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A pattern for a wedding outfit calls for \( 16_{2}^{2} \) yards of lace trim for the dress and \( 8_{8}^{2} \) yards of lace trim for the veil. How many yards of lace trim does the pattern call for?

Ask by Thornton Long. in the United States
Dec 06,2024

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The pattern calls for 24 yards of lace trim.

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The Deep Dive

To find the total amount of lace trim for the wedding outfit, we need to convert the lace requirements from their respective bases to base 10 and then add them together. First, let's convert \( 16_{2}^{2} \) (which seems to be improperly formatted; assuming it means 16 in base 2) to base 10: - Base 2: \( 16_2 \) breaks down as follows: - \( 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 16_{10} \) - So, \( 16_{2}^{2} = 16 \) yards. Now, let's convert \( 8_{8}^{2} \) (which likely means 8 in base 8) to base 10: - Base 8: \( 8_8 \) breaks down as follows: - \( 8 \) in base 8 is actually \( 8_{10} \) since it’s the first digit representing one full set of \( 8 \). - So, \( 8_{8}^{2} = 8 \) yards. Now, we add them together: Total lace trim = \( 16 + 8 = 24 \) yards. The pattern calls for a total of **24 yards of lace trim** for the wedding outfit!

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