Question

Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 111, Hannah closes her eyes while Arianna gently touches 222 paperclip points 333 millimeters (\text{mm})(mm)left parenthesis, start text, m, m, end text, right parenthesis apart on Hannah’s forehead. Then Hannah reports whether she could feel 111 or 222 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 222 more \text{mm}mmstart text, m, m, end text apart. Hannah reports feeling 111 point until the points are 15\,\text{mm}15mm15, start text, m, m, end text apart, when she begins reporting that she feels 222 points. Which inequality best represents the trial numbers in which Hannah feels 222 points

1. The inequality best representing the trial numbers in which Hannah feels 2 points is t > 7.
In the question, we are given that Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 1, Hannah closes her eyes while Arianna gently touches 2 paperclip points 3 millimeters (mm) apart on Hannah’s forehead. Then Hannah reports whether she could feel 1 or 2 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 2 more mm apart. Hannah reports feeling 1 point until the points are 15mm apart, when she begins reporting that she feels 2 points.
We are asked for the inequality that best represents the trial numbers in which Hannah feels 2 points.
We know that for trial 1, the paperclip points are 3 mm away.
After that the gap between the paperclips are exceeded by 2 mm.
Thus, for trials:
2 we have paperclips at 5 mm gap.
3 we have paperclips at 7 mm gap.
4 we have paperclips at 9 mm gap.
5 we have paperclips at 11 mm gap.
6 we have paperclips at 13 mm gap.
7 we have paperclips at 15 mm gap.
8 we have paperclips at 17 mm gap.
9 we have paperclips at 19 mm gap.
and so on.
We are informed that until the gap is 15 mm, she reports 1 points and after that she reports 2 points.
15 mm is for trial 7.
Thus, after 7th trial, she reports 2 points.
Thus, the inequality best representing the trial numbers in which Hannah feels 2 points is t > 7.
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The provided question is incomplete. The complete question is:
“Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 1, Hannah closes her eyes while Arianna gently touches 2 paperclip points 3 millimeters (mm) apart on Hannah’s forehead. Then Hannah reports whether she could feel 1 or 2 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 2 more mm apart. Hannah reports feeling 1 point until the points are 15mm apart, when she begins reporting that she feels 2 points. Which inequality best represents the trial numbers in which Hannah feels 2 points?
a. t > 6
b. t < 6
c. t < 7
d. t > 7″

2. ngockhue
Answer: The inequality best represents the trial numbers in which Hannah feels 2 points is t>7
Step-by-step explanation:
Given: Ariana and Hannah are conducting an experiment to test the difference threshold for sense of touch on forehead.
Initially, the 2 paperclips are 3 mm apart on Hannah’s forehead.
To be more clear about the two points where the paperclips are touched on Hannah’s forehead, let us assume circle C to be Hannah’s forehead and A and B are the two points (as shown in the image).
Hannah feels only 1 point
For trail 1, the paperclips are 3mm apart.
Given, for each next trail, the gap is increased by 2mm.
So, for trail 2, the gap (Distance between 2 points A and B) is 3mm + 2mm = 5mm.
For trail 3, gap is 5mm + 2mm = 7mm
For trail 4, gap is 7mm + 2mm = 9mm
For trail 5, gap is 9mm + 2mm = 11mm
For trail 6, gap is 11mm + 2mm = 13mm
For trail 7, gap is 13mm + 2mm = 15mm
And so on.
According to the question, for a distance greater than 15mm, Hannah starts reporting that she is feeling two points.
Thus, till the 7th trail, Hannah reports 1 point on her forehead and after it she reports 2 points.
Hence,
The inequality best represents the trial numbers in which Hannah feels 2 points is t>7 (where t is the trial number).