Monty Hall Problem: a mathematical exploration of the problem Marlou Dinkla 000768-008 Math Internal Assessment American School of The Hague Word Count: 2500 If you are into brainteasers you might have come across the Monty Hall problem. Another place were you might have stumbled upon it is on science programs like Mythbusters. In talking to my brother about his university math class, we came upon enigmas that involved math. Remembering back to my days in front of the television, I was reminded of a Mythbusters episode were they tried out the Monty Hall problem. Unbeknown to me at the time, was the ability to apply statics in finding out the best course of action.
In this example, two dies are open to differ whereas the third die is not. For that reason, degree of freedom is equal to 2. For data with one category: Degree of freedom = number of observations -1 For data with more than one category represented in a table: Degrees of freedom = (number of rows in the table) – 1 X (number of columns in the table) -1 The chi-square test is used to determine whether two variables are independent or not. If two variables are dependent on each other, their values have a tendency to progress together, either in the opposite direction or in the same. Example Consider a data set of 100 individuals divided into categories of Male, Female and university admission (Yes/No).
For example, it helps you spot right triangles and solve for the third side in a triangle. This proved to be a valuable skill when dealing with comparatively primitive geometry problems in elementary school. In this exploration I will investigate two ways how a Pythagorean triple can be generated. First, the Euclid’s theorem of generating these triplets will be explored and proved that the values generated, with the help of this formula, are in fact a Pythagorean triple corresponding to sides of a right triangle. Next, the Berggren’s Parent/Child relationships will be explored.
Math Exploration Cracking different Ciphers Himanshu Mehta Mr. Classey Rationale This mathematics exploration is focus around the topics of cryptography to be more focused this exploration will look at some of the ciphers which have been used in the past. My decision to pursue this topic was mainly because of my interest in the Enigma Code machine built by German engineer Arthur Scherbius and was used in the World War II. This device is fascinating because it was the most advanced cipher in the 1940’s and was said to be unbreakable if the Germans had implemented the cipher properly. After the war ended “It was thanks to Ultra (project associated with the cracking of the Enigma) that we won the war.” Winston Churchill to King
Since the magic square is a square, all sides are equal or there are the same number of rows and columns. The number of rows or columns is call the order which you can represent as the variable n. The number of small squares or the number of numbers in the magic square would equal n squared. N squared also means n multiplied by itself once showing how the rows and columns are multiplied to find the amount of numbers used in the square. A normal magic square would have the numbers 1 to n squared. Mathematicians figured out the magic sums by using a formula including variables that can be used to find every magic constant in every magic square.
Solution to Task 2 The answer is True. A short description of solution 2: I illustrated this in the solution 1. There is no better way to find the median manually without re-arranging the data in ascending order ………………………………………………… Task 3 What is the interquartile range of the data? Solution to Task 3 The interquartile range is 6 A short description of solution 3: what I did, manually, was that I found the middle location of all data in the lower half of the data leftward of the median (2.8) to get the first quartile (Q1). Then I find the middle location of all data in the upper half of the data rightward of the median (2.8) to get the third quartile (Q3).
Magic is around us every day even in math class there is magic that makes the world more beautiful. Math is involved in many aspect of magic more than you would ever believe Persi Warren Diaconis was born January 31, 1945. Persi is an American mathematician and former professional magician. Persi was one of the people who proved one of these points. Magic has been around for many centuries.
When you multiply or divide measurements, the number of significant figures in the answer is equal to the number of significant figures in the least precise measurement. For the addition or subtraction of measurements, the number of significant figures in the answer is equal to the number of decimal places in the least precise measurement. Nonzero integers always count as significant figures, and exact numbers, quantities obtained without the use of a measuring device, have an infinite number of significant figures. For example, the number 15.1 has three significant figures because none of the integers are zero. However, there are three classes of zeros: leading zeros, captive zeros, and trailing zeros.
Some points barely had much to offer and sources for each benefit only had two, one, or even no sources to back up claims. Universities from where these scholars conduct their research also sound nice but it also could be abused. The credibility is put to question and it is furthermore suspicious with how brief the explanations are on the experiments undertaken. On a more hands on level, I think the two points on reading ability and school performance are better off being merged together. The former even mentions other subjects such as mathematics and science which ultimately disregards the heading of the
For normal permutations the number of possibilities would be 3! = 6 The list of permutations are tabulated as shown abc acb bac bca cab cba The number of possibilities are reduced to just 2 as the bolded words all have letters in its original position . This had reduced the number of possible arrangments in enigma which allowed the code to be broken within a realistic time. For n=3 the number of derrangements notated as !n is only 2 To calculate the number of derangements of enigma . let n=the number of letters=26 And D=Derangement of Since no number can return to its original place, the number of derangements is given as the subfactorial .
The preceding figures shows the Fibonacci and Galois implementations of maximal length shift register m-sequences. As can be seen in these figures, m-sequences contain m shift registers. The shift register set is filled with an m-bit initial seed that can be any value except 0 (if the m bits in the m shift registers are all zero, then it is a degenerate case and the output of the generator is 0). The following examples demonstrate bit generation. 1.
(2x − 3y)^4=16x^4-96x^3y+216x^2y^2-216xy3+81y^4 5. The possible variable terms would have to be a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5 because the exponents of each one of the terms all add up to 8. Task 3 Q&A Using the Fundamental Theorem of Algebra, complete the following: 1. Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100. 2.
Watson’s intelligence is much different than that of a human, for better and for worse. In the better category, the clear difference is their capacity for learning. Humans have storage space the size of a shoebox, according to the video, and learning new tasks and topics can take multiple times seeing it in order to bridge the neurons for a memory. Watson can “memorize” new information in the snap of a finger, with a server size spanning over 8 refrigerators. This allows it to recall 200 million unique pages of data, while processing it at a blistering 80 teraflops, or 80 trillion operations per second.