Fill in the missing parts of the table:

Question

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


a. Response area

b. Response area

c. Response area

d. Response area



Skip to navigation

Answer 1

To fill in the missing parts of the table, we need more context or a rule/law governing the relationship between the number of days (x) and the number of texts (y). However, since we don't have that information, we can make some educated guesses based on common scenarios such as linear relationships.

Here’s how we can approach it with the given data points:

1. Continuity: Assuming there's a linear relationship, you could first determine a common pattern by finding the change in texts as days increase.

Let's analyze the known values to notice any pattern:

1. When \( x = 0 \), \( y = c \) (unknown).
2. When \( x = 7 \), \( y = d = 300 \) (known).
3. The missing \( a \) (the number of days for \( y = 75 \)).
4. The missing \( b \) (the number of days for \( y = 300 \), known as when days are 7).

Computation:

Assuming that:

• The change from \( y = c \) to \( y = 75 \) could be calculated if we know the value of \( c \).
• The change from \( y = 75 \) to \( y = 300 \) could then help us estimate \( a \) and \( b \).

Example Calculation Based on Hypothesis

Let's hypothesize a linear change. From \( y = 75 \) to \( y = 300 \) as you increase days from \( a \) to \( 7 \):

1. If we take a rough guess:
   • If \( c \) is 0 (no texts at day 0), it flows.
   • If the number of texts increases uniformly, we can create a ratio. For example, if there are 75 texts at \( x = a \), we can find a.

Let’s say we find a slope (m):

From \( 0 \rightarrow 300 \) texts between \( 0 \rightarrow 7 \) days gives:

\[ m = \frac{300 - 0}{7 - 0} = \frac{300}{7} \approx 42.857 \text{(average texts per day)} \]

Substitute Known values:

If we take \( c = 0 \):

1. At \( x = 0 \), \( y = 0 \).
2. At \( x = 1 \): \( y \approx 42.857 \).
3. At \( x = 2 \): \( y \approx 85.714\) (closer to 75).
4. At \( x = 3 \): \( y \approx 128.571\).
5. At \( x = 4 \): \( y \approx 171.429\).
6. At \( x = 5 \): \( y \approx 214.286\).
7. At \( x = 6 \): \( y \approx 257.143\).
8. At \( x = 7 \): \( y = 300\).

Now let’s estimate the values:

• For \( y = 75 \approx x \text{ at } a \approx 2 \) days,
• For \( y = 300 \text{ at} x : 7 \).

Missing values:

• a = 2
• b = Keep \( b \) as 7 to \( 300 \) same as \( d \).
• c = 0
• d = 300

The completed table would be:

| x (days) | 0 | 2 | 7 | |----------|---|---|---| | y (texts)| 0 | 75 | 300 |

If you have more specific information or the nature of the texts per day increases, please provide it, and we can refine the results.