A=(T)/(T+E+M+I) A musical software company uses the formula to rate the accuracy rate A of their software in transcribing the pitches in a music recording, where the recorded music has T total notes, and the transcription includes E extra notes, M missed notes, and I incorrect notes. Which of the following equations best shows the number of incorrect notes in terms of the number of total notes, extra notes, and missed notes? Choose 1 answer: (A) I=-E-M (B) I=(1)/(A)-1-E-M (C) I=(T)/(A)-T+E+M (D) I=(T)/(A)-T-E-M

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A=(T)/(T+E+M+I) A musical software company uses the formula to rate the accuracy rate  A of their software in transcribing the pitches in a music recording, where the recorded music has  T total notes, and the transcription includes  E extra notes,  M missed notes, and  I incorrect notes. Which of the following equations best shows the number of incorrect notes in terms of the number of total notes, extra notes, and missed notes? Choose 1 answer: (A)  I=-E-M (B)  I=(1)/(A)-1-E-M (C)  I=(T)/(A)-T+E+M (D)  I=(T)/(A)-T-E-M

Bytelearn · Accepted Answer

Rewrite formula: We start by rewriting the given formula for accuracy rate A: $$ A = \frac{T}{T + E + M + I} $$ Our goal is to solve for I in terms of T, E, and M.Multiply by denominator: First, we multiply both sides of the equation by the denominator to get rid of the fraction: $$ A(T + E + M + I) = T $$Distribute A: Next, we distribute A across the terms in the parentheses: $$ AT + AE + AM + AI = T $$Isolate I: Now, we want to isolate I on one side of the equation. To do this, we subtract AT, AE, and AM from both sides: $$ AI = T - AT - AE - AM $$Factor out T: We factor out T from the terms on the right side of the equation: $$ AI = T(1 - A) - AE - AM $$Divide by A: Finally, we divide both sides by A to solve for I: $$ I = \frac{T(1 - A)}{A} - \frac{AE}{A} - \frac{AM}{A} $$Simplify equation: Simplify the equation by dividing each term on the right side by A: $$ I = \frac{T}{A} - T - E - M $$ This matches option (D) from the given choices.

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