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Mathematics

1 answer:

OLEGan [10]3 years ago

7 0

Answer:

100 beats per minute

Step-by-step explanation:

If it takes 28.8 secs for the piano to play 48 beats, then it would take 60 secs (1 minute) to play x number of beats.

To find the value of x, which is the number of beats the piano makes per minute, let's set the proportion as shown below:

28.8 secs = 48 beats

60 secs = x beats

Cross multiply

28.8*x = 60*48

28.8x = 2,880

Divide both sides by 28.8

x = 2,880/28.8

x = 100

✅Thus, if the Piano plays 48 beats in 28.8 secs, therefore, the tempo of the piano in beats per minute would be 100 BPM

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A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength

irinina [24]

Answer:

Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.

Step-by-step explanation:

We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.

Let $\bar X$ = sample mean comprehensive strength

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean comprehensive strength = 5500 psi

$\sigma$ = standard deviation = 100 psi

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P( $\bar X$ > 4985 psi)

P( $\bar X$ > 4985 psi) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{4985-5500}{\frac{100}{\sqrt{9} } }$ ) = P(Z > -15.45) = P(Z < 15.45)

= 0.99999

Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.

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We would need to know the measurements of the circle to answer this

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3 years ago

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