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12 days ago

The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?

Mathematics

2 answers:

tester [12.3K]12 days ago

7 0

It's simply a matter of substituting answer choices into your inequality to determine which one holds true.
The answer is: (3,-2)

Svet_ta [12.7K]12 days ago

5 0

we know that

If a point qualifies as a solution for the inequality

then

That point must fulfill the inequality

we have

$y\leq -x+1$

The solution to the inequality is the shaded region below the solid red line

refer to the attached figure for greater understanding of the task

Step 1

Point $A(2,3)$

Substitute the values of x and y into the inequality

$x=2\ y=3$

$3\leq -2+1$

$3\leq -1$ -------> is false

consequently

Point A does not satisfy the inequality

Refer to the attached figure------> point A lies outside the shaded area

Step 2

Point $B(3,-2)$

Substitute the values of x and y into the inequality

$x=3\ y=-2$

$-2\leq -3+1$

$-2\leq -2$ -------> is true

thus

Point B qualifies as a solution for the inequality

Refer to the attached figure------> point B resides within the shaded area

Step 3

Point $C(2,1)$

Substitute the values of x and y into the inequality

$x=2\ y=1$

$1\leq -2+1$

$1\leq -1$ -------> is false

therefore

Point C does not qualify as a solution for the inequality

Refer to the attached figure------> point C does not lie within the shaded area

Step 4

Point $D(-1,3)$

Substitute the values of x and y into the inequality

$x=-1\ y=3$

$3\leq 1+1$

$3\leq 2$ -------> is false

therefore

Point D does not qualify as a solution for the inequality

Refer to the attached figure------> point D is not found within the shaded area

the answer is

$B(3,-2)$

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Answer:

a) Null and alternative hypothesis

$H_0: \mu=1503\\\\H_a:\mu< 1503$

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Step-by-step breakdown:

This is a statistical test for the average population mean.

The hypothesis posits that car insurance in Pennsylvania is notably less expensive compared to the national average.

Accordingly, the null and alternative hypotheses are:

$H_0: \mu=1503\\\\H_a:\mu< 1503$

The significance level is set at 0.05.

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A point estimate of the difference between the Pennsylvania mean premium and the national average can be computed using the sample mean:

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Given that the standard deviation of the population is unknown, we approximate it using the sample standard deviation, which is s=160.

The estimated standard error of the mean is determined with the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{160}{\sqrt{25}}=32$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1425-1503}{32}=\dfrac{-78}{32}=-2.438$

The degrees of freedom for this sample size stand at:

$df=n-1=25-1=24$

This constitutes a left-tailed test, with 24 degrees of freedom and t=-2.438, rendering the P-value as (per a t-table):

$\text{P-value}=P(t$

As the P-value (0.0113) falls below the significance level (0.05), the results prove significant.

Thus, the null hypothesis obtains dismissal.

At a 0.05 significance level, there's sufficient evidence to assert that car insurance in Pennsylvania costs notably less than the national average.

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