Geometry math question no guessing and show work you

Use the x-intercept method to find all real solutions of the equation.x^3-10x^2+27x-18=0

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.

Identify the number 127 as a rational or irrational. explain