Find the distance between the points J(−8, 0) and K(1, 4).

Two-fifths () of the square of the variable j (j²)

j²

5 km. To determine the distance, we apply the speed formula that correlates distance with time: v = d / t. Thus, when rearranging for distance, we get: d = v * t. The speed is noted as 6 km/h, but we need to find the time taken - given he departs at 9:15 and returns at 10:05, the total time is 50 minutes. Converting this duration into hours gives us 50 min * 1 h / 60 min = 0.833 h. Hence, the duration for the journey to school is established as 0.833 hours. Substituting into our equation provides: d = 6 * 0.8333, yielding a distance of 5 km between the school and home.

Answer:

0.2 = 20%

Step-by-step explanation:

The combinations that yield a total of 6 or lower include:

(1,1), (1,2), (1,3), (1,4), (1,5),

(2,1), (2,2), (2,3), (2,4),

(3,1), (3,2), (3,3),

(4,1), (4,2),

(5,1)

(15 combinations in total)

The combinations resulting in a total of 4 are:

(1,3), (2,2), (3,1)

(3 combinations in total)

Thus, the probability of obtaining a sum of 4, given that the total is 6 or less is:

P = 3/15 = 0.2 = 20%

Angles known as vertical angles are those that are located across from each other at a common vertex where two lines intersect.

In the illustration, there exists only one pair of vertical angles.

These are Angle TSW and Angle ISN, both converging at the vertex labeled S.

<span>Answer is: B. Angle ISN and Angle TSW.</span>

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.