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Calculate currency conversions for EUR, USD to RWF, and find the missing number in a sequence.
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4 partsStep-by-step solution
10 stepsHere are the solutions to your questions:
Part 1· 2 steps
Currency Conversion
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a) 130 EUR = 4790700 This is a given conversion value.
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b) 700 USD = 993300 RWF This is a given conversion rate.
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c) 150,000 UGSH = 150 RWF This is a given conversion rate.
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d) 110 USD = RWF
Determine the conversion rate for 1 USD from the given information.
$$ 1 \text{ USD} = \frac{993300 \text{ RWF}}{700 \text{ USD}} = 1419 \text{ RWF/USD} $$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. So, .
Part 235
Find the missing numbers
The sequence is: .
Identify the pattern in the initial numbers.
The difference between consecutive numbers is:
The pattern is an increase of 5 for each step.Apply the pattern to find the missing number.
Following the pattern, the number after 30 should be .
If we continue the pattern: , and .
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 is .
Part 3
Cuboid Volume
The volume of a cuboid is . Its base is a square of side .
- a) What is its height?
Calculate the base area of the cuboid.
Since the base is a square with side $20 \text{ cm}$: $$ \text{Base Area} = \text{side} \times \text{side} = 20 \text{ cm} \times 20 \text{ cm} = 400 \text{ cm}^2 $$Use the volume formula to find the height.
The volume of a cuboid is given by $V = \text{Base Area} \times \text{Height}$. $$ 720000 \text{ cm}^3 = 400 \text{ cm}^2 \times \text{Height} $$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?
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
Copy and complete the table
The formula relating Volume (), Base Area (), and Height () is , which can be rearranged to .
- Row 1:
- Volume
- Base Area
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
- Base Area
- Row 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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