The vertices of quadrilateral E F G H are E (-7,3) , F (-4,6) , G (5, -3) , and H (2,-6). What kind of quadrilateral is E F G H?

Answer:

a) Null and alternative hypothesis

b) Point estimate d = -$78

c) Test statistic t = -2.438

P-value = 0.0113

Reject H0. This indicates that the average automobile premium in Pennsylvania is lower than in the nation.

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:

The significance level is set at 0.05.

The sample size is n=25.

The sample mean equates to M=1425.

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

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:

Then, we can calculate the t-statistic as:

The degrees of freedom for this sample size stand at:

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

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.

The graph indicates that x never goes below 0. This means the point (-1,0) is not included in the graph. Therefore, D is the only valid option.

4x+32

4 goes into 4 1 time. (4/4=1)
4 goes into 32 8 times. (32/4=8)
We can factor out 4 from both numbers. 

4(1x+8)
aka 4(x+8)

No.
In order to conduct an analysis like this one, it is essential to select a RANDOM SAMPLE from the entire POPULATION involved in the study. For instance, Pete is attempting to gauge the overall satisfaction of his customers, therefore, he should distribute the surveys to a randomly chosen group of customers rather than only targeting those who have bought the most items. Doing so will yield results that are more REPRESENTATIVE of the overall customer satisfaction. If he limits the surveys to those customers who have purchased the most, he is likely to see inflated satisfaction levels, which would not truly reflect the general sentiment of all customers.

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