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Solve the following problems: 21. -3 - 4 = ? 22. Joshua had 3 1/2 kg of sugar. He used 1 1/4 kg and bought 2 1/2 kg more. How much sugar does he have now? 23. Convert 0.1888... to a fraction.

Mathematics

ScanSolve AI Answer

Step-by-step solution

19 steps

21.

  1. Start at −3-3 on the number line.

  2. Subtracting 4 means moving 4 units to the left from −3-3.

    −3−4=−7-3 - 4 = -7

    The final position on the number line is −7-7.
    The integer is −7\boxed{-7}.

    22.

  3. Convert all mixed numbers to improper fractions.

    Initial sugar: 312=3×2+12=723\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} kg
    Sugar used: 114=1×4+14=541\frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4} kg
    Additional sugar bought: 212=2×2+12=522\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} kg

  4. Calculate the remaining sugar.

    Remaining sugar = Initial sugar - Sugar used + Additional sugar bought

    Remaining=72−54+52\text{Remaining} = \frac{7}{2} - \frac{5}{4} + \frac{5}{2}
  5. Find a common denominator, which is 4.

    Remaining=7×22×2−54+5×22×2\text{Remaining} = \frac{7 \times 2}{2 \times 2} - \frac{5}{4} + \frac{5 \times 2}{2 \times 2} Remaining=144−54+104\text{Remaining} = \frac{14}{4} - \frac{5}{4} + \frac{10}{4}
  6. Perform the addition and subtraction.

    Remaining=14−5+104\text{Remaining} = \frac{14 - 5 + 10}{4} Remaining=9+104\text{Remaining} = \frac{9 + 10}{4} Remaining=194 kg\text{Remaining} = \frac{19}{4} \text{ kg}
  7. Convert the improper fraction back to a mixed number.

    194=434 kg\frac{19}{4} = 4\frac{3}{4} \text{ kg}

    Joshua finally remained with 434 kg\boxed{4\frac{3}{4} \text{ kg}} of sugar.

    23.

  8. Let xx be the given repeating decimal.

    x=0.18˙=0.1888...(1)x = 0.1\dot{8} = 0.1888... \quad (1)
  9. Multiply by 10 to move the non-repeating digit past the decimal point.

    10x=1.888...(2)10x = 1.888... \quad (2)
  10. Multiply by 100 to move one full repeating block past the decimal point.

    100x=18.888...(3)100x = 18.888... \quad (3)
  11. Subtract equation (2) from equation (3) to eliminate the repeating part.

    100x−10x=18.888...−1.888...100x - 10x = 18.888... - 1.888... 90x=1790x = 17
  12. Solve for xx.

    x=1790x = \frac{17}{90}

    The number 0.18˙0.1\dot{8} as a fraction is 1790\boxed{\frac{17}{90}}.

    24.
    The problem asks to calculate the distance covered, but the image of the athletic field does not provide any dimensions (e.g., length of straight sections, radius of semicircles). Without these dimensions, it is impossible to calculate the perimeter of the track or the total distance covered.

    25.

  13. Identify the dimensions of the rectangular tin.

    Height (hh) = 30 cm
    Base length (ll) = 20 cm (since it's a square base)
    Base width (ww) = 20 cm

  14. Calculate the volume of the tin in cubic centimeters.

    The formula for the volume of a rectangular prism is V=l×w×hV = l \times w \times h.

    V=20 cm×20 cm×30 cmV = 20 \text{ cm} \times 20 \text{ cm} \times 30 \text{ cm} V=400 cm2×30 cmV = 400 \text{ cm}^2 \times 30 \text{ cm} V=12000 cm3V = 12000 \text{ cm}^3
  15. Convert the volume from cubic centimeters to cubic meters.

    We know that 1 m=100 cm1 \text{ m} = 100 \text{ cm}.
    Therefore, 1 m3=(100 cm)3=100×100×100 cm3=1,000,000 cm31 \text{ m}^3 = (100 \text{ cm})^3 = 100 \times 100 \times 100 \text{ cm}^3 = 1,000,000 \text{ cm}^3.

    V=12000 cm3×1 m31,000,000 cm3V = 12000 \text{ cm}^3 \times \frac{1 \text{ m}^3}{1,000,000 \text{ cm}^3} V=120001000000 m3V = \frac{12000}{1000000} \text{ m}^3 V=121000 m3V = \frac{12}{1000} \text{ m}^3 V=0.012 m3V = 0.012 \text{ m}^3

    The volume of the paint that can fit in the container is 0.012 m3\boxed{0.012 \text{ m}^3}.

    26.

  16. Identify the given distance and time.

    Distance (DD) = 432 Km
    Time (TT) = 6 hours

  17. Convert the distance from kilometers to meters.

    1 Km=1000 m1 \text{ Km} = 1000 \text{ m}

    D=432 Km×1000 m1 Km=432000 mD = 432 \text{ Km} \times \frac{1000 \text{ m}}{1 \text{ Km}} = 432000 \text{ m}
  18. Convert the time from hours to seconds.

    1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes}
    1 minute=60 seconds1 \text{ minute} = 60 \text{ seconds}

    T=6 hours×60 minutes1 hour×60 seconds1 minuteT = 6 \text{ hours} \times \frac{60 \text{ minutes}}{1 \text{ hour}} \times \frac{60 \text{ seconds}}{1 \text{ minute}} T=6×3600 seconds=21600 secondsT = 6 \times 3600 \text{ seconds} = 21600 \text{ seconds}
  19. Calculate the average speed using the formula Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}.

    Speed=432000 m21600 s\text{Speed} = \frac{432000 \text{ m}}{21600 \text{ s}} Speed=4320216 m/s\text{Speed} = \frac{4320}{216} \text{ m/s} Speed=20 m/s\text{Speed} = 20 \text{ m/s}

    Wangina's average speed is 20 m/s\boxed{20 \text{ m/s}}.

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