Prove that the roots of x^2+(1-k)x+k-3=0 are real for all real values of k.​

Muscles, a membership-only gym is hoping to open a new branch in a small city in pennsylvania that currently has no fitness centers. according to their research approximately 12,600 residents live within driving distance of the gym. muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. based on the past survey research, muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. based on this information and the results of the sample survey, about how many residents should muscles expect to join its new branch? a) 134 b) 504 c) 1,680 d) 3,780

Read the equations in the table below. then drag a description of the situation and a table to represent each equation. indicate whether each of the relationships is proportional or non-proportional.

How do you find principle and simple interest