Lesson 3 Mathematics Is More Than Just Numbers
Mathematics Is Everywhere
____ is beneficial in everyday life.
We use math ____ and skills to understand patterns, define relationships, and predict the future.
____ would be amazed to see the emergence of math in unexpected situations.
Here are a few ____.
The ____ of Airplane Boarding
____ is the most efficient way to board a plane?
The standard procedure starts by boarding first class, ____ business class, and then economy class.
In the case of economy class passengers, they are divided ____ blocks according to their seat rows to board.
This often results in a crowded, ____ situation for passengers.
Mathematicians compared various boarding methods and found that boarding a plane starting from the front row took the longest while starting ____ the back row took the second longest.
From a mathematical point of view, the most efficient way appears to be seating passengers by the window, ____ from the back.
Then, passengers in the aisle seats board next, from ____ to front.
This ____, passengers can store their bags in the overhead bins almost simultaneously without disturbing each other.
Further, since the boarding starts from the ____, there is no need for passengers to pass each other.
Moreover, filling window seats first gets rid of the trouble of aisle ____ passengers having to stand up and move into the aisle while others take their seats.
In short, the most efficient ____ is to start with window seat passengers and move from back to front.
The Mathematics of Passwords
In movies, hackers are often shown sitting in front of a computer, trying to figure out other ____ passwords.
Is your password ____?
That depends on how securely it was ____.
____ to one survey, 26% of adults use passwords that are easy to memorize, such as birthdays or names, and surprisingly, the most common passwords used were "123456," "password," "12345," "12345678," and "qwerty."
The passwords used for ____ phones and banks are often four digits, and these are not very secure.
Each digit can be selected from 10 numbers ____ 0 to 9, so there are $10^4$ possible codes.
A computer can try ____ 10,000 combinations in the blink of an eye.
Let's assume that, for security ____, you create a password with six or more letters.
Choosing a word with six or more letters as a password may be more ____.
Six ____ from the 26-letter alphabet make a possible $26^6$ combinations, or more than 300 million total possibilities.
It's much better than a four-digit combination, though it's still possible for a ____ to check them all in only a few seconds.
Passwords become difficult to hack when they are long and combine ____ characters.
There can be $90^{20}$ combinations for a 20-digit password using around 90 letters, numbers, and ____ characters on a standard computer keyboard.
____, there is a problem here as well.
____ will the user memorize this long password?
Passwords should not be too easy but also ____ too complicated to memorize.
Using a passphrase with a story will make it easy to ____, even if the phrase is long.
For example, if you use a passphrase like "mathfirstenglishlater," which means that you will study math first and English later, it ____ be easy to memorize but difficult to hack.
____ can make your password even more secure by adding capital letters and special characters.
For example, "mathfirst,Englishlater" is a ____ secure password.
The Mathematics of Baseball
Baseball is a game of ____.
It's essential to know how many ____ a batter can get and how many bases they can reach.
____, batting average, which measures how often a player gets a hit, has been considered the most important criterion.
However, in baseball, ____ is another way to reach first base besides a hit, and that's a walk.
Nevertheless, walks aren't included in ____ average, so players who don't get many hits but are good at getting walks could be rated too low.
If players get on base in any way, they ____ scoring opportunities.
Therefore, recent ____ have shown that on-base percentage is much more important for winning than batting averages.
A ____ manager of a professional baseball team in the United States, whose team could not afford to pay the biggest star players, created his own criteria for selecting players.
His system valued how many bases a player ____ per at-bat.
It differed from the traditional batting average by taking into account not only the number of hits but also the types of hits (singles, doubles, triples, and ____ runs).
It ____ 1 point for singles, 2 points for doubles, 3 points for triples, and 4 points for home runs.
Moreover, the system considered a player's ability to draw walks as it contributes to getting on base and overall ____ success.
Using such standards, the team recruited valuable ____ other teams declined to pay.
____ players had low batting averages but excelled at drawing walks and had high on-base percentages.
____ having the third-lowest total player salary in the entire Major Leagues, the team reached the playoffs two years in a row, all thanks to this analytical approach.
In conclusion, ____ is a subject that we use every day, from simple calculations to more complex problem-solving.
It is a powerful tool that we need to navigate the world around us and to ____ efficiently and conveniently.
Therefore, understanding basic math concepts is ____ for making informed decisions.