Arithmetic, List 3

Sequences of heads and tails of a given length, say twenty flips, generally have a certain number of consecutive runs of heads.

The Division Algorithm tells us that a polynomial dividend can be written as the product of the divisor and the quotient added to the remainder.

There is not a set procedure for determining the number of bars or bar width/bin size; however, consistency is key when determining which data values to place inside each interval.

All other intervals are given by irrational numbers based on the twelfth root of two, not nice numbers that can be written as a ratio of two small whole numbers.

Based on this measurement, astronomers then defined an accurate magnitude system in which a difference of five magnitudes corresponds exactly to a brightness ratio of 100:1.

The current best estimate for Earth’s weight is 5.9725 billion trillion metric tons, a difference of only about 1 percent from Cavendish’s finding.

The ratios for equal temperament are all multiples of the twelfth root of two.

The confirmed case-fatality risk, also known as the case-fatality risk, is defined as the " proportion of deaths within a defined population of interest," measuring "the severity of the disease that causes death."

Since L’Hôpital’s rule applies to quotients, we use the natural logarithm function and its properties to reduce a problem evaluating a limit involving exponents to a related problem involving a limit of a quotient.

Adding a rational number over and over, on the other hand, is not dense because eventually you will be repeating the same number.

Most interesting of all, if you take a number x and replace it with its reciprocal 1/x, that is equivalent to flipping the sphere upside down and reflecting it in a mirror.

A particular sequence of DNA—ACT-GAC-CAC-GTG—was therefore used to build an RNA chain, and the RNA chain was translated into a chain of amino acids, ultimately leading to the construction of a protein.

Groups of species grow and then are replaced by other groups through a sequential series of changes as the community matures over time.

When your points are zero distance away from each other, your approximation is perfect: you have found the tangent.

An object approaching us at very high velocities is perceived to have the color of its spectral lines blue-shifted.