Which statement correctly explains how to prove △ABC∼△DEF?

Mathematics

2 answers:

mote1985 [20]1 year ago

4 0

Answer:

Step-by-step explanation:

calculate the ratios AB/DE BC/EF AND AC/DF。their ratios are 1/2

dmitriy555 [2]1 year ago

3 0

Answer:

Step-by-step explanation:

the first because the ratio is always from a small to a large triangle, and it is right, the second is wrong, the sides are not congruent, the third is also wrong, the last ratio is wrong

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19. A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years

Juliette [100K]

Answer:

a) Approximately normal.

b) The mean is 75 years and the standard deviation is 0.8485 years.

c) 0.9909 = 99.09% probability that the mean age exceeds 73 years

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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 $s = \frac{\sigma}{\sqrt{n}}$ .