Let's go through the problems in the image one by one.

Problem 11:

The boiling point of water is 212°F. In degrees Celsius, how much will that 165°F water increase to boil?

To solve this, we use the formula: $C = \frac{5}{9} \times (F - 32)$ where $C$ is the temperature in Celsius and $F$ is the temperature in Fahrenheit.

1. Convert 212°F to Celsius: $C_{\text{boiling}} = \frac{5}{9} \times (212 - 32) = \frac{5}{9} \times 180 = 100°C$

2. Convert 165°F to Celsius: $C_{\text{initial}} = \frac{5}{9} \times (165 - 32) = \frac{5}{9} \times 133 \approx 73.89°C$

3. Find the difference: $\Delta C = 100°C - 73.89°C = 26.11°C$

The answer is approximately 26°C.

Problem 12:

A small theater sold 72 tickets for a play. The ratio of adult tickets to child tickets was 4:1.

• Part A: Draw a diagram and make a table to represent the types of tickets sold.

Let's assume $x$ is the number of child tickets. Since the ratio is 4:1, the number of adult tickets would be $4x$. The total number of tickets sold is: $x + 4x = 72 \quad \Rightarrow \quad 5x = 72 \quad \Rightarrow \quad x = \frac{72}{5} = 14.4$ However, since ticket numbers must be whole numbers, let's consider:

• Child tickets $= 14$
• Adult tickets $= 4 \times 14 = 56$

This calculation needs to be adjusted or clarified since fractional tickets aren't realistic. The correct integer distribution should be calculated with the correct ratio adjustments. I recommend rechecking this since the correct sum needs to match 72.

• Part B: The diagram should visually depict the tickets sold.

Problem 13:

Use the given set of coordinates to write the reflection across the y-axis of each point on the left.

For each point $(x, y)$, the reflection across the y-axis is $(-x, y)$.

• $(2, -3) \rightarrow (-2, -3)$
• $(-4, 8) \rightarrow (4, 8)$
• $(-2, 7) \rightarrow (2, 7)$

So, the reflected coordinates are $(-2, -3), (4, 8), (2, 7)$.

Problem 14:

The drama club spent $608 on food for a party. If there are 15 members and each paid an equal amount, how much did each member pay?

• Part A: Write an equation: $15x = 608$

• Part B: Solve the equation: $x = \frac{608}{15} \approx 40.53$

Each member paid approximately $40.53.

Problem 15:

Complete the Venn diagram to show the common factors of 63 and 45. Then circle the greatest common factor.

The factors are:

• 63: $1, 3, 7, 9, 21, 63$
• 45: $1, 3, 5, 9, 15, 45$

Common factors: $1, 3, 9$.

The greatest common factor is 9.

Would you like any more details or further explanation on any of these problems?

Here are some related questions you might want to consider:

1. What is the relationship between Fahrenheit and Celsius temperatures?
2. How do you find a common factor for two numbers?
3. How can ratios be used to determine quantities?
4. What is the significance of symmetry in coordinate geometry?
5. How can simple equations be used to solve real-world problems?

Tip: Always double-check calculations when they involve rounding or splitting a quantity into specific ratios to ensure accuracy!