by what factor would the torsion constant need to be changed to make the smaller balance wheel oscillate at the original frequency? express your answer using three significant figures.

If quasars are located at the distances that the majority of astronomers think they are, then their luminosities must equal the sum of one hundred trillion (1014) Suns.

Something's luminosity is determined by how much light it emits or reflects. A big, sparkling diamond's brightness is its most distinguishing feature. You might talk about the luminosity of an energetic and vibrant oil painting or be in awe of the luminosity of a spectacular sunset.

Small (2–3 point) training benefits are obtained via lumosity training. If you exercise for 12 and a half hours over several weeks, you can enhance your IQ, working memory, and other cognitive abilities by about 2-3 points.

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This collision violates conservation of both energy and momentum i.e, third option is correct.

According to the law of conservation of momentum, when two bodies collide their total momentum and energy before and after collision are equal.

According to the law of conservation of energy, energy can neither be created nor destroyed. However, it can be transformed from one form to another. It is also known as the first law of thermodynamics.

Given that, the two bodies move with same velocities after collision, means that the law has not been violated since, momentum = mass*velocity (where mass is said to be constant)

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The maximum speed with which the car can round the curve is 12.1 m/s

The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction.

The force produced between surfaces that slide against one another is known as the frictional force.  Because frictional force develops when two surfaces come into contact with one another, it is referred to be a contact force. Walking on the road is an illustration of frictional force.

According to the given information

radius, [tex]$r=30 \mathrm{~m}$[/tex]

coefficient of friction, [tex]$\mu_k=0.50$[/tex]

Here friction : force will balance centripetal force.

[tex]$\begin{aligned} &\left(F_k=\text { Friction force })\right. \\ & F_k=\frac{m v^2}{r} \\ & \mu m_g=\frac{m v^2}{r} \\ & \mu g=\frac{v^2}{r} \\ & v^2=r \mu g=30 \times 0.5 \times 9.8 \\ & v=12.1 \mathrm{~m} / \mathrm{s}\end{aligned}$[/tex]

The maximum speed with which the car can round the curve is 12.1 m/s

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Answer:

Force = 93 N

Explanation:

Given:

m₁ = 1500 kg

R₁ = 0.15 m

R₂ = 0.012 m

g = 9.8 m/s²

_____________

F₂ - ?

1)

Piston area:

S₁ = π·R₁² = 3.14·0.15² ≈ 71·10⁻³ m²

S₂ = π·R₂² = 3.14·0.012² ≈ 0.45·10⁻³ m²

2)

Force:

F₁ = m₁·g = 1500·9.8 = 14 700 N

F₂ = F₁· (S₂ / S₁)

F₂ = 14 700· (0.45·10⁻³ / (71·10⁻³) ≈ 93 N

The frequency is 5 x 10^14 Hz, the speed of light in the medium is 2 x 10 m/s and the wavelength is

4 x 10^-7 m

Given that,

Wavelength X = 600 nm

Refractive index n = 1.5

We know that,

The frequency is the ratio of the speed of light and wavelength of the light.

f = c/λ

f = 3 x 10^8/600 × 10^-9

f = 5 x 10^14 Hz

The speed in the medium is the ratio of the speed of the light in the vacuum and the refractive index.

n = c/v

1.5 = 3 x 10^8/υ

v = 2 × 10^8 m/s

The wave length is the ratio of the speed of the light in the medium and frequency.

λ = v/f

λ = 2 × 10^8/5 x 10^14

λ = 4 × 10^-7 m

Hence, The frequency is 5 x 10^14 Hz, the speed of light in the medium is 2 x 10^8 m/s and the wavelength is 4 x 10^-7 m

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So, by moving the slit towards the laser will increase the slit and screen distance and the screen and the fringe will be bigger, angle of diffraction, wavelength will remain unaltered in this case

What is diffraction?

