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Answer :
To solve the given problem, let's go through it step-by-step:
1. Understanding the Context:
- The question is about the temperature range in Glendale for a particular day.
- We are given a low temperature and a high temperature for the day.
2. Identifying the Details:
- The low temperature for the day is [tex]\(82^{\circ} F\)[/tex].
- The high temperature for the day is [tex]\(101^{\circ} F\)[/tex].
3. Finding the Range for the Temperature:
- We need to express the range of temperatures that occurred during the day using a compound inequality.
- This means we need to figure out the possible values of the temperature ([tex]\(t\)[/tex]) that lie between the low and high temperatures.
4. Building the Compound Inequality:
- The temperature [tex]\(t\)[/tex] at any time during the day should be greater than or equal to the low temperature, which is [tex]\(82^{\circ} F\)[/tex].
- Similarly, [tex]\(t\)[/tex] should be less than or equal to the high temperature, [tex]\(101^{\circ} F\)[/tex].
5. Formulating the Inequality:
- Therefore, the compound inequality representing the temperature at any time during the day is:
[tex]\[
82 \leq t \leq 101
\][/tex]
6. Choosing the Correct Option:
- Look at the options provided:
- a [tex]\(82 \geq t \geq 101\)[/tex] (incorrect, as the inequality signs are reversed)
- b [tex]\(t < 101\)[/tex] (incomplete, as it doesn’t include the lower bound)
- c [tex]\(82 \leq t \leq 101\)[/tex] (correct, matches our inequality)
- d [tex]\(81 < t < 101\)[/tex] (incorrect, as it doesn't include the low temperature and excludes the high temperature)
From this reasoning, option c [tex]\(82 \leq t \leq 101\)[/tex] is the correct answer. This option accurately describes the range of temperatures throughout the day.
1. Understanding the Context:
- The question is about the temperature range in Glendale for a particular day.
- We are given a low temperature and a high temperature for the day.
2. Identifying the Details:
- The low temperature for the day is [tex]\(82^{\circ} F\)[/tex].
- The high temperature for the day is [tex]\(101^{\circ} F\)[/tex].
3. Finding the Range for the Temperature:
- We need to express the range of temperatures that occurred during the day using a compound inequality.
- This means we need to figure out the possible values of the temperature ([tex]\(t\)[/tex]) that lie between the low and high temperatures.
4. Building the Compound Inequality:
- The temperature [tex]\(t\)[/tex] at any time during the day should be greater than or equal to the low temperature, which is [tex]\(82^{\circ} F\)[/tex].
- Similarly, [tex]\(t\)[/tex] should be less than or equal to the high temperature, [tex]\(101^{\circ} F\)[/tex].
5. Formulating the Inequality:
- Therefore, the compound inequality representing the temperature at any time during the day is:
[tex]\[
82 \leq t \leq 101
\][/tex]
6. Choosing the Correct Option:
- Look at the options provided:
- a [tex]\(82 \geq t \geq 101\)[/tex] (incorrect, as the inequality signs are reversed)
- b [tex]\(t < 101\)[/tex] (incomplete, as it doesn’t include the lower bound)
- c [tex]\(82 \leq t \leq 101\)[/tex] (correct, matches our inequality)
- d [tex]\(81 < t < 101\)[/tex] (incorrect, as it doesn't include the low temperature and excludes the high temperature)
From this reasoning, option c [tex]\(82 \leq t \leq 101\)[/tex] is the correct answer. This option accurately describes the range of temperatures throughout the day.
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