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masya89 [10]
3 years ago
10

A type of light bulb is labeled having an average lifetime of 1000 hours. It’s reasonable to model the probability of failure of

these bulbs by an exponential density function with mean µ = 1000. Use this model to find the probability that a bulb fails within the first 300 hours.
Physics
1 answer:
SashulF [63]3 years ago
3 0

Answer:

0.2592 \ or \ 25.92\%

Explanation:

The exponential density function is given as

f(t)=\left \{ {{0} \atop {ce^{ct}}} \right\\0,t

\mu=\frac{1}{c}\\c=\frac{1}{\mu}\\\\=\frac{1}{1000}=0.001\\\\f(t)=0.001e^{-0.001t}

To find probability that bulb fails with the first 300hrs, we integrate from o to 300:

P(0\leq X\leq 300)=\int\limits^{300}_0 {f(t)} \, dt\\\\=\int\limits^{300}_0 {0.001e^{-001t}} \, dt\\ =|-e^{-0.001t}|  \ 0\leq t\leq 300

P(0\leq X\leq 300)=-0.7408+1\\=0.2592

Hence probability of bulb failing within 300hrs is 25.92% or 0.2592

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The displacement vector from your house to the library is 740 m long, pointing 40 ∘ north of east. Part A What are the x-compone
Ilia_Sergeevich [38]

The horizontal component of the displacement is 566.9 m

Explanation:

The horizontal (x-) and vertical (y-) components of a vector on the Cartesian plane can be found as follows:

v_x = v cos \theta

v_y = v sin \theta

where

v is the magnitude of the vector

\theta is the angle representing the direction of the vector, measured as above the x-axis.

In this problem, we have:

v = 740 m (magnitude of the vector)

\theta=40^{\circ} (direction of the vector)

Therefore, the two components are

v_x = (740)(cos 40)=566.9 m

v_y = (740)(sin 40)=475.7 m

Learn more about vector components:

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4 0
3 years ago
Which statement best defines why sound waves are mechanical waves?
Annette [7]
The correct answer among the choices presented above is option A. Sound waves are considered as mechanical waves because they require a medium in which they can travel through. A mechanical wave is a wave that cannot transmit energy in a vacuum. It needs something to move energy.<span />
7 0
3 years ago
Read 2 more answers
A basketball player throws a chall -1 kg up with an initial speed of his hand at shoulder height = 2.15 m Le gravitational poten
Talja [164]

Complete Question:

A basketball player tosses a basketball m=1kg straight up with an initial speed of v=7.5 m/s. He releases the ball at shoulder height h= 2.15m. Let gravitational potential energy be zero at ground level

a)  Give the total mechanical energy of the ball E in terms of maximum height hn it reaches, the mass m, and the gravitational acceleration g.

b) What is the height, hn in meters?

Answer:

a) Energy = mghₙ

b) Height, hₙ = 5.02 m

Explanation:

a) Total energy in terms of maximum height

Let maximum height be hₙ

At maximum height, velocity, V=0

Total mechanical energy , E = mgh + 1/2 mV^2

Since V=0 at maximum height, the total energy in terms of maximum height becomes

Energy = mghₙ

b) Height,  hₙ in meters

mghₙ = mgh + 1/2 mV^2

mghₙ = m(gh + 1/2 V^2)

Divide both sides by mg

hₙ = h + 0.5 (V^2)/g

h = 2.15m

g = 9.8 m/s^2

V = 7.5 m/s

hₙ = 2.15 + 0.5(7.5^2)/9.8

hₙ = 2.15 + 2.87

hₙ = 5.02 m

6 0
3 years ago
B
SVEN [57.7K]

Answer:

Frequency = 1,550Hz

Explanation:

To solve this we can use the equation: f=\frac{v}{\lambda}

(frequency = velocity/wavelength).

We are given the information that the wavelength is 22cm and the speed is 340m/s. The first step is to make sure everything is in the correct units (SI units), and to convert them if needed. The SI Units for velocity and wavelength are m/s and m respectively. This means we need to convert 22cm into meters, which we can do by dividing by 100, (as there are 100cm in a meter). 22/100 = 0.22m

Now we can substitute these values into the formula and calculate to solve:

f=\frac{340}{0.22} \\\\f=1545.454...

Simplify to 3 significant figures:

f = 1,550Hz

(Which I believe is just below a G6 if you were interested)

Hope this helped!

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The combustion of fossil fuels is releasing more co2 into the atmosphere then what would occur naturally
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