• you want to see if a new pair of shoes makes you faster or not.
• you wonder what kind of tomato grows best in your yard.
• a friend asks if you are more accurate shooting with an indoor or outdoor basketball.
• the chicago bears are the best football team
• for the problem you chose, what would be the independent variable?
• how would you measure your dependent variable?
• what would you keep constant?
• which of the four options above doesnt fit? why?
• draw (or attach a drawing) of a possible data table for your experiment.

Question

Accepted Answer

Let's choose the problem "You want to see if a new pair of shoes makes you faster or not" to answer the sub - questions:

### 1. Independent Variable
# Brief Explanations:
The independent variable is the factor that we manipulate in an experiment. In this case, we want to see the effect of the new pair of shoes on speed. So we manipulate whether we are wearing the new shoes or not.
# Answer:
The independent variable is the type of shoes (new shoes vs. old shoes).

### 2. Measuring the Dependent Variable
# Brief Explanations:
The dependent variable is speed, which depends on the type of shoes. To measure speed, we can use the formula $v=\frac{d}{t}$, where $v$ is speed, $d$ is distance, and $t$ is time. We can set a fixed distance (for example, 100 meters) and measure the time it takes to run that distance with the new shoes and with the old shoes.
# Answer:
We can measure the dependent variable (speed) by timing how long it takes to run a fixed distance (e.g., 100 meters) while wearing the new shoes and while wearing the old shoes. Then, use the formula $v = \frac{d}{t}$ (where $d$ is the fixed distance and $t$ is the measured time) to calculate the speed.

### 3. What to Keep Constant
# Brief Explanations:
To ensure a fair test, we need to keep other factors that can affect speed constant. The distance of the run should be the same so that we are comparing speed over the same length. The running surface (e.g., same track or road) should be the same as different surfaces have different levels of friction which can affect speed. Also, the runner (same person) should be used as different people have different running abilities.
# Answer:
We should keep the distance of the run constant, the running surface constant, and the runner constant (i.e., the same person runs in both cases).

### 4. Which Option Doesn't Fit and Why
# Brief Explanations:
The first three options ("You want to see if a new pair of shoes makes you faster or not", "You wonder what kind of tomato grows best in your yard", "A friend asks if you are more accurate shooting with an indoor or outdoor basketball") are testable questions that can be investigated through experiments. The statement "The Chicago Bears are the best football team" is a matter of opinion. There is no objective way to measure "best" in a way that can be tested scientifically (different people have different criteria for what makes a team "best", such as win - loss record, style of play, etc., and it is not a question that can be answered through a controlled experiment like the others).
# Answer:
The option "The Chicago Bears are the best football team" doesn't fit. The other three are testable experimental questions, but this is a subjective opinion with no objective, testable method (unlike the others which can be investigated via experiments with measurable variables).

### 5. Data Table for the Experiment
| Trial | Type of Shoes | Distance (m) | Time (s) | Speed (m/s) |
|-------|---------------|--------------|----------|-------------|
| 1     | Old Shoes     | 100          |          |             |
| 2     | Old Shoes     | 100          |          |             |
| 3     | Old Shoes     | 100          |          |             |
| 4     | New Shoes     | 100          |          |             |
| 5     | New Shoes     | 100          |          |             |
| 6     | New Shoes     | 100          |          |             |

In this table, we have multiple trials for each type of shoes to get a more accurate measure of speed. We record the time taken to run 100 meters for each trial and then calculate the speed using $v=\frac{100}{t}$ (since $d = 100$ meters).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1. Independent Variable

Answer:

2. Measuring the Dependent Variable