A pencil and 6 erasers cost Gh¢15.00. The pencil cost Gh¢6.00. What is the cost of one eraser? 2. Solve the equation 10^x = 0.000001.

Here are the solutions to the problems: 1. A pencil and 6 erasers cost Gh¢15.00. The pencil cost Gh¢6.00. What is the cost of one eraser? Step 1: Let P be the cost of a pencil and E be the cost of an eraser. We are given the equations: P + 6E = 15.00 P = 6.00 Step 2: Substitute the cost of the pencil into the first equation. 6.00 + 6E = 15.00 Step 3: Subtract Gh¢6.00 from both sides to find the cost of 6 erasers. 6E = 15.00 - 6.00 6E = 9.00 Step 4: Divide by 6 to find the cost of one eraser. E = (9.00)/(6) E = 1.50 The cost of one eraser is Gh¢1.50. The correct option is C. Gh¢1.50 2. Solve the equation 10^x = 0.000001. Step 1: Express 0.000001 as a power of 10. 0.000001 = (1)/(1,000,000) = (1)/(10^6) = 10^-6 Step 2: Set the powers equal. 10^x = 10^-6 x = -6 Assumption: The given options are A. -3, B. -2, C. 2, D. 3. Since -6 is not an option, it is highly probable that there is a typo in the question and 0.000001 was intended to be 0.001. If 10^x = 0.001, then 10^x = 10^-3, which means x = -3. We will proceed with this assumption to match an option. Step 1 (Revised with assumption): Assume the equation is 10^x = 0.001. Express 0.001 as a power of 10. 0.001 = (1)/(1000) = (1)/(10^3) = 10^-3 Step 2 (Revised): Set the powers equal. 10^x = 10^-3 x = -3 The correct option, based on the assumption of a typo, is A. -3 3. If p oranges are sold for q pesewas each, find the total selling price in cedis. Step 1: Calculate the total selling price in pesewas. Total selling price in pesewas = (number of oranges) × (price per orange in pesewas) = p × q = pq pesewas Step 2: Convert the total selling price from pesewas to cedis. Since 1 Cedi = 100 pesewas, to convert pesewas to cedis, divide by 100. Total selling price in cedis = (pq)/(100) cedis. The correct option is A. (pq)/(100) 4. Which of the basic properties of rational numbers is used in the following operation? (27 × 24) + (23 × 24) = 50 × 24. The operation shown is: (27 × 24) + (23 × 24) = (27 + 23) × 24 = 50 × 24 This demonstrates the Distributive Property of multiplication over addition, which states that a × c + b × c = (a+b) × c. The correct option is C. Distributive 5. The set P = \prime factors of 24\ and the set Q = \prime factors of 35\. List the members of P Q. Step 1: Find the prime factors of 24. 24 = 2 × 12 = 2 × 2 × 6 = 2 × 2 × 2 × 3 = 2^3 × 3 So, the set of prime factors of 24 is P = \2, 3\. Step 2: Find the prime factors of 35. 35 = 5 × 7 So, the set of prime factors of 35 is Q = \5, 7\. Step 3: Find the union of sets P and Q, denoted as P Q. The union includes all unique elements from both sets. P Q = \2, 3\ \5, 7\ = \2, 3, 5, 7\ The correct option is C. \2, 3, 5, 7\ 6. Find the median of the numbers 25, 57, 17, 33, 73, 81, 42. Step 1: Arrange the numbers in ascending order. 17, 25, 33, 42, 57, 73, 81 Step 2: Count the number of values (n). There are 7 numbers, so n = 7. Step 3: Since n is an odd number, the median is the ((n+1)/(2))-th term. Median position = (7+1)/(2) = (8)/(2) = 4-th term. Step 4: Identify the 4th term in the ordered list. The 4th term is 42. The correct option is B. 42 7. Factorize x(x-2) - 3xy + 6y. Step 1: Expand the first term. x(x-2) - 3xy + 6y = x^2 - 2x - 3xy + 6y Step 2: Group terms with common factors. (x^2 - 2x) + (-3xy + 6y) Step 3: Factor out the common factor from each group. x(x - 2) - 3y(x - 2) Step 4: Factor out the common binomial factor (x-2). (x - 2)(x - 3y) The correct option is A. (x-2)(x-3y) 8. If 15 - px - x^2 = 0, find p, when x = 3. Step 1: Substitute x=3 into the given equation. 15 - p(3) - (3)^2 = 0 Step 2: Simplify the equation. 15 - 3p - 9 = 0 Step 3: Combine the constant terms. 6 - 3p = 0 Step 4: Solve for p. 6 = 3p p = (6)/(3) p = 2 The correct option is C. 2