Question
Electromagnets
Coils of wire Paper clips picked up
10 3
15 6
20 9
25 12
Ms. Owens' class is studying magnets. Ms. Owens showed her students how to make an electromagnet using a nail, a D-cell battery, and plastic coated wire. The students wrapped the wire around the nail and then attached the ends to the battery. When they were finished, they tested their magnets by trying to see how many paperclips their magnets could pick up. They also tested whether they could increase the strength of their electromagnets by using more coils of wire. They recorded the class average of their results in the data table seen here. Review the students' data. Predict how many paper clips the students would pick up if they used 50 coils of wire around bigger nails.
Responses
A 2525
B 5050
C 100100
D 250250
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Coils of wire Paper clips picked up
10 3
15 6
20 9
25 12
Ms. Owens' class is studying magnets. Ms. Owens showed her students how to make an electromagnet using a nail, a D-cell battery, and plastic coated wire. The students wrapped the wire around the nail and then attached the ends to the battery. When they were finished, they tested their magnets by trying to see how many paperclips their magnets could pick up. They also tested whether they could increase the strength of their electromagnets by using more coils of wire. They recorded the class average of their results in the data table seen here. Review the students' data. Predict how many paper clips the students would pick up if they used 50 coils of wire around bigger nails.
Responses
A 2525
B 5050
C 100100
D 250250
Skip to navigation
© Progress Learning 2025, All Rights Reserved.
Terms
|
Privacy
PHONE 1-877-377-9537
|
FAX 1-877-816-0808
Blog
Answers
GPT-4o mini
To predict how many paper clips the students could pick up with 50 coils of wire, we can first look at the existing data to identify the relationship between the number of coils and the number of paper clips picked up.
From the provided data:
- 10 coils -> 3 paper clips
- 15 coils -> 6 paper clips
- 20 coils -> 9 paper clips
- 25 coils -> 12 paper clips
We can see that the number of paper clips picked up increases as we increase the number of coils. We can calculate the rate of increase:
- From 10 to 15 coils (5 additional coils): 6 - 3 = 3 (rate of 0.6 paper clips per coil)
- From 15 to 20 coils (5 additional coils): 9 - 6 = 3 (rate of 0.6 paper clips per coil)
- From 20 to 25 coils (5 additional coils): 12 - 9 = 3 (rate of 0.6 paper clips per coil)
It appears that for every 5 additional coils, the number of paper clips picked up increases by 3. We can express this relationship with the formula:
- \( P = \frac{3}{5}C + b \)
Using the data point at 10 coils (where \( C = 10 \)), we solve for \( b \):
3 = \( \frac{3}{5} \times 10 + b \)
3 = 6 + b
b = 3 - 6
b = -3
Now, the equation becomes:
- \( P = \frac{3}{5}C - 3 \)
If we want to find out for 50 coils:
P = \( \frac{3}{5} \times 50 - 3 \)
P = 30 - 3
P = 27 paper clips
Since none of the answer options directly match this prediction and appear to be exaggerated, it’s likely they are based on a misunderstanding of the scaling of the results derived. Therefore, the conclusion is that none of the options are correct. However, predicting based on linear extrapolation indicates about **27 paper clips** would be the expected outcome with 50 coils around bigger nails; thus if I had to choose from the options presented without analytical justification, the answer would logically lean on correcting towards 27.
Nonetheless, specifically regarding the problem at hand and prediction with relation on consistent patterns, the figures indicated in the provided choices allow for no direct correlation towards the calculated extrapolated value. Please ensure to explore further for dependencies or configurations that could affect magnitude outputs.
From the provided data:
- 10 coils -> 3 paper clips
- 15 coils -> 6 paper clips
- 20 coils -> 9 paper clips
- 25 coils -> 12 paper clips
We can see that the number of paper clips picked up increases as we increase the number of coils. We can calculate the rate of increase:
- From 10 to 15 coils (5 additional coils): 6 - 3 = 3 (rate of 0.6 paper clips per coil)
- From 15 to 20 coils (5 additional coils): 9 - 6 = 3 (rate of 0.6 paper clips per coil)
- From 20 to 25 coils (5 additional coils): 12 - 9 = 3 (rate of 0.6 paper clips per coil)
It appears that for every 5 additional coils, the number of paper clips picked up increases by 3. We can express this relationship with the formula:
- \( P = \frac{3}{5}C + b \)
Using the data point at 10 coils (where \( C = 10 \)), we solve for \( b \):
3 = \( \frac{3}{5} \times 10 + b \)
3 = 6 + b
b = 3 - 6
b = -3
Now, the equation becomes:
- \( P = \frac{3}{5}C - 3 \)
If we want to find out for 50 coils:
P = \( \frac{3}{5} \times 50 - 3 \)
P = 30 - 3
P = 27 paper clips
Since none of the answer options directly match this prediction and appear to be exaggerated, it’s likely they are based on a misunderstanding of the scaling of the results derived. Therefore, the conclusion is that none of the options are correct. However, predicting based on linear extrapolation indicates about **27 paper clips** would be the expected outcome with 50 coils around bigger nails; thus if I had to choose from the options presented without analytical justification, the answer would logically lean on correcting towards 27.
Nonetheless, specifically regarding the problem at hand and prediction with relation on consistent patterns, the figures indicated in the provided choices allow for no direct correlation towards the calculated extrapolated value. Please ensure to explore further for dependencies or configurations that could affect magnitude outputs.