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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3.1.1 Step 1: Identify the diameter of the wheel from the diagram. The diagram shows the height of the rear wheel as 70 cm, which represents its diameter. Diameter = 70 cm Step 2: Calculate the radius. The radius is half of the diameter. Radius = Diameter2 = 70 cm2 = 35 cm The radius of the wheel is 35 cm. 3.1.2 Step 1: Convert the competition distance to centimetres. The competition distance is 23,7 kilometres. We know that 1 km = 1000 m and 1 m = 100 cm. Therefore, 1 km = 1000 × 100 cm = 100\,000 cm. Competition distance = 23,7 km × 100\,000 cmkm = 2\,370\,000 cm Step 2: Calculate the distance of one rotation using the given formula and the radius from 3.1.1. The radius is 35 cm. Distance of one rotation = 2 × 3,142 × radius Distance of one rotation = 2 × 3,142 × 35 cm Distance of one rotation = 219,94 cm Step 3: Determine the number of rotations. Number of rotations = Total distanceDistance of one rotation Number of rotations = 2\,370\,000 cm219,94 cm Number of rotations ≈ 10\,775,666 The wheel would have to rotate approximately 10\,775,67 times. 3.1.3 Step 1: Interpret the given information from the diagram and question. The diagram shows an arrow spanning the entire length of the bike, labeled "Handle bar width 185 cm". The question states, "The size of the handlebar is roughly the distance between the two wheels." Given the diagram's label and the arrow indicating the overall length of the bike (from the front of the front wheel to the back of the rear wheel), it is most reasonable to interpret the 185 cm as the overall length of the bike, and thus, the approximate "size of the handlebar" as referred to in the question. The size of the handlebar is 185 cm. 3.1.4 Step 1: Calculate the radius of the bottle. The bottle has a diameter of 8 cm. Radius = Diameter2 = 8 cm2 = 4 cm Step 2: Calculate the volume of the bottle using the given formula. The height of the bottle is 22 cm. Volume = 3,142 × radius^2 × height Volume = 3,142 × (4 cm)^2 × 22 cm Volume = 3,142 × 16 cm^2 × 22 cm Volume = 3,142 × 352 cm^3 Volume = 1105,984 cm^3 Step 3: Convert 1 litre to cubic centimetres and compare. We are given that 1 mL = 1 cm^3. Since 1 litre = 1000 mL, then 1 litre = 1000 cm^3. The bottle's volume is 1105,984 cm^3. Since 1105,984 cm^3 > 1000 cm^3, the bottle is big enough. The bottle's volume is 1105,984 cm^3, which is greater than 1 litre (1000 cm^3). Therefore, the bottle will be big enough. 3.1.5 Step 1: Substitute the given Fahrenheit temperature into the formula. The formula is: ^ = (1,8 × ^) + 32^. Given ^ = 90^. 90 = (1,8 × ^) + 32 Step 2: Solve for degrees Celsius. Subtract 32 from both sides: 90 - 32 = 1,8 × ^ 58 = 1,8 × ^ Divide by 1,8: ^ = (58)/(1,8) ^ ≈ 32,22 The temperature in degrees Celsius is approximately 32,22^. 3.1.6 Step 1: Identify the total number of bikes sold. The company sold seventeen bikes in total. Total number of bikes = 17 Step 2: Identify the number of green bikes. There are four green bikes. Number of green bikes = 4 Step 3: Calculate the probability of selecting a green bike. Probability (Green bike) = Number of green bikesTotal number of bikes Probability (Green bike) = (4)/(17) The probability of selecting a green bike is (4)/(17). Got more? Send 'em 📸