You pass through five traffic signals on your way to work. Each is either red, yellow, or green. A red is always immediately followed by a yellow; a green is never followed immediately by a green. How many different sequences of colors are possible for the five signals?
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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1.
You pass through five traffic signals on your way to work. Each is either red, yellow, or green. A red is always immediately followed by a yellow; a green is never followed immediately by a green. How many different sequences of colors are possible for the five signals?2.Th e equation a5 + b2 + c2 = 2020 has a solution in positive integers a, b, and c in which a is a factor of c. Find 3a + 2b + c.
3. Let S be the empty set. Add the elements of {1, 2} to S, and after 1 minute randomly remove 1 element of S. Next add the 4 elements of {3, 4, 5, 6} to S and after 30 sec randomly remove 2 of the 5 elements of S. Continue this process forever, each time doubling the number of elements added and removed and halving the time. To the nearest hundredth of a minute, find the average length of time 1 remains in S.
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