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.

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Answer
29.65 \le l < 29.75
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8. The length, cm, of a sheet of paper is 29.7 cm, correct to the nearest millimeter. Complete the statement about the value of .
To find the lower and upper bounds when a measurement is given to the nearest millimeter (which is 0.1 cm), we take half of the precision (0.1 cm / 2 = 0.05 cm).
Step 1: Calculate the lower bound. Lower bound =
Step 2: Calculate the upper bound. Upper bound =
The value of is between the lower bound (inclusive) and the upper bound (exclusive).
9. Lucia invests $5000 at a rate of 4.5% per year simple interest. Calculate the value of her investment after 7 years.
Step 1: Calculate the simple interest earned. The formula for simple interest is , where is the principal, is the annual interest rate, and is the time in years.
Step 2: Calculate the total value of the investment. Total value = Principal + Interest The value of her investment after 7 years is \boxed{\6575}$.
10. Rectangle A measures 3 cm by 8 cm. Five rectangles congruent to A are joined to make a shape. Work out the perimeter of the shape.
Each rectangle has dimensions: width = 3 cm, length = 8 cm. Let's trace the outer edges of the combined shape shown in the diagram.
Step 1: Identify and sum the horizontal segments of the perimeter.
Step 2: Identify and sum the vertical segments of the perimeter.
Step 3: Calculate the total perimeter. Total perimeter = Total horizontal perimeter + Total vertical perimeter Total perimeter = Total perimeter = . The perimeter of the shape is .
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8. The length, l cm, of a sheet of paper is 29.7 cm, correct to the nearest millimeter.
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.