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4 months ago

Q:
# Robert is inspecting a shipment of 22-inch pipes. The lengths of the pipesmay vary by 1%. What is the range of allowable lengths of the pipes?luat his car it averaqed 28 miles per gallon of gas. Now, the

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A:

Answer:[tex]21.78\leq x\leq 22.22[/tex]Step-by-step explanation:Let x represent the actual length of pipe.We have been given that Robert is inspecting a shipment of 22-inch pipes. The lengths of the pipes may vary by 1%.To find the range of allowable lengths of the pipes, we will use tolerance calculation formula.[tex]|\text{Atual}-\text{Ideal}|\leq \text{Tolerance}[/tex]The variation in the lengths of pipes is 1% of ideal length that is 22.[tex]22\times \frac{1}{100}=0.22[/tex]Upon substituting, our given values, we will get:[tex]|x-22|\leq 0.22[/tex]Use absolute value rule: If [tex]|u|\leq a[/tex], then [tex]-a\leq u\leq a[/tex][tex]-0.22\leq x-22\leq 0.22[/tex]Adding 22 on all sides:[tex]-0.22+22\leq x-22+22\leq 0.22+22[/tex][tex]21.78\leq x\leq 22.22[/tex]Therefore, the range of allowable lengths of the pipes is [tex]21.78\leq x\leq 22.22[/tex].