Connecting Algebra and GeometryConsider the collec- tion of all rectangles that have lengths 2 in. less than twice
their widths. Find the possible widths (in inches) of these
rectangles if their perimeters are less than 200 in.

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.