When waves flow through an aperture or around objects, they spread out, which is referred to as diffraction. It happens when the wavelength of the incident wave and the size of the aperture or obstruction are on the same order of magnitude. The majority of the wave is blocked at extremely small aperture diameters. Large apertures prevent severe diffraction from occurring as the wave passes past or through the obstruction.

What is wavelength?

Wavelength is the separation between the corresponding points of two successive waves. When two points or particles are referred to be "corresponding points," it means that they are both in the same phase means, points that have completed identical fractions of their periodic motion.

Hence, by moving the slit towards the laser will increase the slit and screen distance, and the screen and the fringe will be bigger, angle of diffraction, wavelength will remain unaltered in this case.

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Five times per second is the typical frequency at which another pendulum swings back and forth. 2S

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Generator component within an absorption refrigeration system requires heat transfer from a high temperature source.

The evaporator "buckets" or collects heat from the chilled area. Low pressure causes the "bucket" to undergo a state shift (latent heat transfer) as it takes in heat. The "bucket" of low pressure and heat is then transported to the compressor by the evaporator. The component of the refrigeration system that actually cools things down is called the evaporator. The evaporator is situated in the region to be cooled because its purpose is to absorb heat into the refrigeration system (from where you don't want it to).

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A circular loop of wire with a radius of 13.0 cm and oriented in the horizontal XY-plane is located in a region of the uniform magnetic field. A field of 1.7 T is directed along the positive z-direction, which is upward. A) If the loop is removed from the field region in a time interval of 2.9 ms,

The average emf that will be induced in the wire loop during the extraction process=

e =(pi) r^2B/t

e = pi*169*10^-4*1.7/(2.9*10^-3) = 31.12 V

In classical geometry, a radius of a circle or sphere is any of the line segments from its middle to its perimeter, and in greater present-day usage, it is also their length. The call comes from the latin radius, which means ray but additionally, the spoke of a chariot wheel.

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The emf created around the wooden loop is equivalent to the emf generated around the wire loop if the loops are moved precisely the same distance from and closer to the magnets.

Give an explanation about EMF.

The electric potential created by either modifying the magnetic field or by an electrochemical cell is known as electromotive force (emf).

Due to the fact that Faraday's law is independent of the material and only considers how the flux is changing, the emf produced around the wooden loop is equivalent to the emf produced around the wire loop. Due to the fact that the loop material moves close to the end of the bar magnet, modifying the magnetic flux through the loop, even though it is not a part of the magnetic flux expression, an emf is nevertheless produced.

Hence, the answer is the emf created around the wooden loop is equivalent to the emf generated around the wire loop if the loops are moved precisely the same distance from and closer to the magnets.

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The maximum angle with respect to the normal that this light can strike the emerald/air interface such that the light wave exits into the air is: 39.34.

Total Internal Reflection

[tex]M_{1}[/tex] sin(∅[tex]_{c}[/tex]) = M[tex]_{2}[/tex] Sin(90)

sin(∅[tex]_{c}[/tex])= M[tex]{2}[/tex]/M[tex]_{1}[/tex] = 1/1.57 = 0.636

∅[tex]_{c}[/tex]= 39.49

∅ = 39.34

v = c/λ

c = 1000/5.56e - 6 = 1.798 × [tex]10^{8}[/tex] m/s

v = 1.798 × [tex]10^{8}[/tex]/400e-9 = 4.496 × [tex]10^{14}[/tex] Hz

What is refraction index?

In optics, the refractive index (or refractive index) of an optical medium is a dimensionless number that indicates the ability of the medium to diffract light.

The index of refraction determines how much a light path bends or refracts as it enters a material. This is described by Snell's law of refraction n1 sin θ1 = n2 sin θ2. where θ1 and θ2 are the angles of incidence and refraction, respectively, for a ray that crosses the interface between two media with indices of refraction n1 and n2. The index of refraction also determines the amount of light reflected upon reaching an interface, the critical angle for total internal reflection, its intensity (Fresnel equation), and Brewster's angle.

