Question

Fill in the missing parts of the table:

x - # of days 0 a. 7 b.
y - # of texts c. 75 d. 300

Answer 1

To fill in the missing parts of the table, let's denote the values clearly:

| x - # of days | 0 | a. 7 | b. |
|---------------|---|------|------|
| y - # of texts | c. | 75 | d. 300 |

From the information provided:

1. **For y at x = a (7 days)**, we know it’s 75 texts, so we can fill in that value.
2. **For y at x = b**, we know it’s 300 texts.

Now, to find the values of c and the correspondence of x for a and b, we need to set a basis for filling the table.

Assuming a linear relationship between the number of days and the number of texts, we can solve for the missing values.

1. **When x = 0 (c)**, let's assume there are no texts sent on day 0, which gives us:
- c = 0.

2. **Now for b**, the relationship can be derived based on the information we have:
- Over a span of 7 days, there are 75 texts sent.
- To find the average number of texts per day over these 7 days:
\[
\text{Average texts per day} = \frac{75}{7} \approx 10.71 \text{ texts/day}
\]

3. **Assuming we keep increasing linearly to 300 texts for another period (which we can denote as change in days from 7 to b)**, we could find this equation by creating a proportionate measure.

So let’s assume that from day 7 to day b, where b values we can hypothesize as 30 days total (an example) to reach 300:
- From 75 texts at 7 days, to reach 300, the additional texts would be:
\[
300 - 75 = 225 \text{ texts}
\]

- The days between x = 7 and x = 30 (additional 23 days):
\[
\text{Average for 23 days} = \frac{225}{23} \approx 9.78 \text{ texts/day}
\]

To summarize, in full the filled table is:

| x - # of days | 0 | 7 | 30 |
|---------------|---|----|----|
| y - # of texts| 0 | 75 | 300 |

So filling in the table including placeholders would look like:

- a = 7
- b = 30
- c = 0
- d = 300

Thus completing the information necessary. If specific values for a and b are available or differ, let us know for adjusted calculations!