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guapka [62]
2 years ago
14

Sound travels through a guitar string at 600 m/s, making a sound wave in the air with a speed of 333 m/s. In 1–2 sentences, expl

ain how the wavelength and frequency of the wave in the string compare to the wavelength and frequency of the wave in the air.
Please HELP!
Mathematics
1 answer:
Shalnov [3]2 years ago
4 0

Answer:

Step-by-step explanation:

Wave velocity of the sound = frequency * wavelength.

The frequency and wavelength depend on the medium through which the sound passes and they are both greater in the guitar string than in air as the string is denser than the air. So the sound travles faster through the guitar string.

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9x^2-25=(3x)^2 - 5^2 =(3x-5)(3x+5)

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Answer:

a) 0.0065 = 0.65% probability of receiving no emails during an hour.

b) 0.1212 = 12.12% probability of receiving at least three emails during an hour

c) The expected number of emails received during 15 minutes is 1.2604.

d) 0.2835 = 28.35% probability that no emails are received during 15 minutes

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

In this question.

121 emails per day.

A day has 24 hours, so per hour, 121/24 = 5.0417, which means that \mu = 5.0417n, in which n is the number of hours.

A. What is the probability of receiving no emails during an hour?

n = 1, so \mu = 5.0417

This is P(X = 0).

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065

0.0065 = 0.65% probability of receiving no emails during an hour

B. What is the probability of receiving at least three emails during an hour?

Either you receive less than three emails during an hour, or you receive at least 3. The sum of the probabilities of these events is decimal 1. So

P(X < 3) + P(X \geq 3) = 1

We want P(X \geq 3)

Then

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065

P(X = 1) = \frac{e^{-5.0417}*(5.0417)^{1}}{(1)!} = 0.0326

P(X = 2) = \frac{e^{-5.0417}*(5.0417)^{2}}{(2)!} = 0.0821

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0065 + 0.0326 + 0.0821 = 0.1212

0.1212 = 12.12% probability of receiving at least three emails during an hour

C. What is the expected number of emails received during 15 minutes?

15 minutes is a fourth of an hour, so n = 1/4 and \mu = \frac{5.0417}{4} = 1.2604

The expected number of emails received during 15 minutes is 1.2604.

D. What is the probability that no emails are received during 15 minutes?

P(X = 0) = \frac{e^{-1.2604}*(1.2604)^{0}}{(0)!} = 0.2835

0.2835 = 28.35% probability that no emails are received during 15 minutes

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3 years ago
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