## How many triangles can you draw using all the diagonals from one vertex of a regular hexagon?

Assuming a regular hexagon: If you draw all diagonals of a regular hexagon you have 3⋅6=18 possible triangles, but 3 of those are the same (the equilateral triangles) so we have 18−3=15 possible triangles.

## How many triangles could be formed by drawing a line from one vertex to each of the others?

Every diagonal drawn from a single vertex of a polygon creates one triangle within the polygon, except for the last diagonal, which creates two triangles. For each triangle created within the polygon, 180 degrees of interior angles are created.

## How many triangles are formed by drawing a diagonal from vertex A to all non adjacent vertices in a regular octagon?

The sum of the interior angles of an octagon = (n-2)*straight angles. So the number of triangles at any vertex of an octagon = (8–2) = 6 triangles. Considering the 8 vertices, a total of 48 triangles are possible in an octagon.

## How many triangles can be made if all the diagonals from a vertex of a 10 sided polygon are drawn?

These eight triangles are formed by joining any vertex of the decagon to any other vertex. Thus, the triangles are formed by drawing the diagonals of the decagon.

8 triangles

## How do DND rolls work?

You generate a number between 1 and 100 by rolling two different ten-sided dice numbered from 0 to 9. One die (designated before you roll) gives the tens digit, and the other gives the ones digit. If you roll a 7 and a 1, for example, the number rolled is 71.

## What is the entropy of a fair four sided die?

Here, the entropy is at most 1 bit, and to communicate the outcome of a coin flip (2 possible values) will require an average of at most 1 bit (exactly 1 bit for a fair coin). The result of a fair die (6 possible values) would have entropy log26 bits.

## What is entropy of a random variable?

Definition: Entropy is a measure of uncertainty of a random variable. The entropy of a discrete random variable X with alphabet X is H(X) = -) p(x) log p(2) DEX When the base of the logarithm is 2, entropy is measured in bits. Hence, when Y is given, some uncertainty about X goes away.

## What is entropy a measure of?

entropy, the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system.

## What is the definition of free energy?

Free energy or Gibbs free energy G, is the energy available in a system to do useful work and is different from the total energy change of a chemical reaction.