Suppose we choose three initial centroids x, y, and z, and cluster the points according to which of x, y, or z they are closest. The result will be three apparent clusters, which may or may not coincide with the true clusters A, B, and C. Say that one of the true clusters is correct if there is an apparent cluster that consists of all and only the points in that true cluster. Assuming initial centroids x, y, and z are chosen independently and at random, what is the probability that A is correct

Girardo is using the model below to solve the equation . girardo uses the following steps: step 1 add 4 negative x-tiles to both sides step 2 add 1 negative unit tile to both sides step 3 the solution is which step could be adjusted so that gerardo's final step results in a positive x-value? in step 1, he should have added 4 positive x-tiles to both sides. in step 1, he should have added 3 negative x-tiles to both sides. in step 2, he should have added 4 negative unit tiles to both sides. in step 2, he should have added 1 positive unit tile to both sides.

Select the graph of the solution. click until the correct graph appears. |x| = 3

Asmall business produces and sells balls. the fixed costs are $20 and each ball costs $4.32 to produce. each ball sells for $8.32. write the equations for the total cost, c, and the revenue, r, then use the graphing method to determine how many balls must be sold to break even.