5 m/s

Therefore, the car is moving at approximately 12.5 meters per second.

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Answer:

1.3515x10^5pa

Explanation:

Plss see attached file

The instrument that can measure the diameter of pencil should have a very small least count. Thus we can use screw gauge to measure the diameter of a pencil. The screw gauge has a least count of 0.001 mm.

Therefore ,we can measure the diameter of a pencil with high accuracy using screw gauge.

A 66.1-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. He then drops through a height of 1.59 m, and ends with a speed of 8.51 m/s. The nonconservative work done on the boy is approximately -42.7 kilojoules.

To find the nonconservative work done on the boy, we need to consider the change in the boy's mechanical energy during the process. Mechanical energy is the sum of the boy's kinetic energy (KE) and gravitational potential energy (PE).

The initial mechanical energy of the boy is given by the sum of his kinetic energy and potential energy when he catches the wave:

E_initial = KE_initial + PE_initial

The final mechanical energy of the boy is given by the sum of his kinetic energy and potential energy after he drops through the height:

E_final = KE_final + PE_final

The nonconservative work done on the boy is equal to the change in mechanical energy:

Work_nonconservative = E_final - E_initial

Let's calculate each term:

KE_initial = (1/2) * m * v_initial^2

= (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = m * g * h_initial

= 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * m * v_final^2

= (1/2) * 66.1 kg * (8.51 m/s)^2

PE_final = m * g * h_final

= 66.1 kg * 9.8 m/s^2 * 0

Since the boy ends at ground level, the final potential energy is zero.

Substituting the values into the equation for nonconservative work:

Work_nonconservative = (KE_final + PE_final) - (KE_initial + PE_initial)

Simplifying:

Work_nonconservative = KE_final - KE_initial - PE_initial

Calculating the values:

KE_initial = (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * 66.1 kg * (8.51 m/s)^2

Substituting the values:

Work_nonconservative = [(1/2) * 66.1 kg * (8.51 m/s)^2] - [(1/2) * 66.1 kg * (1.60 m/s)^2 - 66.1 kg * 9.8 m/s^2 * 1.59 m]

Calculating the result:

Work_nonconservative ≈ -42.7 kJ

Therefore, the nonconservative work done on the boy is approximately -42.7 kilojoules. The negative sign indicates that work is done on the boy, meaning that energy is transferred away from the boy during the process.

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Answer:

The avarage power of the body is 96.898 watts.

Explanation:

We must notice that given definition of power implies a constant consumption of energy, so that we should assume that energy consumption is constant. A Calorie is equal to 4186 joules. If we know that \(E = 2000\,Cal\) and \(t = 1\,day\), the power of body, measured in watts, is:

\(P = \frac{(2000\,Cal)\cdot \left(4186\,\frac{J}{Cal} \right)}{(1\,day)\cdot \left(24\,\frac{h}{day} \right)\cdot \left(3600\,\frac{s}{h} \right)}\)

\(P = 96.898\,W\)

The avarage power of the body is 96.898 watts.

The weight of the drop 4.19 × 10⁻¹⁸ and the electric field strength needed to balance its weight is 2.36 × 10⁵N/C.

Test = k | Q | r 2 when E = F q. The size of the electric field produced by a point charge Q is determined by this equation. The distance r in the denominator is the separation between the point of interest and the point charge, Q, or the center of a spherical charge.

a) The weight is just the mass of the drop times the acceleration of gravity.

W = mg

Or in terms of density.

W = рVg

We can calculate the volume (R=1 m = 0.000001 m) if we assume that a drop's volume is spherical.

V = 4/3πR³

V = 4/3π(10⁻⁶)³

V = 4.19 × 10⁻¹⁸

Then, using equation (1), the weight will be:

W = 920 × 4.19 × 10⁻¹⁸×9.81

W = 3.78 × 10⁻¹⁴

b) To balance the weight, the electric field times the charge must be the same value in the opposite direction, which means:

W - qE = 0

E = W/q electron

E = 3.78 × 10⁻¹⁴/1.60 × 10⁻¹⁹

E = 2.36 × 10⁵N/C.

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We have that the more energy per second to radiated by the hotter  is mathematically given as

Energy per second=256

Question Parameters:

One star has a temperature of 20,000 K

and another star has a temperature of 8,000

Generally the equation for the Energy per second   is mathematically given as

Energy per second is Proportional to T^4

Where

T=20000/8000

T=4

therefore

Energy per second=4^4

Energy per second=256

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The increase in length of the iron wire when warmed from 20°C to 45°C is approximately 8.25 millimeters. The specific heat capacity of the object is approximately 9.62 J/kg°C. The heat capacity of the object is approximately 1.83 J/°C.

ΔL = L × α × ΔT

Where:

ΔL is the change in length

L is the original length of the wire

α is the coefficient of linear expansion for iron

ΔT is the change in temperature

The coefficient of linear expansion for iron is typically 1.1 x \(10^(^-^5^)\) °\(C^(^-^1^)\).

Given:

L = 30 m (original length of the wire)

α = 1.1 x \(10^(^-^5^)\) °\(C^(^-^1^)\) (coefficient of linear expansion)

ΔT = 45°C - 20°C = 25°C (change in temperature)

ΔL = 30 m × (1.1 x \(10^(^-^5^)\) °\(C^(^-^1^)\)) × 25°C

= 30 m × 1.1 x\(10^(^-^5^)\) × 25

= 8.25 x \(10^(^-^3^)\) m

2) Q = mcΔT

Where:

Q is the heat energy transferred

m is the mass of the object

c is the specific heat capacity

ΔT is the change in temperature

Given:

Q = 2200 J (heat energy transferred)

m = 190 g (mass of the object)

ΔT = 12°C (change in temperature)

a. Specific heat capacity (c):

one need to rearrange the formula to solve for c:

c = Q / (m × ΔT)

Substituting the given values:

c = 2200 J / (190 g × 12°C)

First, need to convert the mass to kilograms:

m = 190 g = 190 g / 1000 = 0.19 kg

Now can calculate the specific heat capacity:

c = 2200 J / (0.19 kg × 12°C)

= 9.62 J/(kg°C)

b. Heat capacity (C):

The heat capacity is the amount of heat energy required to raise the temperature of the object by 1 degree Celsius.

C = mc

Substituting the given values:

C = 0.19 kg × 9.62 J/(kg°C)

= 1.83 J/°C

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The body has levels of organization that build on each other. Cells make up tissues, tissues make up organs, and organs make up organ systems. The function of an organ system depends on the integrated activity of its organs. For instance, digestive system organs cooperate to process food.

The answer is : C

Answer:

decrease

Explanation:

weight

As water accumulates in the car, its speed decrease according to Newton's second law of motion

Newton's second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

according to newton's second law

force = mass * acceleration

as water accumulate in the car , mass will increase

since mass and acceleration are inversely proportional to each other

hence , acceleration will decrease and speed will decrease

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Answer:

find it yourself too lazy for math but here's the step

Explanation:

it's the object mass multiplied by the velocity.

Answer:

d

Explanation:

there is not enough information about the liquid to know the force required for each. ie. stirring a cup of water is different than stirring a cup of pudding.