This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hey rose, good to see you again. Here are the solutions to the questions: Question 9: Which of the following numbers is not a probability? A probability value must be between 0 and 1, inclusive (0 P 1). a) 0.1 is a valid probability. b) -1 is not a valid probability because it is less than 0. c) (1)/(4) = 0.25 is a valid probability. d) 120\% = 1.2 is not a valid probability because it is greater than 1. Both (b) and (d) are not valid probabilities. However, in multiple-choice questions of this nature, a negative value is often highlighted as a fundamental impossibility for probability. The correct option is b). Explanation: A probability cannot be a negative number. Question 10: If a card is drawn at random from a deck of cards (52 cards), the probability of getting a king equals to: Step 1: Identify the total number of possible outcomes. There are 52 cards in a standard deck. So, the total number of outcomes is 52. Step 2: Identify the number of favorable outcomes. There are 4 kings in a standard deck (King of Spades, King of Hearts, King of Diamonds, King of Clubs). So, the number of favorable outcomes is 4. Step 3: Calculate the probability. The probability of an event is given by the formula: P(event) = Number of favorable outcomesTotal number of possible outcomes P(getting a king) = (4)/(52) Step 4: Simplify the fraction. (4)/(52) = (1)/(13) The correct option is c) (1)/(13). Question 11: A business woman requested for a loan of 4,000,000 FRW from a bank that requires her to pay 60,000 FRW as interest after 3 months. The interest rate is: Step 1: Identify the given values. Principal (P) = 4,000,000 FRW Interest (I) = 60,000 FRW Time (T) = 3 months Step 2: Convert the time to years. Since the interest rate is typically annual, convert 3 months to years: T = (3)/(12) years = (1)/(4) years Step 3: Use the simple interest formula to find the interest rate (R). The formula for simple interest is I = P · R · T. To find the rate (R), rearrange the formula: R = (I)/(P · T) Step 4: Substitute the values and calculate R. R = 60,000 FRW4,000,000 FRW · (1)/(4) years R = (60,000)/(1,000,000) R = 0.06 Step 5: Convert the decimal rate to a percentage. R = 0.06 × 100\% = 6\% The correct option is a) 6%. Send me the next one 📸