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# How to find general patterns trends in a sequence of random numbers

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task is to move all the reds from the left to the right and all the blacks from the right to the left. The middlebox is empty to allow moves. The moves follow strict rules. Rule # 1: the reds can only move to the right and the blacks can only move to the left. No backward moves are allowed Rule # 2: Equally applicable to the black and the reds, each dot can only move one step forward in the box in front of it is empty, and can skip the contiguous box is occupied by a different colored dot to the following box if empty. While moving your pieces, carefully record all the moves you made. Start first with the 5-boxes set, then the 7-boxes set Try the same rules for a 9-boxes set and then for an 11-boxes set. Record all your moves on paper Examine all four cases and find a pattern that relates the number of moves to the number of dots. Explain how you arrived at this conclusion Create a general formula that will give the number of moves based on the number of dots regardless of how many dots you have.
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vertical strut extending from the lower arch to the roadway (as shown in the image). Here the lower arch is 80m above sea level and the upper arch is 49m above the roadway. At the vertices, the lower arch is 118m above sea level and the upper arch is 73m above the roadway. Find the quadratic equations which describe the parabolas of the lower arch in: vertex form, y=a(x-h)^2+k; intercept form, y=a(x-α)(x-β) general form, y=ax^2+bx+c The lower arch intersects the roadway 181.5m from the vertex. Calculate how much higher is the upper arch than the lower at the middle of the bridge? Using technology, determine the total length of all 19 pairs of equally-spaced, vertical struts between the lower arch and the roadway.
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