1. **Problem:** Diego measured diameters and circumferences of circular objects. One measurement is inaccurate. Identify which and explain. 2. **Formula:** Circumference $C = \pi d$, where $d$ is diameter. 3. **Step 1:** Calculate expected circumference for each object using $\pi \approx 3.14$. - Half dollar coin: $C = 3.14 \times 3 = 9.42$ cm (measured 10 cm) - Flying disc: $C = 3.14 \times 23 = 72.22$ cm (measured 28 cm) - Jar lid: $C = 3.14 \times 8 = 25.12$ cm (measured 25 cm) - Flower pot: $C = 3.14 \times 15 = 47.1$ cm (measured 48 cm) 4. **Step 2:** Compare measured vs expected. - Flying disc's circumference 28 cm is far less than expected 72.22 cm, so this measurement is inaccurate. --- 5. **Problem:** Complete the table using $\pi \approx 3.14$. 6. **Step 1:** Use $C = \pi d$ or $d = \frac{C}{\pi}$. - Hula hoop: $d=35$ in, so $C = 3.14 \times 35 = 109.9$ in - Circular pond: $C=556$ ft, so $d = \frac{556}{3.14} \approx 177.07$ ft - Magnifying glass: $d=5.2$ cm, so $C = 3.14 \times 5.2 = 16.33$ cm - Car tire: $C=71.6$ in, so $d = \frac{71.6}{3.14} \approx 22.83$ in --- 7. **Problem:** Circle with center A, segment CD length 15 cm. 8. **Step 1:** Radius is segment from center to circumference. - Given $AB$ is radius, length $15$ cm. 9. **Step 2:** Diameter is twice radius. - Given $CB$ is diameter, length $2 \times 15 = 30$ cm. --- 10. **Problem:** Equation $y = 1.5x + 2$. Find four $(x,y)$ pairs. 11. **Step 1:** Choose $x=0,1,2,3$. - $x=0$: $y=1.5(0)+2=2$ - $x=1$: $y=1.5(1)+2=3.5$ - $x=2$: $y=1.5(2)+2=5$ - $x=3$: $y=1.5(3)+2=6.5$ 12. **Step 2:** Points: $(0,2), (1,3.5), (2,5), (3,6.5)$. 13. **Step 3:** Is this proportional? No, because proportional relationships have $y=mx$ with zero intercept. Here intercept is 2. **Final answers:** - Inaccurate measurement: Flying disc circumference (28 cm). - Completed table: - Hula hoop circumference: 109.9 in - Circular pond diameter: 177.07 ft - Magnifying glass circumference: 16.33 cm - Car tire diameter: 22.83 in - Radius $AB = 15$ cm - Diameter $CB = 30$ cm - Four points: $(0,2), (1,3.5), (2,5), (3,6.5)$ - Not proportional because of nonzero intercept.