Question

the table shows the relationship between the number of minutes that a hose has been on and the number of gallons of water that have been added to a plastic pool. which statement is true?
minutes hose on: 0, 5, 10, 15, 20
gallons of water in pool: 0, 40, 80, 120, 160
the relationship is multiplicative because the number of minutes can be found by multiplying the number of gallons by 8.
the relationship is multiplicative because the number of gallons can be found by multiplying the number of minutes by 8.
the relationship is additive because text cut off
the relationship is additive because text cut off

Explanation:

To determine the correct statement, we analyze the relationship between minutes and gallons:

Step 1: Check the pattern for gallons vs. minutes

For each minute value, calculate gallons:

• At \( 5 \) minutes: \( 5 \times 8 = 40 \) gallons.
• At \( 10 \) minutes: \( 10 \times 8 = 80 \) gallons.
• At \( 15 \) minutes: \( 15 \times 8 = 120 \) gallons.
• At \( 20 \) minutes: \( 20 \times 8 = 160 \) gallons.

Step 2: Evaluate the statements

• First statement: "Minutes = Gallons × 8" is false (e.g., \( 40 \times 8 = 320

eq 5 \)).

• Second statement: "Gallons = Minutes × 8" matches the pattern (e.g., \( 5 \times 8 = 40 \), \( 10 \times 8 = 80 \), etc.).

We analyze the relationship between minutes (hose on) and gallons (water in pool). By checking the pattern, we see that gallons = minutes × 8 (e.g., 5 minutes × 8 = 40 gallons, 10 minutes × 8 = 80 gallons, etc.). The first statement (minutes = gallons × 8) is false (e.g., 40 × 8 ≠ 5). Thus, the second statement is true.

Answer:

The relationship is multiplicative because the number of gallons can be found by multiplying the number of minutes by 8.