The curve with the equation y=ax^3-4x+1 is parallel to the line y=50x-1 at the point with x coordinate 3. (a) find the gradient of the curve at the point with x coordinate 4

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

Use matrices to solve this linear system: 5x1 − 2x2 = −30 2x1 − x2 = −13 x1 = x2 =

Calculate the mean value (expected value) of the following discrete variable x (10 points): x = 0, 1, 2, 3, 4, 5, 6 p(x) = 0.2, 0.2, 0.15, 0.15, 0.15, 0.1, 0.05