Mathematics, 20.11.2020 19:30 waterborn9800
FREE POINTS
J SOLVE THE Collatz conjecture
If the number is even, divide it by two.
If the number is odd, triple it and add one.
In modular arithmetic notation, define the function f as follows:
{\displaystyle f(n)={\begin{cases}{\frac {n}{2}}&{\text{if }}n\equiv 0{\pmod {2}}\\[4px]3n+1&{\text{if }}n\equiv 1{\pmod {2}}.\end{cases}}}{\displaystyle f(n)={\begin{cases}{\frac {n}{2}}&{\text{if }}n\equiv 0{\pmod {2}}\\[4px]3n+1&{\text{if }}n\equiv 1{\pmod {2}}.\end{cases}}}
Now form a sequence by performing this operation repeatedly, beginning with any positive integer, and taking the result at each step as the input at the next.
In notation:
{\displaystyle a_{i}={\begin{cases}n&{\text{fo r }}i=0\\f(a_{i-1})&{\text{for }}i>0\end{cases}}}a_{i}={\begin{ cases}n&{\text{for }}i=0\\f(a_{i-1})&{\text{for }}i>0\end{cases}}
(that is: ai is the value of f applied to n recursively i times; ai = fi(n)).
The Collatz conjecture is: This process will eventually reach the number 1, regardless of which positive integer is chosen initially.
That smallest i such that ai = 1 is called the total stopping time of n.[3] The conjecture asserts that every n has a well-defined total stopping time. If, for some n, such an i doesn't exist, we say that n has infinite total stopping time and the conjecture is false.
If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1, or increase without bound. No such sequence has been found.
NAH jk have a good day
Answers: 3
Mathematics, 21.06.2019 17:30
Assume that 1400 births are randomly selected and 1378 of the births are girls. use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high. choose the correct answer below. a. the number of girls is neither significantly low nor significantly high. b. the number of girls is significantly high. c. the number of girls is significantly low. d. it is impossible to make a judgment with the given information.
Answers: 1
Mathematics, 21.06.2019 20:30
Create a question with this scenario you could ask that could be answered only by graphing or using logarithm. david estimated he had about 20 fish in his pond. a year later, there were about 1.5 times as many fish. the year after that, the number of fish increased by a factor of 1.5 again. the number of fish is modeled by f(x)=20(1.5)^x.
Answers: 1
FREE POINTS
J SOLVE THE Collatz conjecture
If the number is even, divide it by two.
If t...
If the number is even, divide it by two.
If t...
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