$A=\frac{T}{T+E+M+I}$ $\newline$ 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? $\newline$ Choose $1$ answer: $\newline$ (A) $I=-E-M$ $\newline$ (B) $I=\frac{1}{A}-1-E-M$ $\newline$ (C) $I=\frac{T}{A}-T+E+M$ $\newline$ (D) $I=\frac{T}{A}-T-E-M$

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Algebra 1

Solve rational equations

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A=\frac{T}{T+E+M+I}

\newline

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?

\newline

Choose

1

answer:

\newline

(A)

I=-E-M

\newline

(B)

I=\frac{1}{A}-1-E-M

\newline

(C)

I=\frac{T}{A}-T+E+M

\newline

(D)

I=\frac{T}{A}-T-E-M

Rewrite formula: We start by rewriting the given formula for accuracy rate A: $\newline$ $A = \frac{T}{T + E + M + I}$ $\newline$ 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: $\newline$ $A(T + E + M + I) = T$
Distribute A: Next, we distribute A across the terms in the parentheses: $\newline$ $AT + AE + AM + AI = T$
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: $\newline$ $AI = T - AT - AE - AM$
Factor out T: We factor out T from the terms on the right side of the equation: $\newline$ $AI = T(1 - A) - AE - AM$
Divide by A: Finally, we divide both sides by A to solve for I: $\newline$ $I = \frac{T(1 - A)}{A} - \frac{AE}{A} - \frac{AM}{A}$
Simplify equation: Simplify the equation by dividing each term on the right side by A: $\newline$ $I = \frac{T}{A} - T - E - M$ $\newline$ This matches option (D) from the given choices.