Which system of inequalities is represented by the graph?

Mathematics

2 answers:

Nikolay [14]3 years ago

7 0

The answer would be the 3rd option

ziro4ka [17]3 years ago

3 0

We are given a graph of the system of inequalities.

Given system of inequalities:

1) y < 2x

y ≤ 1

2) y > 2x

y ≥ 1

3) y ≤ 2x

y < 1

4) y ≥ 2x

y > 1.

In the show graph, we can see that red shaded portion have a dotted line.

And the graph is shaded above the dotted line.

Because graph is shaded above the dotted line, it should be only greater than sign.

<h3>So, the inequality y > 1 would best fit for that above shaded portion of the graph.</h3><h3>We, can see in 4th option we have y > 1 ( y is greater than 1).</h3><h3>Therefore, correct option is 4th option :</h3><h3> y ≥ 2x</h3><h3>y > 1</h3>

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1. The SAT test scores have an average value of 1200 with a standard deviation of 105. A random sample of 35 scores is selected

AveGali [126]

Answer:

a) The shape is bell shaped, because of the single peak at the center, that is the mean.

The mean of the sampling distribution of the sample mean is 1200.

The standard deviation of the sampling distribution of the sample mean for samples of size 35 is 17.75.

b) There is a 2.07% probability that the sample mean will be larger than 1235.

c) 85.68% probability that the sample mean will fall within 25 points of the population mean.

d) There is a 7.22% probability that the sample mean will be less than 1175.

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

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

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 This p-value is the probability that the value of the measure is greater than X.

In this case, we have that:

The SAT test scores have an average value of 1200 with a standard deviation of 105. A random sample of 35 scores is selected for study. So $\mu = 1200, \sigma = 105, n = 35$ .

A) What is the shape, mean(expected value) and standard deviation of the sampling distribution of the sample mean for samples of size 35?

The shape is bell shaped, because of the single peak at the center, that is the mean.

The mean of the sampling distribution of the sample mean is the same as the sample mean. So, the mean of the sampling distribution of the sample mean is 1200.

The standard deviation of the sampling distribution of the sample mean for samples of size 35 is the sample standard deviation divided by the square root of the size of the sampling distribution.

$s = \frac{105}{sqrt{35}} = 17.75$