Question

the ideal length of a particular metal rod is 30.5 cm. the measured length may vary from the ideal length by at most 0.015 cm. what is the range of acceptable lengths for the rod? a. $30.485 \leq x \leq 30.515$ b. $30.485 \geq x \leq 30.515$ c. $30.485 \geq x \geq 30.515$ d. $x \leq 30.485$ or $x \geq 30.515$

Explanation:

Step1: Find the minimum length

The ideal length is 30.5 cm, and it can vary by at most 0.015 cm. So the minimum length is $30.5 - 0.015 = 30.485$ cm.

Step2: Find the maximum length

The maximum length is $30.5 + 0.015 = 30.515$ cm.

Step3: Determine the range

The acceptable length \( x \) should be greater than or equal to the minimum length and less than or equal to the maximum length, so \( 30.485 \leq x \leq 30.515 \).

Answer:

A. \( 30.485 \leq x \leq 30.515 \)