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The work done by the gas is 190,000 J.

What is work?
Work in physics is the energy that is transferred to or from a object when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance travelled for a constant force directed in the same direction as the motion. When a force is applied, it is said to have a component that moves the point of application, or it is said to have positive work. If the component of a force at the point of application is in the opposite direction of the displacement, the force is said to do negative work.

The work done by the gas can be calculated using the equation W = P∆V. In this equation, P represents the constant pressure of 400 kPa, ∆V is the change in volume, and W is the work done by the gas.

Since the volume of the gas changed from 900 cm3 to 425 cm3, the change in volume is ∆V = 900 cm3 - 425 cm3 = 475 cm3. Plugging this into the equation above, we get W = 400 kPa x 475 cm3 = 190,000 J.

Therefore, the work done by the gas is 190,000 J.

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The spring constant of this elastic cord is 562.64 Nm.The frequency of the motion with the 210 N is 0.817Hz.

Elastic cord is a fairly versatile stretchy rope. it is small diameter makes it ideal for indoor craft makes use of and light duty strapping. Use this elastic string for sewing initiatives, scrapbooking, and kids' crafts.

Calculation:-

Spring constant K = f/x

= 75/0.61 - L

= 75/0.61 - 0.4767

= 562.64 Nm

Frequency when 210 N is hanging is

extension X = 0.85 -L

= 0.87 - 0.4767

= 0.3733

Frequency = 1/2π√g/X

= 1/2π √9.8/0.3733

= 0.816 Hz.

The free movement of a frame with appreciate to time is called motion. for example-the fan, the dirt falling from the carpet, the water that flows from the tap, a ball rolling around, a shifting car etc. Even the universe is in chronic motion.

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Pendulum length must be made for it to keep perfect time of 100 or 0.0167 % or 0.017 % nearly.

Time is the  measure of to  non-stop, consistent change by  in our surroundings, or it is  usually from a specific to  viewpoint.

Total number of seconds in a normal day is 24×60×60 = 86400 seconds

We know that time period of pendulum is

T= 2π √l/g

Then we use fractional error method

∆T/T = 1/2 ( ∆l /l )

Here l is length of pendulum string

So 7.2/86400 = 1/2 ( ∆l/l)

∆l/l = 0.000167

So percentage change is

∆l/l *100 or 0.0167 % or 0.017 % nearly.

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Answer:

Below

Explanation:

AVERAGE velocity = ( 28.8 - 0 ) / 2 = 14.4 m/s

74 m / 14.4 m/s = 5.14 s

To calculate the maximum speed of the Bugatti Veyron, we can use the equation $F_d = \frac{1}{2} \rho v^2 c A$,

which relates the drag force $F_d$ acting on an object to the density of the fluid $\rho$, the speed $v$ of the object, the drag coefficient $c$, and the cross-sectional area $A$ of the object.

In this case, we are given the mass of the car, the drag coefficient, and the force that the engine can impart on the road, so we can solve for the maximum speed.

First, we need to convert the mass of the car to its weight, which is the force of gravity acting on the car. The weight of the car is given by the equation $W = mg$, where $m$ is the mass of the car and $g$ is the acceleration due to gravity.

We can convert the mass of the car from kilograms to newtons by multiplying it by $g$, which is approximately 9.8 m/s$^2$. This gives us a weight of $W = 1834 \text{ kg} \times 9.8 \text{ m/s}^2 = 17983.2 \text{ N}$.

Next, we need to calculate the cross-sectional area of the car. Since we are given the shape of the car and the drag coefficient, we can assume that the car has a streamlined shape with a length $L$ that is much greater than its width or height.

In this case, the cross-sectional area of the car is approximately equal to its width $w$ times its height $h$, or $A \approx wh$. If we assume that the width of the car is $w = 1.8$ meters and the height is $h = 1.2$ meters, then the cross-sectional area is $A \approx 2.16 \text{ m}^2$.

