Shortest path counting: A chess rook can move horizontally or vertically to any square in the same row or the same column of a chessboard. Find the number of shortest paths by which a rook can move from one corner of a chessboard to the diagonally opposite corner. The length of a path is measured by the number of squares it passes through, including the first and the last squares. Solve the problem:

Which of the following parabolas opens down?

What rule describes a dilation with a scale factor of 4 and the center of dilation at the origin?

Agroup of student volunteers participates in a study designed to assess several behavioral interventions for improving output in a repetitive task. prior to the beginning of the study, all volunteers unknowingly observed, and their output is measured. at the beginning of the study, prior to any intervention, the volunteers perform the same task under the observation of a study administrator, and their overall output increases. which of the following terms describes this phenomenon? a. simpson's paradox b. hawthorne effect are d. novelty effect d. pygmalion effect e. observer-expectancy effect