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3 years ago

Which graph shows the solution to this system of inequalities?

Mathematics

2 answers:

Mice21 [21]3 years ago

7 0

Answer:

The answer is Graph Z

Step-by-step explanation:

There is a mistake in your equations. Expression 1 is not a function as is its not defined as y but looking at the graphs I can infer that is 4x-2y>=4 , but I prove it here. The graph with positive slope crosess points (-1,0) and (0,2) so the slope is

m = (2-0)/(0--1) = 2

So following the point slope form of the graph y = mx+b this graph represent y=2x+2

expressing it in the way you show it:

y=2x+2

2x - y = -2

4x-2y = -4 (multiplying by 2)

Now the solution of the problem. The solution space of a system of inequalities is the space where the possible solutions of both equations cross. To find which graph corresponds to which equation we can express it in explicit form y = mx+b

Equation(1)

4x-2y >= -4

2y>=4x+4

y>2x+2

Equation 2

2x + y > -3

y>-2x-3

So the graph with positive slope is equation 1 and the other is equation 2.

Now, when we have a inequality that has an equal sign it means that the points of the line that defines the line are also included in the solution set. Taking this into account only Graph Y or Z are possible answers because Equation 1 has equal sign and equation 2 so in Eq 1 the line is also a set of possible solutions ( shown in the graph by the bold line without spaces between). To find the solution set, an easy way is to replace a specific point in the equations and see if the follow the equations.An easy point is (0,0)

So (0,0) in Eq 1

4x-2y>= -4

(0,0) replaced

0>= -4 . This is true so (0,0) is the solution set of Equation 1 4x-2y>= -4. So the answers are at the right of this graph.

(0,0) in Eq 2

2x + y > -3

0>-3 Is also true. So (0,0) is the solution set of Equation of 2x + y > -3. So the answers are at the right of this graph. The intersection of both areas is the one corresponding to Graph Z.

denis23 [38]3 years ago

5 0

I'm sorry not to have the full answer but I do believe it is either graph W or Z!

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Answer:

Null hypothesis : $\mu \leq 0.4$

Alternative hypothesis: $\mu >0.4$

And for this case a type of error I for this case would be reject the null hypothesis that the population mean is lower or equal than 0.4 when actually is true.

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Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.

Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power

Solution to the problem

For this case we are trying to check the following hypothesis:

Null hypothesis : $\mu \leq 0.4$

Alternative hypothesis: $\mu >0.4$

And for this case a type of error I for this case would be reject the null hypothesis that the population mean is lower or equal than 0.4 when actually is true.

A Type I error would occur if, in fact, μ ≤ 0.4 ppm, but the results of the sampling lead to the conclusion that μ > 0.4 ppm

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