8) Choose the correct linear system of inequalities for the graph given.

Answer:

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.

If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.

Finally, pick one point that is not on either line ( (0,0) is usually the easiest) and decide whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.

Graph each of the inequalities in the system in a similar way. The solution of the system of inequalities is the intersection region of all the solutions in the system.

Example 1:

Solve the system of inequalities by graphing:

y≤x−2y>−3x+5

First, graph the inequality y≤x−2 . The related equation is y=x−2 .

Since the inequality is ≤ , not a strict one, the border line is solid.

Graph the straight line.

Consider a point that is not on the line - say, (0,0) - and substitute in the inequality y≤x−2 .

0≤0−20≤−2

This is false. So, the solution does not contain the point (0,0) . Shade the lower half of the line.

Similarly, draw a dashed line for the related equation of the second inequality y>−3x+5 which has a strict inequality. The point (0,0) does not satisfy the inequality, so shade the half that does not contain the point (0,0) .

The solution of the system of inequalities is the intersection region of the solutions of the two inequalities.

Example 2:

Solve the system of inequalities by graphing:

2x+3y≥128x−4y>1x<4

Rewrite the first two inequalities with y alone on one side.

3y≥−2x+12y≥−23x+4−4y>−8x+1y<2x−14

Now, graph the inequality y≥−23x+4 . The related equation is y=−23x+4 .

Since the inequality is ≥ , not a strict one, the border line is solid.

Graph the straight line.

Consider a point that is not on the line - say, (0,0) - and substitute in the inequality.

0≥−23(0)+40≥4

This is false. So, the solution does not contain the point (0,0) . Shade upper half of the line.

Similarly, draw a dashed line of related equation of the second inequality y<2x−14 which has a strict inequality. The point (0,0) does not satisfy the inequality, so shade the half that does not contain the point (0,0) .

Draw a dashed vertical line x=4 which is the related equation of the third inequality.

Here point (0,0) satisfies the inequality, so shade the half that contains the point.

The solution of the system of inequalities is the intersection region of the solutions of the three inequalities.

Step-by-step explanation:

I got it right

What is the Vertex and Y-intercept of f(x)=3x^2-6x+4? Please show your work.

pls answer what you can and I will give brainliest.

1. A population variance is used to calculate the t statistic for a hypothesis test.
(True/False)

2. Holding everything else constant, increasing the sample size (n) decreases estimated standard error (SM) and increases the likelihood of a significant result.
(True/False)

3. With = .01, a two-tailed t test for a sample of n = 20 subjects would have critical t boundary values of t = ±2.861
(True/False)

4. A sample of n = 15 scores would produce a t statistic of df = 16.
(True/False)

5. Using the single sample t statistic formula (M - divided by SM) for a hypothesis test: First, calculate the obtained t statistic for: M = 12, = 6, with SM = 2.

Second, find the critical t boundary values for the critical region in the t Distribution Table (p. 537).

Now, describe the decision regarding the null hypothesis for a two-tailed test with =.05 and df=8: _________.
(Reject Null Hypothesis/Fail to reject Null Hypothesis)

6. An independent-measures t test design could be used to evaluate the difference in verbal skills between 3-year old girls and 3-year old boys.
(True/False)

7. The null hypothesis for the independent-measures t test states that there is no difference between the two population means.
(True/False)

8. The homogeneity of variance assumption requires that the two samples have equal variances.
(True/False)

9. One sample has n = 6 and SS = 20, and a second sample has n = 6 and SS = 30. The pooled variance for the two samples is 50/10 = 5.
(True/False)

10. An independent-measures study uses a separate sample to represent each of the treatment conditions or populations being compared.
(True/False)

11. The goal of an independent measures research study is to evaluate mean differences between two populations (or treatment conditions).
(True/False)

12. For the difference scores: 3, -8, 6, -4, -2, the value of MD = -1.
(True/False)

13. A researcher obtains a t statistic of t = 2.00 from a repeated-measures study using n = 17 participants. If effect size is measured using r2, then r2 = 4/20 = 0.20
(True/False)

14. The repeated-measures t test design is suited to situations in which there are relatively few subjects available for study
(True/False)

15. The repeated-measures t test design is helpful because it uses fewer subjects for two samples.
(True/False)

16. The researcher’s goal for a repeated-measures t test is to use a sample of difference scores to answer questions about the general population, and particularly to find out if there is any difference between the two treatment conditions for the general population.
(True/False)

17. Independent observations are an assumption for the repeated-measures t test design.
(True/False)

18.
Two assumptions of the t test are: ________.

Assumption 1: ________

Assumption 2: ________

THANKS <3

PLEASE HELP WILL MARK BRAINLIEST THANK YOU

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D The equation should De
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