Now that we have all of the required information, we can solve for the maximum speed of the car. The maximum speed is achieved when the drag force acting on the car is equal to the force that the engine can impart on the road. This means that the maximum speed $v_\text{max}$ is given by the equation

$$F_d = \frac{1}{2} \rho v_\text{max}^2 c A = F_\text{engine}$$

where $\rho$ is the density of the air, $c$ is the drag coefficient, $A$ is the cross-sectional area of the car, and $F_\text{engine}$ is the maximum force that the engine can impart on the road.

We are given that the drag coefficient is 0.342 kg/m and the maximum force that the engine can impart on the road is 4522 N. The density of the air is approximately 1.225 kg/m$^3$ at sea level. Plugging these values into the equation, we get

$$\frac{1}{2} \times 1.225 \text{ kg/m}^3 \times v_\text{max}^2 \times 0.342 \text{ kg/m} \times 2.16 \text{ m}^2 = 4522 \text{ N}$$

Solving for the maximum speed, we get $v_\text{max} \approx 242.5$ m/s. This is the maximum speed of the Bugatti Veyron if we neglect all other sources of friction and assume that the car has a streamlined.

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Loftiest to smallest temperature

Mercury

Earth

Mars

Jupiter

Neptune

What's the average face temperature?

Planetary face temperatures range from over 400 °C on Mercury and Venus to below-200 °C on distant globes. The factors that determine temperature are the complex balance of heat entered and lost.

Thus, for these five globes, temperature correlates with distance from the Sun. The near to the sun, the hotter the earth. Note, still, that this isn't always the case, as the earth's temperature also depends on its reflectance and the strength of the greenhouse effect( if present). For illustration, although Venus is nearly doubly as far from the Sun, the average temperature on Venus is advanced than on Mercury due to the greenhouse effect.

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The voltage drop across resistors r2 in volts is 6.6 volts.

Resistor is defined as an electrical component that regulates voltage and temperature. Resistors are frequently employed in electronic circuits to reduce current flow, divide voltages, impede transmission signals, and bias active parts. The resistor controls the electron flow to prevent overly rapid current from damaging the breadboard, wires, battery,

The Voltage drop can be calculated as

Give voltage of battery = 113 V

R2 has current = 1.9 A

And resistance = 4.7 ohms

Voltage = 1.9 + 4.7

             = 6.6 V

Thus, the voltage drop across resistors r2 in volts is 6.6 volts.

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The worn idler arm is the component that is most likely at fault.

What occurs when a wheel hits a dip or home and moves downward?

When you hit any bump or dip in a road, your vehicle's suspension and springs move so the tire can stay in contact with the road and absorb the energy. The shock absorbers dampen the movement of the springs by converting the spring's kinetic energy into thermal (heat) energy.

What are the symptoms of a bad idler arm?

What are the warning signs of a bad idler arm? If you notice your steering wheel feels loose or has extra play before the tires respond, this may be a sign of an issue with your idler arm or pitman's arm. If these arms fail completely, you will lose all steering in your vehicle.

Can a worn idler arms cause play?

A steering wheel with too much play that shimmies, shakes, or vibrates too loosely can be a symptom of a bad idler arm. Poor steering likely means the ball joints are worn.

How important is an idler arm?

Idler's arms are particularly important for two reasons. First, as mentioned, the idler arm supports the right end of the track rod. Without it, the track rod would not hold the right wheel in place or turn it effectively, if at all. Second, the idler arm maintains proper toe angle.

Thus, a worn idler arm is a correct answer.

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The answer is (b), meaning that we haven't been looking for planets so at distances for long enough.

(Astronomy) The solar system is made up of the sun and the objects gravitationally attracted to it, such as the planets Mercury, Venus, Mars, Mars, Octavian, Saturn, Uranus, and Neptune, as well as the minor planets Eris, Pluto, and Ceres.

