Mathematical Proportions and Calculations

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Questions and Answers

How many bottles will the machine fill in five hours if it fills 840 bottles in six hours?

  • 700 bottles
  • 700 bottles
  • 750 bottles
  • 800 bottles (correct)

How much red pigment is needed if 1 part requires 75 mL of base and you have 1800 mL of base?

  • 5 parts (correct)
  • 10 parts
  • 15 parts
  • 8 parts

If the scale of Rashmi's map is 1 cm representing 18 km, what distance does she drive on the map for a road journey of 72 km?

  • 5 cm
  • 3.5 cm
  • 2.5 cm
  • 4 cm (correct)

Given that 2 kg of sugar contains $9 \times 10^6$ sugar crystals, how many crystals are there in 1.2 kg of sugar?

<p>$5.4 \times 10^6$ crystals (D)</p> Signup and view all the answers

If a bacteria photograph is enlarged 20,000 times, what would be its enlarged length if the actual length of the bacteria is 0.0001 m?

<p>1 cm (B)</p> Signup and view all the answers

Are the parking charges at the railway station directly proportional to the parking time?

<p>No, the charges increase but not at a constant rate. (A)</p> Signup and view all the answers

Flashcards

Direct Proportion

Two quantities are in direct proportion if they increase or decrease at the same rate.

Ratio

A ratio compares two quantities of the same unit.

Proportion

A proportion states that two ratios are equal.

Scale drawing

A scale drawing uses a scale to represent a real-life object, where every measurement in the drawing corresponds to a certain measurement in the real object.

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Scale

A scale is a ratio that compares the size of a drawing or model to the size of the real object.

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Study Notes

Car Parking Charges

  • Parking charges are not in direct proportion to parking time.
  • Different time slots have different fees.
    • Up to 4 hours: 60
    • 8 hours: 100
    • 12 hours: 140
    • 24 hours: 180

Paint Mixture Proportions

  • A paint mixture uses a ratio of 1 part red pigment to 8 parts base.
  • Parts of red pigment | Parts of base
    • 1 | 8
    • 4 | 32
    • 7 | 56
    • 12 | 96
    • 20 | 160

Paint Mixture Calculation

  • If 1 part of red pigment requires 75 mL of base, to use 1800 mL base, one would need 24 parts of red pigment.

Machine Production Rate

  • A machine fills 140 bottles per hour.
  • In five hours, the machine will fill 700 bottles.
  • A machine in a soft drink factory fills 840 bottles in six hours. This means it fills 840/6 = 140 bottles per hour. In five hours, it will fill 140 bottles/hour * 5 hours = 700 bottles.

Bacteria Enlargement

  • Actual bacteria length is 10^-7 cm.
  • Enlarged length at 20,000x is 2.5 cm.
  • A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. This means the actual length of the bacteria is 5 cm / 50,000 = 10^-7 cm.
  • If the photograph is enlarged 20,000 times, its enlarged length would be (10^-7 cm * 20,000) = 2×10−3 cm = 0.002 cm

Model Ship Dimensions

  • Model ship mast is 9 cm high, actual ship mast is 12 m high, scale is 1/1333.33.
  • If actual ship length is 28 m, model ship length is 21 cm.

Sugar Crystals Calculation

  • 2 kg of sugar contains 9 × 10^6 crystals.
    • 5 kg of sugar would contain 2.25 × 10^7 crystals.
    • 1.2 kg of sugar would contain 5.4 × 10^6 crystals.

Road Map Scale

  • Map scale is 1 cm : 18 km.
  • 72 km distance on road would correspond to 4 cm on map.

Pole Shadow Length and Height

  • A 5.6 m pole casts a 3.2 m shadow.
    • A 10.5 m pole would cast a 6 m shadow.
    • A 5 m shadow corresponds to a pole of 8.75 m.

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