Write the converse of the following statement and determine its truth value:

Response:

15.9

Detailed explanation:

P(S) = Probability of Smash = 0.05 (5%)
P(M) = Probability of Modest = 0.5 (50%)
P(F) = Probability of Flop = 0.45 (45%)
Based on this, we utilize the model for discrete random variables, leading to:
E(X) = (0.05 * 5.2) + (0.5 * 0.9) + (0.45 * 0)
= 0.26 + 0.45 + 0
= 0.71 Mill'

Response:

Alan's survey aims to determine the art preferences among students at the local high school.

To conduct a thorough investigation, he needs to consider all students in the school as the target population since that is his goal.

Nevertheless, in many cases involving statistical studies, it's impractical to include the entire population. In such instances, a sample that accurately reflects the overall student body is employed.

This sample is a subset of the population and must share the same characteristics and attributes; otherwise, the findings may be skewed.

Thus, a feasible sample would consist of a specific number of students from each grade level, including freshmen, sophomores, juniors, and seniors. This approach ensures the sample accurately represents the larger population.

Response:

The loop's length is roughly 49.58 km.

Step-by-step details:

Given:

Duration to cycle the loop = 2 hours and 30 minutes

It is known that;

60 minutes = 1 hour

30 minutes = 0.5 hour

therefore, 2 hours and 30 minutes =

∴ Time to cycle the loop = 2.5 hours

Let 's' denote the cycling speed.

Denote the total loop distance as 'd'

From our understanding;

Distance equals speed times time.

Representing this as an equation we have;

Given:

If her speed increased by 1 km/hr, the time taken around the loop would decrease by 7 minutes.

As a result, we can say;

Speed =

The time then will be shortened by 7 minutes.

7 minutes = 0.12 hours

Consequently, time = 2.5 - 0.12 = 2.38

Again, Distance is calculated as speed times time.

This can be expressed with equations;

The distances are equivalent in both scenarios, thus we will determine speed by equating the equations.

So, Speed = 19.83 km/hr

Loop length (d) =

Therefore, the loop length is approximately 49.58 km.