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3 years ago

Which rigid motion is verified below?"

Mathematics

1 answer:

scoundrel [369]3 years ago

6 0

<h3>Answer: C) Translation</h3>

This is the geometric term for "shifting" or "sliding". In this case, every point has been moved 1 unit to the right.

Translations are considered a rigid motion because the blue and black triangles are the same size and shape (ie they are congruent).

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Pls answer you’ll get 100 points

Dahasolnce [82]

Take 2points

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Equation in two point form

$\\ \sf\longmapsto y-y_1=\left(\dfrac{y_2-y_1}{x_2-x_1}\right)x-x_1$

$\\ \sf\longmapsto y-0=\dfrac{2-0}{3-0}(x-0)$

$\\ \sf\longmapsto y=\dfrac{2}{3}x$

Option D is correct

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Find 131.2% of 477. Round to the nearest tenth.

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Which graph represents the piecewise-defined function?

soldier1979 [14.2K]

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Step-by-step explanation:

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A number x divided by -1 is at less than 45

Elanso [62]

Answer:

x is greater than 45

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Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame

lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678$

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

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

By the Central Limit Theorem

$Z = \frac{207.9 - 208}{0.1678}$

$Z = -0.6$

$Z = -0.6$ has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

6 0

3 years ago