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ikadub [295]
2 years ago
10

Which ordered pair is a solution for 3x + 4y < 12?

Mathematics
1 answer:
Andre45 [30]2 years ago
5 0

Answer:

D, (1,2)

Step-by-step explanation:

It all comes down to substitution. In this case the coefficient of x is 3 and the coefficient of y is 4. The format of these coordinates being (x,y).

1. Plug in your x value (1 in this circumstance) and solve:

3(1) + 4y < 12

3 + 4y < 12

2. Plug in your y value (2 in this circumstance) and solve:

3 + 4(2) < 12

3 + 8 < 12

3. Solve

3 + 8 = 11

11 < 12

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2 years ago
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 201.9-cm and a standard dev
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Answer:

There is a 0.08% probability that the average length of a randomly selected bundle of steel rods is greater than 204.1-cm.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

In this problem, we have that:

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 201.9-cm and a standard deviation of 2.1-cm. This means that \mu = 201.9, \sigma = 2.1.

For shipment, 9 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is greater than 204.1-cm.

By the Central Limit Theorem, since we are using the mean of the sample, we have to use the standard deviation of the sample in the Z formula. That is:

s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{9}} = 0.7

This probability is 1 subtracted by the pvalue of Z when X = 204.1.

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