Multiplying and Dividing Integers
... 23. Analyze Relationships Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was -200 feet. Then she continued to hike down for another 20 minutes at a different rate. Her change in elevation for this part of the hike was -300 feet. During which portion of the hike did ...
... 23. Analyze Relationships Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was -200 feet. Then she continued to hike down for another 20 minutes at a different rate. Her change in elevation for this part of the hike was -300 feet. During which portion of the hike did ...
Topics in Logic and Proofs
... We have seen that a logic operator, such as p → q, is defined by its truth table. In other words, a different table gives a different logic operator. Question. How many different logic operators involving p and q are possible? There is no doubt, however, that some of these operators are actually int ...
... We have seen that a logic operator, such as p → q, is defined by its truth table. In other words, a different table gives a different logic operator. Question. How many different logic operators involving p and q are possible? There is no doubt, however, that some of these operators are actually int ...
Section 9.6 Sequences
... More Growing Patterns • Def: A geometric sequence starts with any number as the 1st entry, and then each subsequent entry is obtained by multiplying or dividing by some fixed number. This fixed number, when using multiplication, is called the ratio. ...
... More Growing Patterns • Def: A geometric sequence starts with any number as the 1st entry, and then each subsequent entry is obtained by multiplying or dividing by some fixed number. This fixed number, when using multiplication, is called the ratio. ...
4.4 ADDING and SUBTRACTING LIKE FRACTIONS and LEAST
... When we SIMPLIFY a fraction, we wish to write its equivalent using the smallest numbers possible. For example, 1/2 would be the simplified form of the fraction 2/4. Sometimes it is possible to simplify a fraction just by performing the operation of division as suggested by the division bar! 15/3 for ...
... When we SIMPLIFY a fraction, we wish to write its equivalent using the smallest numbers possible. For example, 1/2 would be the simplified form of the fraction 2/4. Sometimes it is possible to simplify a fraction just by performing the operation of division as suggested by the division bar! 15/3 for ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.