{(1,2), (-2,3), (1,3), (-2,2)} is what type of relation?

Mathematics

1 answer:

sveta [45]3 years ago

3 0

Answer:

B. Many-to-many

Step-by-step explanation:

We have the following ordered pairs:

(1,2)

(-2,3)

(1,3)

(-2,2)

First let's define the following concepts:

One-to-one: A function is said to be one-to-one if every y value has exactly one x value mapped onto it.
Many-to-one: If there are y values that have more than one x value mapped onto them.

One-to-many: If there are x values that have more than one y value mapped onto them. (NOT A FUNCTION)

Many-to-many: If there are x values that have more than one y value mapped onto them and at the same time, there are y values that have more than one x value mapped onto them (NOT A FUNCTION)

From all the ordered pairs, we find that the points (1,2) and (1,3) have the same x-value for diferent y-values. Also we find that the points (1,2) and (-2, 2) have different x-values for the same y-value.

Therefore, the ordered pairs DO NOT belong to a function and can be considered MANY-TO MANY.

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Klio2033 [76]

Answer:

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Explanation:

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The distribution of SAT II Math scores is approximately normal with mean 660 and standard deviation 90. The probability that 100

gayaneshka [121]

Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is of 660, hence $\mu = 660$ .

The standard deviation is of 90, hence $\sigma = 90$ .

A sample of 100 is taken, hence $n = 100, s = \frac{90}{\sqrt{100}} = 9$ .

The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:

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

By the Central Limit Theorem

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