Form a matrix of four by four to represent the information from four grade nine streams' mathematics contest results.

Here are the solutions to the problems: *27. During a mathematics contest the following results were realised from four grade nine streams: Stream | North | South | East | West ---|---|---|---|--- Exceeding Expectations | 9 | 10 | 8 | 6 Meeting Expectations | 4 | 2 | 9 | 14 Approaching Expectations | 11 | 12 | 8 | 2 Below Expectations | 2 | 3 | 1 | 4 Form a matrix of four by four to represent the information.* Step 1: Identify the rows and columns from the table. Rows correspond to the expectation categories: Exceeding, Meeting, Approaching, Below. Columns correspond to the streams: North, South, East, West. Step 2: Arrange the data into a 4 × 4 matrix. 9 & 10 & 8 & 6 \\ 4 & 2 & 9 & 14 \\ 11 & 12 & 8 & 2 \\ 2 & 3 & 1 & 4 The matrix representing the information is 9 & 10 & 8 & 6 \\ 4 & 2 & 9 & 14 \\ 11 & 12 & 8 & 2 \\ 2 & 3 & 1 & 4 . 28. Prepare a matrix of your choice of integers between -2 and 6 of order two by two. Step 1: Understand the requirements. The matrix must be of order 2 × 2, meaning it has 2 rows and 2 columns. The elements must be integers between -2 and 6 (inclusive). This means the integers can be -2, -1, 0, 1, 2, 3, 4, 5, 6. Step 2: Choose four integers from the allowed range and arrange them into a 2 × 2 matrix. For example, we can choose 1, 0, 5, and -1. A possible matrix is 1 & 0 \\ 5 & -1 . (Other valid answers are possible, as the choice is arbitrary within the given constraints.) 29. Evaluate: 3 & 4 \\ 9 & 4 \\ 6 & 0 - -2 & 9 \\ -3 & -4 \\ -6 & 6 Step 1: Perform matrix subtraction by subtracting corresponding elements. 3 - (-2) & 4 - 9 \\ 9 - (-3) & 4 - (-4) \\ 6 - (-6) & 0 - 6 Step 2: Simplify each element. 3 + 2 & 4 - 9 \\ 9 + 3 & 4 + 4 \\ 6 + 6 & 0 - 6 5 & -5 \\ 12 & 8 \\ 12 & -6 The evaluated matrix is 5 & -5 \\ 12 & 8 \\ 12 & -6 . 30. What is the order of 6 & 3 & 9 \\ 3 & 4 & 0 Step 1: Count the number of rows. There are 2 rows in the matrix. Step 2: Count the number of columns. There are 3 columns in the matrix. Step 3: State the order as (number of rows) × (number of columns). The order of the matrix is 2 × 3. 31. A girl is twice as old as a boy who is x years old now. Their father is 25 years older than the girl. If the sum of their ages is 75, how old is the girl now? Step 1: Define the ages of the boy, girl, and father in terms of x. Boy's age = x years Girl's age = 2 × x = 2x years Father's age = Girl's age + 25 = 2x + 25 years Step 2: Set up an equation for the sum of their ages. Sum of ages = Boy's age + Girl's age + Father's age 75 = x + 2x + (2x + 25) Step 3: Solve the equation for x. 75 = x + 2x + 2x + 25 75 = 5x + 25 Subtract 25 from both sides: 75 - 25 = 5x 50 = 5x Divide by 5: x = (50)/(5) x = 10 Step 4: Calculate the girl's age using the value of x. Girl's age = 2x = 2 × 10 = 20 years The girl is 20 years old. Last free one today — make it count tomorrow, or type /upgrade for unlimited.