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The Fibonacci Sequence is a recursively defined sequence determined by the function:
Fn = 0 if n = 0Fn = 1 if n = 1Fn-2 + Fn-1 if n ≥ 2
where n is a natural number.
The first few terms of the sequence are:F0 = 0, F1 = 1, F2 = 1, F3 = 2, F4 = 3, F5 = 5, F6 = 8, F7 = 13, F8 =21 .....
Consider the formula ( Fn)^2 + ( Fn+1 )^2 = F2n+1.
a) Show that the formula is true for n = 0 and n = 1.
b) Prove the formula is true for all natural numbers n by induction.
Because the bonus is a deductible expense, the amount of income tax (T) at a 40% rate is 40% of the income after deducting the bonus.
Together, Louisa and Jill scored more than 30 points in the basketball game. If Jill scored 12 points, how many points P did Louisa score?
Calculate the Galois group.
Write the equation in slope intercept form y + 2 = - 6(x-1). Determine the equation of each line. Write the answer in slope intercept form. The line through (4,0) that is perpendicular to the line x + y = 3.
A Turing machine exists with tape symbols 0, 1, and B, that takes a bit string as input and replaces all 0s with 1s; it does not change any of the 1s.
in a study designed to predict blood cholesterol levels from amount of daily saturated fat in grams x1 and number of
In 2000, the average cost of tuition and fees at public four- year colleges was $3500, and in 2005 it was $5100. The supporting information is listed below. Note that the known value for 2001 is $3700.
victoria has some money from her birthday and the amount is modeled by the function hx 200. she read about a bank that
How many bags of potato chips and ice cream bars did omar eat when 88 grams of fat and 1505 calories were consumed?
Mary wants to make a line graph to show how the temperature outside changed during the course of one day. She measured the temperature once every hour from 7:00 am to 7:00 pm she records this information in a table.
Two sessions of swimming lessons were held at a pool. In the first session 40 students attended. Of these 40 students 60% were girls.
Simplify the following inequality
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