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Paul [167]
3 years ago
10

Maria drew two parallel lines KL and MN intersected by a transversal PQ, as shown below:

Mathematics
2 answers:
Mice21 [21]3 years ago
8 0

Answer:

Option b is correct.

Step-by-step explanation:

Given that Maria drew two parallel lines KL and MN intersected by a transversal PQ,

Two parallel lines KL and MN with PQ as a transversal intersecting KL at point R and MN at point S as shown in attachment.

we have to find which theorem could Maria use to show the measure of ∠KRQ is equal to the measure of ∠PSN

The two angles ∠KRQ and ∠PSN are the interior angles but on the different sides of transversal i.e these are alternate interior angles.

Hence,  Alternate Interior Angles Theorem could Maria use to show the measure of angle KRQ is equal to the measure of angle PSN.

Correct Option is b.

Bumek [7]3 years ago
7 0

I just took the quiz and got a 100. It is Alternate Interior Angles.

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Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random
yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

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.

For sums, we have that the mean is \mu*n and the standard deviation is s = \sigma \sqrt{n}

In this problem, we have that:

\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{4000 - 3500}{160}

Z = 3.13

Z = 3.13 has a pvalue of 0.9991

X = 3000

Z = \frac{X - \mu}{s}

Z = \frac{3000 - 3500}{160}

Z = -3.13

Z = -3.13 has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

5 0
3 years ago
The two sets of lines are parallel. If the measure of angle A is 110°, what is the measure of angle B?
Mrrafil [7]

Answer:

Sum of 2 interior angles =180

1 angle+70=180

Another angle=110

Step-by-step explanation:

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