1.3 The budget of R6 144 will be spent equally on 6 items: food, drinks, entertainment, decorations, transportation and gifts. Calculate, using the long division method, how much will each item get.

Mathematics
1.3 The budget of R6 144 will be spent equally on 6 items: food, drinks, entertainment, decorations, transportation and gifts. Calculate, using the long division method, how much will each item get.

ScanSolve AI Answer

Answer

30 balons

1.1 Quants balons s'ajusten a la paret?

Step 1: Convert dimensions to cm (same units as balloon width).

Longitud: 2m=200cm2\,m = 200\,\mathrm{cm}
Alçada: 1.5m=150cm1.5\,m = 150\,\mathrm{cm}
Ample baló: 30cm30\,\mathrm{cm}

Step 2: Balons al llarg de la longitud (divisió llarga):

30\longdiv20018020\begin{array}{r|r} & 30\longdiv{200}\\ - & 180\\ \hline & 20 \end{array}

30×6=180cm30 \times 6 = 180\,\mathrm{cm}
200180=20cm200 - 180 = 20\,\mathrm{cm} (resta)
6\therefore 6 balons al llarg.

Step 3: Balons al llarg de l'alçada (divisió llarga):

30\longdiv1501500\begin{array}{r|r} & 30\longdiv{150}\\ - & 150\\ \hline & 0 \end{array}

30×5=150cm30 \times 5 = 150\,\mathrm{cm}
150150=0cm150 - 150 = 0\,\mathrm{cm}
5\therefore 5 balons d'alçada.

Step 4: Total balons:
6×5=306 \times 5 = 30 balons.

30 balons

1.2 Pressupost de la festa (cost baló 0.20\euro0.20\,\mathrm{\euro})

Step 1: Cost total:
30×0.20=6\euro30 \times 0.20 = 6\,\mathrm{\euro}

6,\mathrm{\euro}

1.3 Àrees (paret, espai en l'aire, globus)

Step 1: Àrea paret:
2m×1.5m=3m22\,m \times 1.5\,m = 3\,m^2

Step 2: Diàmetre baló 30cm=0.3m30\,cm = 0.3\,\mathrm{m}, radi r=0.15m=320mr = 0.15\,m = \frac{3}{20}\,\mathrm{m}
Àrea 1 baló:
πr2=π(320)2=π9400=9π400m2\pi r^2 = \pi \left(\frac{3}{20}\right)^2 = \pi \cdot \frac{9}{400} = \frac{9\pi}{400}\,m^2

Step 3: Àrea total globus:
30×9π400=270π400=27π40m230 \times \frac{9\pi}{400} = \frac{270\pi}{400} = \frac{27\pi}{40}\,m^2

Step 4: Espai en l'aire (descobert):
327π40m23 - \frac{27\pi}{40}\,m^2

Àrea paret: 3\,\mathrm{m^{2}
Àrea globus: 27π40m2\dfrac{27\pi}{40}\,m^{2}
Espai aire: 327π40m23 - \dfrac{27\pi}{40}\,m^{2}}

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Quick Answer

1.1 Quants balons s'ajusten a la paret? Step 1: Convert dimensions to cm (same units as balloon width).

1.3 The budget of R6 144 will be spent equally on 6 items: food, drinks, entertainment, decorations, transportation and gifts. Calculate, using the long division method, how much will each item get.
Mathematics

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.

ScanSolve AI Answer
1.1 Quants balons s'ajusten a la paret? Step 1: Convert dimensions to cm (same units as balloon width). Longitud: 2\,m = 200\,cm Alçada: 1.5\,m = 150\,cm Ample baló: 30\,cm Step 2: Balons al llarg de la longitud (divisió llarga): r|r & 30200\\ & 180\\ & 20 30 × 6 = 180\,cm 200 - 180 = 20\,cm (resta) 6 balons al llarg. Step 3: Balons al llarg de l'alçada (divisió llarga): r|r & 30150\\ & 150\\ & 0 30 × 5 = 150\,cm 150 - 150 = 0\,cm 5 balons d'alçada. Step 4: Total balons: 6 × 5 = 30 balons. 30 balons 1.2 Pressupost de la festa (cost baló 0.20\,) Step 1: Cost total: 30 × 0.20 = 6\, 6\, 1.3 Àrees (paret, espai en l'aire, globus) Step 1: Àrea paret: 2\,m × 1.5\,m = 3\,m^2 Step 2: Diàmetre baló 30\,cm = 0.3\,m, radi r = 0.15\,m = (3)/(20)\,m Àrea 1 baló: r^2 = ((3)/(20))^2 = · (9)/(400) = (9)/(400)\,m^2 Step 3: Àrea total globus: 30 × (9)/(400) = (270)/(400) = (27)/(40)\,m^2 Step 4: Espai en l'aire (descobert): 3 - (27)/(40)\,m^2 Àrea paret: 3\,m^2 Àrea globus: (27)/(40)\,m^2 Espai aire: 3 - (27)/(40)\,m^2