Question

e • shelf length: 20.6 cm

• desired shelf length: 17.6 cm
• acceptable error: 3%

will the shelf fit? circle one.
yes no
f • shelf length: 17.2 cm

• desired shelf length: 20.7 cm
• acceptable error: 10%

will the shelf fit? circle one.
yes no
g • shelf length: 25.9 cm

• desired shelf length: 23.7 cm
• acceptable error: 7%

will the shelf fit? circle one.
yes no
h • shelf length: 21.8 cm

• desired shelf length: 21.7 cm
• acceptable error: 2%

will the shelf fit? circle one.
yes no

Explanation:

Step1: Calculate the error percentage for each case

The formula for error percentage is \( \text{Error}\%=\frac{\vert\text{Shelf length}-\text{Desired shelf length}\vert}{\text{Desired shelf length}}\times100\)

Case e

• Shelf length \(L = 20.6\) cm, Desired length \(D=17.6\) cm
• \( \text{Error}\%=\frac{\vert20.6 - 17.6\vert}{17.6}\times100=\frac{3}{17.6}\times100\approx17.05\%\)
• Since \(17.05\%>3\%\), the answer is No

Case f

• Shelf length \(L = 17.2\) cm, Desired length \(D = 20.7\) cm
• \( \text{Error}\%=\frac{\vert17.2-20.7\vert}{20.7}\times100=\frac{3.5}{20.7}\times100\approx16.91\%\)
• Since \(16.91\%>10\%\), the answer is No

Case g

• Shelf length \(L = 25.9\) cm, Desired length \(D=23.7\) cm
• \( \text{Error}\%=\frac{\vert25.9 - 23.7\vert}{23.7}\times100=\frac{2.2}{23.7}\times100\approx9.28\%\)
• Since \(9.28\%<7\%\), the answer is No

Case h

• Shelf length \(L = 21.8\) cm, Desired length \(D = 21.7\) cm
• \( \text{Error}\%=\frac{\vert21.8-21.7\vert}{21.7}\times100=\frac{0.1}{21.7}\times100\approx0.46\%\)
• Since \(0.46\%<2\%\), the answer is Yes

Answer:

e. No
f. No
g. No
h. Yes