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### 2. a. Sets X and Y
- [tex]\( X \)[/tex] is the set of whole numbers from 4 to 13:
[tex]\[ X = \{4, 5, 6, 7, 8, 9, 10, 11, 12, 13\} \][/tex]
- [tex]\( Y \)[/tex] is the set of multiples of 3 between 2 and 20:
[tex]\[ Y = \{3, 6, 9, 12, 15, 18\} \][/tex]
### 2. b. Least Common Multiple (LCM) of 15 and 12
- The prime factorization of 15 is [tex]\( 3 \times 5 \)[/tex].
- The prime factorization of 12 is [tex]\( 2^2 \times 3 \)[/tex].
To find the LCM, we take the highest power of each prime number that appears in the factorizations:
[tex]\[ \text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60. \][/tex]
So, the LCM of 15 and 12 is 60.
### 2. c. Express 50% as a fraction in its lowest term
- 50% means 50 out of 100:
[tex]\[ 50\% = \frac{50}{100} = \frac{1}{2} \quad \text{(simplified)} \][/tex]
### 3. a. Perimeter of the figure
It is mentioned that [tex]\( 4x + 3 \)[/tex] is a side length of a square.
- Assuming a side length (interpretating [tex]\(4x+3\)[/tex] as a number):
Let [tex]\( s = 4 + 3 = 7 \)[/tex] (assuming [tex]\(x = 1\)[/tex]).
- The perimeter [tex]\( P \)[/tex] of a square with side length [tex]\( s \)[/tex] is given by:
[tex]\[ P = 4s = 4 \times 7 = 28. \][/tex]
### 3. b. Area of a rectangle
- Given length [tex]\( l = 14 \)[/tex] cm and width [tex]\( w = 10 \)[/tex] cm:
[tex]\[ \text{Area} = l \times w = 14 \times 10 = 140 \text{ cm}^2 \][/tex]
### 3. c. Arrange the ratios in ascending order
- Convert each ratio to its decimal form:
[tex]\[ \frac{7}{8} = 0.875, \quad \frac{1}{2} = 0.5, \quad \frac{3}{4} = 0.75. \][/tex]
- Arrange the ratios from smallest to largest by their decimal values:
[tex]\[ \frac{1}{2} \ (1:2), \ \frac{3}{4} \ (3:4), \ \frac{7}{8} \ (7:8) \][/tex]
So, in ascending order: [tex]\( 1:2, 3:4, 7:8 \)[/tex].
### 4. a. Complete the table
[tex]\[ \begin{array}{|l|c|c|c|c|} \hline \text{Common fraction} & \frac{1}{10} & \frac{1}{5} & \frac{1}{4} & \frac{2}{5} \\ \hline \text{Percentage} & 10\% & 20\% & 25\% & 40\% \\ \hline \text{Decimal} & 0.1 & 0.2 & 0.25 & 0.4 \\ \hline \end{array} \][/tex]
### 4. b. Write the numbers in words
- [tex]\( 320,467,098 \)[/tex]:
[tex]\[ \text{Three hundred twenty million, four hundred sixty-seven thousand, ninety-eight}. \][/tex]
- [tex]\( 2,384,598 \)[/tex]:
[tex]\[ \text{Two million, three hundred eighty-four thousand, five hundred ninety-eight}. \][/tex]
### 4. c. Round off [tex]\( 12,987,657 \)[/tex]
- To the nearest tens:
[tex]\[ 12,987,657 \approx 12,987,660. \][/tex]
- To the nearest hundreds:
[tex]\[ 12,987,657 \approx 12,987,700. \][/tex]
### 2. a. Sets X and Y
- [tex]\( X \)[/tex] is the set of whole numbers from 4 to 13:
[tex]\[ X = \{4, 5, 6, 7, 8, 9, 10, 11, 12, 13\} \][/tex]
- [tex]\( Y \)[/tex] is the set of multiples of 3 between 2 and 20:
[tex]\[ Y = \{3, 6, 9, 12, 15, 18\} \][/tex]
### 2. b. Least Common Multiple (LCM) of 15 and 12
- The prime factorization of 15 is [tex]\( 3 \times 5 \)[/tex].
- The prime factorization of 12 is [tex]\( 2^2 \times 3 \)[/tex].
To find the LCM, we take the highest power of each prime number that appears in the factorizations:
[tex]\[ \text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60. \][/tex]
So, the LCM of 15 and 12 is 60.
### 2. c. Express 50% as a fraction in its lowest term
- 50% means 50 out of 100:
[tex]\[ 50\% = \frac{50}{100} = \frac{1}{2} \quad \text{(simplified)} \][/tex]
### 3. a. Perimeter of the figure
It is mentioned that [tex]\( 4x + 3 \)[/tex] is a side length of a square.
- Assuming a side length (interpretating [tex]\(4x+3\)[/tex] as a number):
Let [tex]\( s = 4 + 3 = 7 \)[/tex] (assuming [tex]\(x = 1\)[/tex]).
- The perimeter [tex]\( P \)[/tex] of a square with side length [tex]\( s \)[/tex] is given by:
[tex]\[ P = 4s = 4 \times 7 = 28. \][/tex]
### 3. b. Area of a rectangle
- Given length [tex]\( l = 14 \)[/tex] cm and width [tex]\( w = 10 \)[/tex] cm:
[tex]\[ \text{Area} = l \times w = 14 \times 10 = 140 \text{ cm}^2 \][/tex]
### 3. c. Arrange the ratios in ascending order
- Convert each ratio to its decimal form:
[tex]\[ \frac{7}{8} = 0.875, \quad \frac{1}{2} = 0.5, \quad \frac{3}{4} = 0.75. \][/tex]
- Arrange the ratios from smallest to largest by their decimal values:
[tex]\[ \frac{1}{2} \ (1:2), \ \frac{3}{4} \ (3:4), \ \frac{7}{8} \ (7:8) \][/tex]
So, in ascending order: [tex]\( 1:2, 3:4, 7:8 \)[/tex].
### 4. a. Complete the table
[tex]\[ \begin{array}{|l|c|c|c|c|} \hline \text{Common fraction} & \frac{1}{10} & \frac{1}{5} & \frac{1}{4} & \frac{2}{5} \\ \hline \text{Percentage} & 10\% & 20\% & 25\% & 40\% \\ \hline \text{Decimal} & 0.1 & 0.2 & 0.25 & 0.4 \\ \hline \end{array} \][/tex]
### 4. b. Write the numbers in words
- [tex]\( 320,467,098 \)[/tex]:
[tex]\[ \text{Three hundred twenty million, four hundred sixty-seven thousand, ninety-eight}. \][/tex]
- [tex]\( 2,384,598 \)[/tex]:
[tex]\[ \text{Two million, three hundred eighty-four thousand, five hundred ninety-eight}. \][/tex]
### 4. c. Round off [tex]\( 12,987,657 \)[/tex]
- To the nearest tens:
[tex]\[ 12,987,657 \approx 12,987,660. \][/tex]
- To the nearest hundreds:
[tex]\[ 12,987,657 \approx 12,987,700. \][/tex]
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