The world sustains us and gives us the resources we require. Last but not least, experts claim that if our planet disappeared, we and everything else on the world would have died. The one and only planet capable of supporting life is Earth.

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The recoil speed of the flatcar is0.5 m/s.

The cannon's momentum equals the flatcar's momentum according to Newton's third law of motion.

mv = MV........................ Equation 1:

where m is the cannon's mass, v is its velocity, and m is the flatcar's mass, v is its velocity.

Assign V as the subject of the equation V = mv/M... Equation 2

Given: M = 1000 kg

m = 10 kg,

and v = 50 m/s

Replace with V = 1050/1000 V = 500/1000

V = 0.5 m/s in equation 2.

Consequently, the flatcar's speed is equal to 0.5 meters per second.

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The pressure in the connecting pipe is 88 pa.

Stress is the pressure applied perpendicular to the floor of an object according to unit place over which that force is sent. Gauge strain is the strain relative to the ambient pressure. diverse gadgets are used to explicit strain.

Calculation:-

radius of pipe = 1.5 cm

speed = 5 m/s

The speed is increases to 11.0 m/s

density of the fluid = 900 kg kg/m³

Pressure = 1.30 × 10⁵ N/m²

The pressure in the connecting pipe in pa = ρdv/dl

                                                                        = 88 pa.

Stress is defined because the bodily pressure exerted on an item. The force applied is perpendicular to the surface of objects in step with unit place. The primary components for strain is F/A (force in keeping with unit location). Unit of pressure is Pascals (Pa). forms of Pressures are Absolute, Atmospheric, Differential, and Gauge pressure.

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Velocity of golf ball after collision with golf club using law of conservation of momentum is 65.21 m/s

What is momentum ?

Momentum seem to be directly dependent on the value of mass as well as velocity of the object in the direction of motion.  it is quantified by "mass velocity". Since mass is a scalar quantity but velocity is a vector, momentum is a vector quantity.

From the given information-

mass of golf club = 200 g

mass golf ball = 46 g

velocity of club before collision = 55 m/s

velocity club after collision =40 m/s

velocity of golf ball before collision = 0 m/s

You need to use conservation of momentum here.

momentum = mass x velocity

Prior to impact, the golf club has a momentum of 0.200 kg * 55 m/s = 11.00 kg m/s.

The ball's not moving before impact, so it has a momentum of zero. Therefore the total momentum before impact will be 11.00 kg m/s. Conservation of momentum dictates the total momentum of the two objects after impact will also be 11.00 kg m/s.

We know the speed of the club after the impact, so the momentum of the club after impqact is 0.200 kg * 40 m/s =8 kg m/s.

So the momentum of the ball must be 11.00 kg m/s - 8 kg m/s = 3 kg m/s, and dividing by the mass of the ball (0.046 kg) gives the speed of the ball, 65.217 m/s

Velocity of golf ball after collision wit golf club is 65.21 m/s

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Beginning velocity is required for a projectile to be launched from the ground up to the Washington Monument's 555-feet summit.

Casey was convinced to make the height of the tower 10 times the width of the base, which meant that the Washington Monument's ideal height was 555 feet rather than the 600 feet that Mills had originally envisioned.

When compared to a memorial, why is the Washington Monument a "monument"? A memorial honors or pays tribute to a person who has passed away. A monument has a crucial distinction: it is created to honor or remember a living person.

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When wind speeds up as it blows over the top of a hill, atmospheric pressure there increases.

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It will take 24 days for the radiation level of barium-131 to drop to 1/4 of its original level.

We know that radioactive reactions are 1st order reactions.

Given half life of Barium-131 is approximately 12 days.

So to drop to 1/4 of it's original level it will take more 12 days i.e. one more half life.

Total days are : 12+12=24 days

So it will take 24 days for the radiation level of barium-131 to drop to 1/4 of its original level.

