The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. given n values (all of which are positive), the geometric mean is the nth root of their product. the average growth factor for money compounded at annual interest rates of 8.5%, 4.1%, and 2.7% can be found by computing the geometric mean of 1.085, 1.041, and 1.027. find that average growth factor, or geometric mean. what single percentage growth would be the same as having three successive growth rates of 8.5%, 4.1%, and 2.7%? is that result the same as the mean of 8.5%, 4.1%, and 2.7%?

(a) Average growth factor =

                                           =

                                           =  

                                           = 1.05068

(b) Single percentage growth rate = (Average growth factor - 1) × 100

                                                         = (1.05068 - 1) × 100

                                                         = 5.068 %

(c) The mean of 8.5%, 4.1% and 2.7% =

                                                             = 5.1%

Therefore, the single percentage growth rate is not the same as the mean of 8.5%, 4.1%, and 2.7%.

sorry idk it

explanation:

among other factors, composers started writing dynamic markings in their scores because "new instruments allowed for more dynamic ranges and contrast."

dynamics allude to the loudness or softness of music. dynamics offer an approach to demonstrate articulation in sheet music. they to drive the enthusiastic substance of music through volume and force. maybe you could alter both the volume and the shading profundity on your screen at the same time. we can likewise think about the force side of elements as the quality of a note. a few notes are intended to be played delicately and gently, while others are intended to be played all the more firmly.  

some dynamics markings have a letter 'm,' which remains for mezzo, signifying 'medium.' so a mezzo piano unique stamping resembles this (mp) and intends to play medium calm, while a mezzo specialty dynamic resembles this (mf) and intends to play medium loud.