Make up any vector y in R4 whose entries add up to 1. Compute P[infinity]y, and compare your result to P[infinity]x0. How does the initial distribution vector y of the electorate seem to affect the distribution in the long term? By looking at the matrix P[infinity], give a mathematical explanation.

Aplan to budget time for studying and activities is referred to as a study routine. study habits. study skills. a study schedule.

Write a program that reads a file consisting of students’ test scores in the range 0–200. it should then determine the number of students having scores in each of the following ranges: 0–24, 25–49, 50–74, 75–99, 100–124, 125–149, 150–174, and 175–200. output the score ranges and the number of students. (run your program with the following input data: 76, 89, 150, 135, 200, 76, 12, 100, 150, 28, 178, 189, 167, 200, 175, 150, 87, 99, 129, 149, 176, 200, 87, 35, 157, 189.)

Martha is designing a single-player game. her manager suggests that she plan the design to incorporate future modifications. which principle of game design relates to planning for future modifications?