Set A of six numbers has a standard deviation of 3 and set B of four numbers has a standard deviation of 5. Both sets of numbers have an equal mean. If the two sets of numbers are combined, find the variance.

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.

Solve this system of equations. 12x − 18y = 27 4x − 6y = 10

Write the sine and cosine values of a, b, respectively, in the figure for (1) and (2) + explanation.