The Fibonacci numbers are defined as follows. f1 = f2 = 1 and, for n ≥ 3, fn = f(n1) + f(n - 2). The Fibonacci numbers with four or fewer digits are: f1 = 1, f2 = 1, f3 = 2, f4 = 3, f5 = 5, f6 = 8, f7 = 13, f8 = 21, f9 = 34, f10 = 55, f11 = 89, f12 = 144, f13 = 233, f14 = 377, f15 = 610, f16 = 987, f17 = 1597, f18 = 2584, f19 = 4181, and f20 = 6765. Prove that the Fibonacci number f3 n is even.

Which system of linear inequalities is graphed? can somebody pleasssse

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

You use math in day-to-day routines when grocery shopping, going to the bank or mall, and while cooking. how do you imagine you will use math in your healthcare career?