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sergeinik [125]
3 years ago
14

Find the volume of a cube whose side length is 5x^2

Mathematics
2 answers:
marishachu [46]3 years ago
6 0
If the side length is 5 x 2, 5 x 2 = 10, so 10 x 3 is 30.  Hope this helped!
sammy [17]3 years ago
3 0
V = s³
V = (5x²)³
V = (5x²)(5x²)(5x²)
V = 5x²+²+²
V = 5x^6
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5) Two machines M1, M2 are used to manufacture resistors with a design
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Since M1 has the higher probability of being in the desired range, we choose M1.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two machines M1, M2 are used to manufacture resistors with a design specification of 1000 ohm with 10% tolerance.

So we need the machines to be within 1000 - 0.1*1000 = 900 ohms and 1000 + 0.1*1000 = 1100 ohms.

For each machine, we need to find the probabilty of the machine being in this range. We choose the one with the higher probability.

M1:

Resistors of M1 are found to follow normal distribution with mean 1050 ohm and standard deviation of 100 ohm. This means that \mu = 1050, \sigma = 100

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Z = -1.5 has a pvalue of 0.0668

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M2:

M2 are found to follow normal distribution with mean 1000 ohm and standard deviation of 120 ohm. This means that \mu = 1000, \sigma = 120

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Z = 0.83

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Z = -0.83

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M2 has a 59.34% probability of being in the desired range.

Since M1 has the higher probability of being in the desired range, we choose M1.

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