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Mathematically, the answer to the following question's a part is: [tex]C_{v} = \frac{Rs}{2}[/tex] and b part is: s=17.

a) Using the equipartition theorem,

U = [tex]\frac{1}{2} k_{b} T[/tex]

= [tex]\frac{1}{2} n_{R} T[/tex]

Degree of freedom for 's'

= [tex]\frac{1}{2} sn R T[/tex]

Then, molar specific heat [tex]C_{v} = \frac{1}{n} \frac{dU}{dT}[/tex]

Mentioning it in terms of R and s;

[tex]C_{v} = \frac{1}{n} \frac{dU}{dT} (\frac{1}{2} sn RT)[/tex]

[tex]C_{v} = \frac{Rs}{2}[/tex]

b) As per question,

[tex]C_{v}[/tex] = 70.6 J/mol.K and R = 8.314 J/mol.K

Using the formula, [tex]C_{v} = \frac{Rs}{2}[/tex]

70.6 J/mol.K = [tex]\frac{(8.314 J/mol.K) X s}{2}[/tex]

taking 2 on the left side by moving it from the division

70.6 J/mol.K x 2 = 8.314 J/mol.K x s

= [tex]\frac{70.6 J/mol.K X 2}{8.314 J/mol.K}[/tex]

s = 16.983 then we round it off to the nearest figure

We get, s = 17

Each degree of freedom that only appears quadratically in the total energy has an average energy of 1/2 kBT in thermal equilibrium, which increases the system's heat capacity by 1/2 kB, according to the equipartition theorem, also known as the law of equipartition, the equipartition of energy, or simply equipartition. The classical physics presumption that this concept holds true in all situation is refuted by the quantum theory.

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The diameter of the smallest jovian planet is 3.96 times larger than the diameter of the largest terrestrial planet.

The jovian planets or also called giant gaseous planets are those that are far away in the solar system, which includes Jupiter, Saturn, Uranus, and Neptune, while terrestrial rocky planets include Mercury, Venus, the Earth planet and Mars.

Therefore, with this data, we can see that the jovian and terrestrial planets are different based on the composition of their surfaces and also due to the distance to the Sun.

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(a) Formulae for magnification (m) = distance of image/image of object

                                             =.025/3.2 = 0.00781

so, magnification of eye = 0.00781

now. m = image size / actual size

so, image size = actual size x m

                        = 1.7 x 0.00781

                        = 0.0132 m

(b) similarly, in this case the size of the image can be calculated as follows:

m = distance of image/image of object = 0.00595

image size = actual size x m = 0.0101

What is magnification?

Magnification in physics can be defined as the ratio of size of the image to the size of the object. Magnification in simple terms means enlargement in the size of the image of an object.

It can be denoted by the formulae:

[tex]magnification = \frac{size of the image}{size of the object}[/tex]

It has no SI unit.

Why Magnification has no SI unit?

It has no SI unit because it is a ratio of length.

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The 85% confidence interval estimate of the true population proportion of disks which are defective is 0.100 +/- 0.010

= (0.095, 0.110),Lower: 0.095 ,Upper: 0.110

Confidence intervals are a set of values with a known probability that the value of a parameter will fall within them.

The confidence interval of statistical data can be written as.

p+/-z√(p(1-p)/n)

We are given that,

Proportion of disks that are not defective = p' = 1283/1475 = 0.950

Proportion of disks that are defective = p = 1 - p' = 1 - 0.950 = 0.05

Thus , p = 0.05

Number of samples= n = 1350

Confidence interval = 85%

z value(at 85% confidence) = 1.28

Substituting the values we have;

0.100 +/- 1.28√(0.100(1-0.05)/1350)

0.100 +/- 1.28(0.00703703)

0.100 +/- 0.0090073984

0.100 +/- 0.010

= (0.095, 0.110)

According to the 85% confidence interval, the actual population percentage of defective discs is 0.100 +/- 0.010

Therefore, interval = (0.095, 0.110), Lower: 0.095, Upper: 0.110 can be used to describe the population portion.

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