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3 years ago

How to find angles of a parallelogram

Mathematics

1 answer:

irina [24]3 years ago

3 0

Answer:

There are six important properties of parallelograms to know:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The diagonals of a parallelogram bisect each other.

Each diagonal of a parallelogram separates it into two congruent triangles.

Step-by-step explanation:

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Answer:

a) 9.18% f the New York City commutes are for less than 29 minutes.

b) 26.39% are between 29 and 36 minutes.

c) 67.55% are between 29 and 44 minutes

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:

$\mu = 38.7, \sigma = 7.3$

What percent of the New York City commutes are for less than 29 minutes?

This is the pvalue of Z when X = 29.

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

$Z = \frac{29 - 38.7}{7.3}$

$Z = -1.33$

$Z = -1.33$ has a pvalue of 0.0918.

So 9.18% f the New York City commutes are for less than 29 minutes.

What percent are between 29 and 36 minutes?

This is the pvalue of Z when X = 36 subtracted by the pvalue of Z when X = 29.

X = 36

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

$Z = \frac{36 - 38.7}{7.3}$

$Z = -0.37$

$Z = -0.37$ has a pvalue of 0.3557.

X = 29

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

$Z = \frac{29 - 38.7}{7.3}$

$Z = -1.33$

$Z = -1.33$ has a pvalue of 0.0918.

So 0.3557 - 0.0918 = 0.2639 = 26.39% are between 29 and 36 minutes.

What percent are between 29 and 44 minutes?

This is the pvalue of Z when X = 44 subtracted by the pvalue of Z when X = 29.

X = 44

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

$Z = \frac{44 - 38.7}{7.3}$

$Z = 0.73$

$Z = -0.37$ has a pvalue of 0.7673.

X = 29

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

$Z = \frac{29 - 38.7}{7.3}$

$Z = -1.33$

$Z = -1.33$ has a pvalue of 0.0918.

So 0.7673 - 0.0918 = 0.6755 = 67.55% are between 29 and 44 minutes

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