Math Review Sheet
... Sum of the digits is divisible by 3 How do you know if a number is divisible by 4? Last two digits are divisible by 4 How do you know if a number is divisible by 5? Last digit is either a 0 or a 5 How do you know if a number is divisible by 6? Number is even and divisible by 3 How do you know if a n ...
... Sum of the digits is divisible by 3 How do you know if a number is divisible by 4? Last two digits are divisible by 4 How do you know if a number is divisible by 5? Last digit is either a 0 or a 5 How do you know if a number is divisible by 6? Number is even and divisible by 3 How do you know if a n ...
The r-Bell Numbers
... If we construct partitions on n + r elements and the first r elements are in distinct blocks, then we have two possibilities: 1) the last element, n + r, belongs to a block containing one of the first elements. Such partition can be constructed such that we construct a partition of {1, 2, . . . , n ...
... If we construct partitions on n + r elements and the first r elements are in distinct blocks, then we have two possibilities: 1) the last element, n + r, belongs to a block containing one of the first elements. Such partition can be constructed such that we construct a partition of {1, 2, . . . , n ...
Full text
... The problem of determining which integers k are equal to the sum of the digits of Fk was first brought to my attention at the Fibonacci Conference in Pullman, Washington, this summer (1994). Professor Dan Fielder presented this as an open problem, having obtained all solutions for k < 2000. There se ...
... The problem of determining which integers k are equal to the sum of the digits of Fk was first brought to my attention at the Fibonacci Conference in Pullman, Washington, this summer (1994). Professor Dan Fielder presented this as an open problem, having obtained all solutions for k < 2000. There se ...
Maths Homework sheet 1 Homework Sheets
... What is the probability of choosing the Queen of Spades at random from a pack of cards? ...
... What is the probability of choosing the Queen of Spades at random from a pack of cards? ...
Rational Numbers
... A geometric sequence is a list of numbers in which each number after the first is found by multiplying the preceding number in the list by the same number. For example, in the sequence 1, 3, 9, 27, 81, . . . , each number after the first is found by multiplying the preceding number in the list by 3. ...
... A geometric sequence is a list of numbers in which each number after the first is found by multiplying the preceding number in the list by the same number. For example, in the sequence 1, 3, 9, 27, 81, . . . , each number after the first is found by multiplying the preceding number in the list by 3. ...
A2 - Webs
... My security code number consists of 6 digits, each of which is an odd prime number. How many possibilities are there for my code number? (Digits may be used more than once.) There are three odd primes, so there are 36 729 B4 Seven fence posts are equally spaced along a straight road. The distance ...
... My security code number consists of 6 digits, each of which is an odd prime number. How many possibilities are there for my code number? (Digits may be used more than once.) There are three odd primes, so there are 36 729 B4 Seven fence posts are equally spaced along a straight road. The distance ...
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)