ady.com'studenvaschiosrd/home Lpe-RWots for kive Gmail 96-3tnc) 2 Rapt Thentivezahnsin Meec mpkithcoamy Men- Trvekhacto Frients Acoand Fite Practice: Analyze Two Varlable Relationships - Quik - Level 7 Reocty A company uses a medum-size box to ship difierent equipmemh. The toble shows the weid of the equipment and the total weight of the packige. Which statement is true? To find any value of \( p \), subtract 3 from the corresponding value of 20 . If the weight of the equipment is 15 oz , then the totol weight of the packoge is 30 oz . The equation \( p=3 z \) models the relotionship. If the weight of the equipment is 20 oz , then the totol weight of the package is 23 oz .

It looks like you're working with a problem that involves analyzing the relationship between the weight of equipment and the total weight of the package. Let's break down the information and evaluate each statement to determine which one is true. ### Understanding the Problem - **Given:** A table shows the weight of the equipment (**\( z \)**) and the total weight of the package (**\( p \)**). - **Objective:** Identify the true statement about the relationship between \( z \) and \( p \). ### Evaluating the Statements 1. **"To find any value of \( p \), subtract 3 from the corresponding value of 20."** - **Interpretation:** This statement is unclear due to potential typos. It might be trying to say \( p = z - 3 \), but even then, it's ambiguous. - **Verdict:** **Unclear/Incorrect** 2. **"If the weight of the equipment is 15 oz, then the total weight of the package is 30 oz."** - **Interpretation:** Suggests a linear relationship where \( p = 2z \). - **Verification:** If \( z = 15 \), then \( p = 2 \times 15 = 30 \) oz. - **Verdict:** **Potentially True** 3. **"The equation \( p = 3z \) models the relationship."** - **Interpretation:** Implies \( p \) is three times \( z \). - **Verification:** If \( z = 15 \), then \( p = 3 \times 15 = 45 \) oz, which contradicts statement 2. - **Verdict:** **False** 4. **"If the weight of the equipment is 20 oz, then the total weight of the package is 23 oz."** - **Interpretation:** Suggests a relationship like \( p = z + 3 \). - **Verification:** If \( z = 20 \), then \( p = 20 + 3 = 23 \) oz. - **Verdict:** **Potentially True** ### Determining the Correct Relationship Given the two potentially true statements: - **Statement 2:** \( p = 2z \) (consistent when \( z = 15 \)) - **Statement 4:** \( p = z + 3 \) (consistent when \( z = 20 \)) These suggest different linear relationships. To find a single equation that fits both points: 1. **Using Point 1:** \( (15, 30) \) 2. **Using Point 2:** \( (20, 23) \) We can calculate the slope (\( m \)): \[ m = \frac{23 - 30}{20 - 15} = \frac{-7}{5} = -1.4 \] Now, using the point-slope form: \[ p = -1.4z + b \] Using \( z = 15 \) and \( p = 30 \): \[ 30 = -1.4(15) + b \\ 30 = -21 + b \\ b = 51 \] So, the equation modeling the relationship is: \[ p = -1.4z + 51 \] ### Conclusion **None of the provided statements perfectly describe the relationship based on the calculated equation.** However, among the options given, the statement that **"If the weight of the equipment is 15 oz, then the total weight of the package is 30 oz."** aligns partially with the derived relationship and is the most accurate based on the information available. **True Statement:** - **"If the weight of the equipment is 15 oz, then the total weight of the package is 30 oz."**