Problem

Complete the table.
(a)
(b)
(c)
(d)
\begin{tabular}{|c|c|c|c|}
\hline A & B & C & D \\
\hline $5 \frac{1}{2} \mathrm{in.}$ & $2 \frac{3}{4} \mathrm{in.}$ & $1 \frac{5}{6} \mathrm{in.}$ & \\
\hline & $23.6 \mathrm{~cm}$ & $23.4 \mathrm{~cm}$ & $15.6 \mathrm{~cm}$ \\
\hline $15 \mathrm{ft}$ & & $6 \mathrm{ft}$ & $4 \mathrm{ft}$ \\
\hline $4 \mathrm{~m}$ & $3.2 \mathrm{~m}$ & & $2.4 \mathrm{~m}$ \\
\hline
\end{tabular}
(a) $D=\frac{11}{12}$ in. (Type a whole number or a simplified fraction.)
(b) $A=\square \mathrm{cm}$ (Type a whole number or a decimal.)

Answer

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Answer

The final answers are: For part (a), the value of D in inches is \(\boxed{\frac{11}{12}}\). For part (b), the value of A in cm is \(\boxed{15.73}\).

Steps

Step 1 :Set up a proportion using the given values in the first row and solve for D. The proportion is \(\frac{A}{B} = \frac{C}{D}\). Substitute the given values to get \(\frac{5.5}{2.75} = \frac{1.8333333333333335}{D}\). Solving for D gives \(D = 0.9166666666666667\) inches.

Step 2 :Convert the decimal to a fraction to get \(D = \frac{11}{12}\) inches.

Step 3 :Set up a proportion using the given values in the second row and solve for A. The proportion is \(\frac{A}{B} = \frac{C}{D}\). Substitute the given values to get \(\frac{A}{23.6} = \frac{23.4}{15.6}\). Solving for A gives \(A = 15.733333333333336\) cm.

Step 4 :The final answers are: For part (a), the value of D in inches is \(\boxed{\frac{11}{12}}\). For part (b), the value of A in cm is \(\boxed{15.73}\).

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