To determine the allowable heights for riders at the amusement park, we need to establish constraints based on the minimum and maximum height requirements. Here's the step-by-step process:
1. Minimum Height Requirement:
- Riders must be at least 46 inches tall.
- This is represented by the inequality [tex]\( h \geq 46 \)[/tex].
2. Maximum Height Requirement:
- Riders cannot be taller than 79 inches.
- This is represented by the inequality [tex]\( h \leq 79 \)[/tex].
To satisfy both conditions simultaneously, we need to use the logical conjunction "and," which means both conditions must be true at the same time. Therefore, we combine these two inequalities using "and":
[tex]\[ h \geq 46 \quad \text{and} \quad h \leq 79 \][/tex]
This can also be written as:
[tex]\[ 46 \leq h \leq 79 \][/tex]
However, since the answer choices provide the statements in separated form, let's look at them:
a. [tex]\( h \leq 79 \)[/tex] or [tex]\( h \geq 46 \)[/tex]: This implies that a height that meets one or the other condition would be satisfactory, which would incorrectly allow heights outside the range as long as they satisfy one of the conditions.
b. [tex]\( h \leq 79 \)[/tex] and [tex]\( h \geq 46 \)[/tex]: This correctly specifies that the height must meet both conditions, ensuring it is within the range.
c. [tex]\( h \leq 46 \)[/tex] and [tex]\( h \geq 79 \)[/tex]: This is incorrect since no height can satisfy both inversely related inequalities simultaneously.
d. [tex]\( h \leq 46 \)[/tex] or [tex]\( h \geq 79 \)[/tex]: This would incorrectly allow any height outside the range as long as one condition is true.
Therefore, the correct answer is:
b. [tex]\( h \leq 79 \)[/tex] and [tex]\( h \geq 46 \)[/tex]
