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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Question 5: Evaluate the following a) Step 1: Evaluate the expression inside the square brackets. 5 × 3 × 7 = 15 × 7 = 105 Step 2: Substitute the value back into the original expression. (-11) - 105 - 9 Step 3: Perform the subtractions from left to right. -11 - 105 = -116 -116 - 9 = -125 The value is -125. b) Step 1: Evaluate the multiplication in the numerator. 15 × 3 = 45 Step 2: Evaluate the expression inside the inner brackets in the numerator. (-12) × 3 = -36 Step 3: Evaluate the expression inside the square brackets in the numerator. -36 + (-5) = -36 - 5 = -41 Step 4: Substitute these values back into the numerator. 45 + 3 + 90 - (-41) 45 + 3 + 90 + 41 Step 5: Add the numbers in the numerator. 48 + 90 + 41 = 138 + 41 = 179 Step 6: Divide the numerator by the denominator. (179)/(10) = 17.9 The value is 17.9. Question 6: The temperatures of major cities around the world on a particular day were shown in the table below. a) List 3 cities with the highest maximum temperatures in order, starting with the hottest. Step 1: Identify the maximum temperatures from the table: Bahrain: 39^ C Cairo: 36^ C Melbourne: 33^ C Amsterdam: 9^ C London: 9^ C New York: 7^ C Oslo: 5^ C Helsinki: 4^ C Stockholm: 3^ C Step 2: Order the top three from highest to lowest. I. Bahrain II. Cairo III. Melbourne b) List the cities with the three minimum temperatures in order, starting with the coldest. Step 1: Identify the minimum temperatures from the table: Stockholm: -9^ C Helsinki: -4^ C New York: -2^ C Oslo: -1^ C London: 1^ C Amsterdam: 5^ C Melbourne: 19^ C Cairo: 24^ C Bahrain: 28^ C Step 2: Order the top three from coldest to warmest. I. Stockholm II. Helsinki III. New York c) How many degrees did the temperatures rise in: The temperature rise is calculated as Maximum Temperature - Minimum Temperature. i) Cairo? 36^ C - 24^ C = 12^ C The temperature rise is 12^ C. ii) London? 9^ C - 1^ C = 8^ C The temperature rise is 8^ C. iii) New York? 7^ C - (-2^ C) = 7^ C + 2^ C = 9^ C The temperature rise is 9^ C. iv) Stockholm? 3^ C - (-9^ C) = 3^ C + 9^ C = 12^ C The temperature rise is 12^ C. v) Oslo? 5^ C - (-1^ C) = 5^ C + 1^ C = 6^ C The temperature rise is 6^ C. d) Find the minimum temperature in Helsinki the next day if it was 2^ C lower than the minimum shown on the table. Step 1: Identify the minimum temperature for Helsinki from the table. Helsinki minimum: -4^ C Step 2: Subtract 2^ C from this temperature. -4^ C - 2^ C = -6^ C The minimum temperature in Helsinki the next day was -6^ C. e) On the same day, the coldest temperature recorded worldwide was -62^ C at Oimyakon in Siberia. How much was this colder than the maximum temperature in Melbourne? Step 1: Identify the maximum temperature for Melbourne from the table. Melbourne maximum: 33^ C Step 2: Calculate the difference between Melbourne's maximum temperature and Oimyakon's temperature. 33^ C - (-62^ C) = 33^ C + 62^ C = 95^ C Oimyakon was 95^ C colder than the maximum temperature in Melbourne. f) On the same day the hottest temperature recorded worldwide was 54^ C at Eurolaba in Western Australia. How much hotter was this than the temperature in Oimyakon? Step 1: Identify the temperature in Eurolaba and Oimyakon. Eurolaba: 54^ C Oimyakon: -62^ C Step 2: Calculate the difference between Eurolaba's temperature and Oimyakon's temperature. 54^ C - (-62^ C) = 54^ C + 62^ C = 116^ C Eurolaba was 116^ C hotter than the temperature in Oimyakon. 3 done, 2 left today. You're making progress.