103. gwyneth is conducting an experiment. she rolls 1,000 dice simultaneously and removes any that have a six showing. she then rerolls all of the dice that remain and again removes any that have a six showing. gwyneth does this over and over again—rerolling the remaining dice and then removing those that land with a six showing.
f. for all of the values in the domain of f�, is there any value for which f will predict an average number of 0 dice remaining? explain why or why not. be sure to use the domain of the function and the graph to support your reasoning.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

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answer: it actually depends on which is the independent variable and which is the dependent variable. let us say we're looking at a linear equation. y=2x+3. we theoretically could switch the equation to be x=(y-3)/2 and it would be the same line. so either a causes b or it can be that b causes a. so technically the answer is false

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