Question

one pound equals 0.45 kilogram. cathy weighs 81.36 kilograms on the bathroom scales. determine her weight in pounds. to complete a planter box project, mr. michaels will purchase cedar boards that are 2 inches wide and 8 feet long. he will need to cut down the length of the boards into pieces that are 1\frac{1}{3} inches long. how many pieces can mr. michaels cut from each 8 - foot - long board? each pair of polygons is similar. determine the missing side measures.

Explanation:

Step1: Convert feet to inches

Since \(1\) foot \( = 12\) inches, an \(8 -\)foot - long board has a length of \(L=8\times12 = 96\) inches.

Step2: Convert the length of each piece to an improper fraction

The length of each piece is \(1\frac{1}{3}\) inches. Using the formula \(a\frac{b}{c}=\frac{ac + b}{c}\), we have \(1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{4}{3}\) inches.

Step3: Calculate the number of pieces

To find the number of pieces \(n\), we divide the total length of the board by the length of each piece. Using the formula \(n=\frac{\text{Total Length}}{\text{Length of each piece}}\), we get \(n=\frac{96}{\frac{4}{3}}\).
When dividing by a fraction, we multiply by its reciprocal. So \(n = 96\times\frac{3}{4}\).
We can simplify \(96\div4 = 24\), then \(24\times3=72\).

Answer:

\(72\) pieces.