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Mathematics

1 answer:

LenaWriter [7]3 years ago

3 0

Answer:

yes, triangle DEF is similar to triangle DBC, BC corresponds to EF, and angle DCB corresponds to angle F.

Step-by-step explanation:

Part A: Angle D is congruent to angle D by the reflexive property. Since line BC is parallel to line EF then angle DCB = angle DFE by corresponding angles. Hence triangle DEF is similar to triangle DBS by the AA Similarity Postulate.

Part B: BC corresponds to EF because they are in the same order and the triangles listed DEF and DBC

Part C: Angle DCB corresponds to angle F since they are corresponding angles with the two given parallel lines BC and EF.

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Step-by-step explanation:

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

Normal probability distribution:

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a 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

In this problem, we have that:

$\mu = 8, \sigma = 0.03$