What is the image of (-2,9)after a dilation by a scale factor of 5 centered at the origin?

Mathematics

1 answer:

asambeis [7]3 years ago

7 0

Answer:

(- 10, 45 )

Step-by-step explanation:

Since the dilatation is centred at the origin, then multiply each of the coordinates by the scale factor, that is

(- 2, 9 ) → (- 2 × 5, 9 × 5 ) → (- 10, 45 )

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A distribution of values is normal with a mean of 220 and a standard deviation of 13. From this distribution, you are drawing sa

Paraphin [41]

Answer:

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

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 distributied random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$