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QuestionHow much clearance is needed for 5 layers of insulation that are 3123 \frac{1}{2} inches thick each? Options: F. 101210 \frac{1}{2}, G. 121212 \frac{1}{2}, H. 16, J. 171217 \frac{1}{2}, K. 19.

Studdy Solution

STEP 1

Assumptions1. The thickness of each bat of insulation is 313 \frac{1}{} inches. We are installing5 layers of batting3. The thickness of the batting layers adds up linearly, i.e., the total thickness is the sum of the individual thicknesses

STEP 2

First, we need to convert the mixed fraction to an improper fraction to make the calculation easier.12=72 \frac{1}{2} = \frac{7}{2}

STEP 3

Now, we need to find the total thickness of the5 layers of batting. We can do this by multiplying the thickness of one layer by the number of layers.
Total thickness=Thickness of one layertimesNumber of layersTotal\, thickness = Thickness\, of\, one\, layer \\times Number\, of\, layers

STEP 4

Plug in the given values for the thickness of one layer and the number of layers to calculate the total thickness.
Total thickness=72 inchestimesTotal\, thickness = \frac{7}{2} \, inches \\times

STEP 5

Calculate the total thickness.
Total thickness=72 inchestimes5=352 inchesTotal\, thickness = \frac{7}{2} \, inches \\times5 = \frac{35}{2} \, inches

STEP 6

Convert the improper fraction back to a mixed number to get the final answer.
352=1712\frac{35}{2} =17 \frac{1}{2}So, you need a clearance of 171217 \frac{1}{2} inches to install5 layers of batting.

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