Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass m and radius r about an axis perpendicular to the hoop's plane at an edge.

Abbey purchased a house using a fixed rate mortgage. the annual interest rate is 4.2% compounded monthly for 20 years. the mortgage amount is $235,000. what is the monthly payment on the mortgage? this isn't a multiple choice question have to show my work

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply

Identify the expression equivalent to 4(x + x + 7) − 2x + 8 − 4 by substituting x = 1 and x = 2.