Many people use mobile apps and online software to manage and create personalized budgets. Suppose your task is to develop an online tool for personal budgeting. What information would be included or entered? What types of features would the tool have?

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 + 4x + 5 = 0

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

Acircle has a radius of 12.6cm what is the exact length of an arc formed by a central angle measuring 120