I'll go through each question in the uploaded image and provide solutions.

Question 22

Transformation Type:
It appears that the triangle DEF has been moved from its original position to the "image" position. Based on the alignment, this is likely a reflection across a line.

Question 23

Accepted Mass Calculation:
The minimum accepted mass for the soccer ball would be $15 - 0.7 = 14.3$ oz.

Question 24

Perimeter of Regular Octagon:
For an octagon with each side measuring 17 mm, the perimeter $P$ is: $P = 8 \times 17 = 136 \, \text{mm}$

Question 25

Area of Scalene Triangle: The area $A$ of a triangle with base $b = 17$ inches and height $h = 7$ inches is given by: $A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 17 \times 7 = 59.5 \, \text{in}^2$

Question 26

Surface Area of the Podium: To find the surface area of the podium, we would add up the areas of each visible face. This is a composite shape with different rectangular faces.

1. Front and back faces (6 m x 0.5 m each): $2 \times (6 \times 0.5) = 6$ m²
2. Two side faces (3 m x 0.5 m each): $2 \times (3 \times 0.5) = 3$ m²
3. Top face (including steps): adding areas of individual rectangles on top

I'll provide a detailed calculation for this if needed.

Question 27

Volume of the Prism: The volume $V$ of a triangular prism with base area $A$ and height $h$ is: $A = \frac{1}{2} \times 10 \times 10 = 50 \, \text{ft}^2$ $V = A \times h = 50 \times 3 = 150 \, \text{ft}^3$

Question 28

Length of Side $a$ Using the Pythagorean Theorem: Given $b = 15$ and $c = 17$, where $c$ is the hypotenuse: $a^2 + b^2 = c^2$ $a^2 + 15^2 = 17^2$ $a^2 + 225 = 289$ $a^2 = 64$ $a = 8$

Question 29

Animal with 30 Teeth:
From the graph, the dog has a total of 30 teeth.

Question 30

Probability Problem (Draught Board):
The probability that a fly lands on a square containing a black draught:

• There are 16 black and 16 white squares.
• Probability $= \frac{\text{Number of black squares}}{\text{Total squares}} = \frac{16}{32} = \frac{1}{2}$.

Question 31

Problem Solving with Bags: Select Bag 1 because it is the only one with two green apples, allowing you to determine the labeling of the other bags.

Question 32

Palindrome Counting:
Palindromic numbers between 10 and 400 include two-digit and three-digit palindromes, such as 11, 22, ..., 99, 101, 111, ..., 393.

Would you like more detailed explanations for any of these answers or have specific questions? Here are related questions for further exploration:

1. What is the difference between reflection and translation in transformations?
2. How do we find the height of a triangle if it's not given?
3. What other shapes have formulas for perimeter similar to regular polygons?
4. What strategies are useful in probability problems involving uniform distributions?
5. Can we generalize the approach to finding palindromes in other number ranges?

Tip: For surface area problems, break down complex shapes into simpler ones and calculate each face individually for accuracy.