406 daxon Math \( 0 / 5 \) (9n) mixed up. Then one tile is selected. \begin{tabular}{l|l|l|l|l|l|l|} \hline\( A \) & \( C \) & \( A \) & \( S \) & \( L \) & \( B \) & \( E \) \\ \hline \end{tabular} (a) What is the probability that the letter selected is \( A \) A (b) What is the probability that the letter selected a vowel? (c) What is the probability that the letter selected compor before \( G \) in the alphabet? 28. Each angle of quadrilateral \( A B C D \) (00, 73) is a right angle. If \( A B \) is 10 cm and \( B C \) is 5 cm , what is the area of the quadrilateral? 29. Which of these terms does not apply to quadrilatern (4) \( A B C D \) in problem 28 ? A. rectangle B. parallelogram C. rhombus 30. Write \( 25,000,000 \) in expanded notation using powers of 10,

Let's break down the problem step by step. ### Part 1: Probability Questions We have the letters arranged in the following way: \[ \begin{tabular}{l|l|l|l|l|l|l|} \hline A & C & A & S & L & B & E \\ \hline \end{tabular} \] #### (a) What is the probability that the letter selected is \( A \)? **Step 1:** Count the total number of letters. There are 7 letters in total: \( A, C, A, S, L, B, E \). **Step 2:** Count the number of times \( A \) appears. The letter \( A \) appears 2 times. **Step 3:** Calculate the probability. The probability \( P(A) \) is given by the formula: \[ P(A) = \frac{\text{Number of A's}}{\text{Total number of letters}} = \frac{2}{7} \] #### (b) What is the probability that the letter selected is a vowel? **Step 1:** Identify the vowels in the set. The vowels present are \( A \) and \( E \). **Step 2:** Count the number of vowels. The letter \( A \) appears 2 times and \( E \) appears 1 time, giving us a total of 3 vowels. **Step 3:** Calculate the probability. The probability \( P(\text{vowel}) \) is given by: \[ P(\text{vowel}) = \frac{\text{Number of vowels}}{\text{Total number of letters}} = \frac{3}{7} \] #### (c) What is the probability that the letter selected comes before \( G \) in the alphabet? **Step 1:** Identify the letters that come before \( G \). The letters in the set are \( A, C, A, S, L, B, E \). The letters that come before \( G \) are \( A, C, B, E \). **Step 2:** Count the number of letters that come before \( G \). The letters \( A \) (2 times), \( C \) (1 time), \( B \) (1 time), and \( E \) (1 time) give us a total of 5 letters. **Step 3:** Calculate the probability. The probability \( P(\text{before G}) \) is given by: \[ P(\text{before G}) = \frac{\text{Number of letters before G}}{\text{Total number of letters}} = \frac{5}{7} \] ### Part 2: Quadrilateral Area Given that each angle of quadrilateral \( ABCD \) is a right angle, and the lengths of \( AB \) and \( BC \) are 10 cm and 5 cm respectively, we can determine the area. **Step 1:** Identify the shape. Since all angles are right angles, \( ABCD \) is a rectangle. **Step 2:** Calculate the area. The area \( A \) of a rectangle is given by: \[ A = \text{length} \times \text{width} = AB \times BC = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2 \] ### Part 3: Identify the term that does not apply to quadrilateral \( ABCD \) The options are: - A. rectangle - B. parallelogram - C. rhombus Since \( ABCD \) is a rectangle, it is not a rhombus unless all sides are equal, which they are not (10 cm and 5 cm). Therefore, the term that does not apply is: **Answer:** C. rhombus ### Part 4: Write \( 25,000,000 \) in expanded notation using powers of 10 **Step 1:** Break down the number. \[ 25,000,000 = 2.5 \times 10^7 \] **Step 2:** Write in expanded notation. The expanded notation is: \[ 2 \times 10^7 + 5 \times 10^6 \] ### Summary of Answers 1. \( P(A) = \frac{2}{7} \) 2. \( P(\text{vowel}) = \frac{3}{7} \) 3. \( P(\text{before G}) = \frac{5}{7} \) 4. Area of quadrilateral \( ABCD = 50 \, \text{cm}^2 \) 5. The term that does not apply is C. rhombus. 6. Expanded notation of \( 25,000,000 = 2 \times 10^7 + 5 \times 10^6 \)