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NikAS [45]
3 years ago
16

Which is the graph of the linear inequality x – 2y > –6?

Mathematics
2 answers:
Zina [86]3 years ago
8 0

Answer:

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Step-by-step explanation:

The first step is writing in the general form of the first order equation

y = f(x) or y > f(x) or y < f(x)

And

f(x) = ax + b

In which a is the slope.

We have that:

x - 2y > -6

-2y > -6 - x

When multiplying by -1, the signal changes, from > to <

2y < x + 6

y < 0.5x + 3

The slope is positive, since 0.5 is positive.

Since it is y lesser than, it is everything below and to the right of f(x) is painted.

The line is dashed because this is just lesser, not lesser or equal.

The correct answer is:

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Marrrta [24]3 years ago
4 0

Answer:

D. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Step-by-step explanation:

Given inequality is x-2y > -6

Now assume that x-2y = -6

The above equation is a line which meets the x-axis at (-6,0) and y-axis at (0,3)

We know that the slope of the line joining the points (a , b) and (c , d) is

m=\frac{d-b}{c-a}

now the slope the given line is m=\frac{3-0}{0-(-6)} = \frac{1}{2}.

The given line has a positive slope.

The given two points in all the options is (-4 , 2) and (4 , 4).

For any point above this line say (0 , 4) does not satisfy the given inequality.

So all the points lied below the given line towards the origin satisfy the given inequality.

Now for deciding wether it is a solid or dashed straight line the following is used,

If the inequality is > or < then it is a dashed line otherwise (in the case of ≤ and  ≥) it is a solid line.

So from all the above we can conclude that the option is

On a coordinate plane , a dashed straight line which has a positive slope and goes through (-4 , 2) and (4 , 4).Everything below and to the right of the line is shaded.

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Step-by-step explanation:

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Answer:

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Step by step:

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Luda [366]

Answer:

We conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

Step-by-step explanation:

We are given that a coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces.

A random sample of 15 containers were weighed and the mean weight was 31.8 ounces with a sample standard deviation of 0.48 ounces.

Let \mu = <u><em>mean weight of coffee in its containers.</em></u>

SO, Null Hypothesis, H_0 : \mu \geq 32 ounces     {means that the mean weight of coffee in its containers is at least 32 ounces}

Alternate Hypothesis, H_A : \mu < 32 ounces      {means that the mean weight of coffee in its containers is less than 32 ounces}

The test statistics that would be used here <u>One-sample t-test statistics</u> as we don't know about population standard deviation;

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where, \bar X = sample mean weight = 31.8 ounces

             s = sample standard deviation = 0.48 ounces

             n = sample of containers = 15

So, <u><em>the test statistics</em></u>  =  \frac{31.8 -32}{\frac{0.48}{\sqrt{15} } }  ~ t_1_4  

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The value of t test statistics is -1.614.

<u>Now, at 0.01 significance level the t table gives critical value of -2.624 at 14 degree of freedom for left-tailed test.</u>

Since our test statistic is more than the critical value of t as -1.614 > -2.624, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.

Therefore, we conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

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Step-by-step explanation:

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