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Calculate currency conversions for EUR, USD to RWF, and find the missing number in a sequence.

Mathematics

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4 parts
1

110 USD=156090 RWF110 \text{ USD} = 156090 \text{ RWF}

130 EUR=4790700 RWF130 \text{ EUR} = 4790700 \text{ RWF}

2
35
3

1800 cm1800 \text{ cm}

400 cm2400 \text{ cm}^2

4

5 cm5 \text{ cm}

17 cm17 \text{ cm}

Step-by-step solution

10 steps

Here are the solutions to your questions:

Part 1· 2 steps

Currency Conversion

  • a) 130 EUR = 4790700 This is a given conversion value.

  • b) 700 USD = 993300 RWF This is a given conversion rate.

  • c) 150,000 UGSH = 150 RWF This is a given conversion rate.

  • d) 110 USD = RWF

  1. Determine the conversion rate for 1 USD from the given information.

    $$
    1 \text{ USD} = \frac{993300 \text{ RWF}}{700 \text{ USD}} = 1419 \text{ RWF/USD}
    $$
    
  2. Calculate the value for 110 USD.

    $$
    110 \text{ USD} = 110 \times 1419 \text{ RWF}
    $$
    $$
    110 \text{ USD} = 156090 \text{ RWF}
    $$
    So, $\boxed{110 \text{ USD} = 156090 \text{ RWF}}$.
    
    • e) 130 EUR = RWF From the first line, the value is directly given. 130 EUR=4790700 RWF130 \text{ EUR} = 4790700 \text{ RWF} So, 130 EUR=4790700 RWF\boxed{130 \text{ EUR} = 4790700 \text{ RWF}}.

Part 235

Find the missing numbers

The sequence is: 15,20,25,30,_,39,40,4515, 20, 25, 30, \_, 39, 40, 45.

  1. Identify the pattern in the initial numbers.

    The difference between consecutive numbers is:
    20−15=520 - 15 = 5
    25−20=525 - 20 = 5
    30−25=530 - 25 = 5
    The pattern is an increase of 5 for each step.

  2. Apply the pattern to find the missing number.

    Following the pattern, the number after 30 should be 30+5=3530 + 5 = 35.
    If we continue the pattern: 35+5=4035 + 5 = 40, and 40+5=4540 + 5 = 45.
    The numbers 40 and 45 fit this pattern. The number 39 in the original list appears to be an error or an outlier.

    The missing number in the sequence 15,20,25,30,_,40,4515, 20, 25, 30, \_, 40, 45 is 35\boxed{35}.

Part 3

1800 cm1800 \text{ cm}

Cuboid Volume

The volume of a cuboid is 720000 cm3720000 \text{ cm}^3. Its base is a square of side 20 cm20 \text{ cm}.

  • a) What is its height?
  1. Calculate the base area of the cuboid.

    Since the base is a square with side $20 \text{ cm}$:
    $$
    \text{Base Area} = \text{side} \times \text{side} = 20 \text{ cm} \times 20 \text{ cm} = 400 \text{ cm}^2
    $$
    
  2. Use the volume formula to find the height.

    The volume of a cuboid is given by $V = \text{Base Area} \times \text{Height}$.
    $$
    720000 \text{ cm}^3 = 400 \text{ cm}^2 \times \text{Height}
    $$
    
  3. Solve for the height.

    $$
    \text{Height} = \frac{720000 \text{ cm}^3}{400 \text{ cm}^2}
    $$
    $$
    \text{Height} = 1800 \text{ cm}
    $$
    The height of the cuboid is $\boxed{1800 \text{ cm}}$.
    
    • b) What is its base area?
  4. Calculate the base area.

    Since the base is a square with side $20 \text{ cm}$:
    $$
    \text{Base Area} = \text{side} \times \text{side} = 20 \text{ cm} \times 20 \text{ cm}
    $$
    $$
    \text{Base Area} = 400 \text{ cm}^2
    $$
    The base area of the cuboid is $\boxed{400 \text{ cm}^2}$.
    

Part 4

5 cm5 \text{ cm}

Copy and complete the table

The formula relating Volume (VV), Base Area (AA), and Height (HH) is V=A×HV = A \times H, which can be rearranged to H=VAH = \frac{V}{A}.

  • Row 1:
    • Volume =375 cm3= 375 \text{ cm}^3
    • Base Area =75 cm2= 75 \text{ cm}^2
  1. Calculate the height.

    $$
    \text{Height} = \frac{375 \text{ cm}^3}{75 \text{ cm}^2}
    $$
    $$
    \text{Height} = 5 \text{ cm}
    $$
    The height is $\boxed{5 \text{ cm}}$.
    
    • Row 2:
      • Volume =850 cm3= 850 \text{ cm}^3
      • Base Area =50 cm2= 50 \text{ cm}^2
  2. Calculate the height.

    $$
    \text{Height} = \frac{850 \text{ cm}^3}{50 \text{ cm}^2}
    $$
    $$
    \text{Height} = 17 \text{ cm}
    $$
    The height is $\boxed{17 \text{ cm}}$.
    
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