Question

Given x is time (in seconds) and y is heartbeats, what is the average number of beats per second?
3 beats per second
1 1/2 beats per second
2/3 beats per second
2 beats per second
coordinates are (4, 6) (6, 9) (10, 15) and (12, 18)

Answer 1

To find the average number of beats per second, we can calculate the total number of beats and divide it by the total time in seconds.

We will use the coordinates given:

1. (4, 6): 6 beats at 4 seconds
2. (6, 9): 9 beats at 6 seconds
3. (10, 15): 15 beats at 10 seconds
4. (12, 18): 18 beats at 12 seconds

Using the coordinates, we first calculate the total heartbeats:

- At 4 seconds: 6 beats
- At 6 seconds: 9 beats
- At 10 seconds: 15 beats
- At 12 seconds: 18 beats

Now, we find the total number of beats and the total time:

**Total beats:**
- 6 + 9 + 15 + 18 = 48 beats

**Total time:**
- The time represented by the last coordinate is 12 seconds.

Now, we can calculate the average number of beats per second:

\[
\text{Average beats per second} = \frac{\text{Total beats}}{\text{Total time}} = \frac{48 \text{ beats}}{12 \text{ seconds}} = 4 \text{ beats per second}
\]

Thus, the average number of beats per second is **4 beats per second**.

Since this is not one of the options you provided, there may be an error in the question or the way time and beats are interpreted. If you were looking for the average rate over intervals or as specific portions, please clarify, but based on the given data, the calculations yield 4 beats per second.

Answer 2

choose one

Answer 3

Based on the options provided, none directly match the calculated average of 4 beats per second. However, if I must choose one from the list, I will select:

**3 beats per second.**

This is the closest option to the calculated average.

Answer 4

Time walking (minutes) 20 30 40 60 80
Calories burned 100 150 200 300 400

The table shows a relationship between the amount of time spent walking and the number of calories burned. Determine if the relationship is proportional.
The relationship is proportional.
The relationship cannot be determined from the information provided.
The relationship is non-proportional; the graph would be an arc.
The relationship is non-proportional; the graph does not pass through the origin.

Answer 5

To determine if the relationship between time walking (in minutes) and calories burned is proportional, we need to check two main criteria:

1. **Constant Ratio:** For a proportional relationship, the ratio of calories burned to time should remain constant.

2. **Passes Through the Origin:** A proportional relationship should also pass through the origin (0,0). This means that if no time is spent walking, no calories should be burned.

Let's look at the data given:

| Time (minutes) | Calories burned |
|----------------|-----------------|
| 20 | 100 |
| 30 | 150 |
| 40 | 200 |
| 60 | 300 |
| 80 | 400 |

Now, let's calculate the ratio of calories burned to time for each pair:

1. For 20 minutes: \( \frac{100}{20} = 5 \)
2. For 30 minutes: \( \frac{150}{30} = 5 \)
3. For 40 minutes: \( \frac{200}{40} = 5 \)
4. For 60 minutes: \( \frac{300}{60} = 5 \)
5. For 80 minutes: \( \frac{400}{80} = 5 \)

Since the ratio is constant (5) for each time interval, this suggests that the relationship is proportional.

Next, considering if the relationship passes through the origin:
- If we assume the origin point (0,0) implies that if zero time is spent walking, no calories are burned, which is logically true in this context.

Based on this analysis, we can conclude:

**The relationship is proportional.**