The merchant gets 15 ingots for every 2 spice bags. To find the total for 12 bags, divide 12 by 2 to get 6 pairs, then multiply 6 by 15, resulting in 90 copper ingots.
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The square root spiral starts with a base triangle of sides 1 and 1, giving a hypotenuse of root 2. Each successive triangle adds a side of 1, yielding hypotenuses of root 2, root 3, root 4, and continuing sequentially.
The denominator is 2 cubed times 5, which equals 40. Since the highest power between the prime factors 2 and 5 is 3, the terminating decimal expansion will have exactly 3 decimal places.
To find 6 rational numbers between 3 and 4, convert them into fractions with a denominator of 7, giving 21/7 and 28/7. The intermediate numbers are 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.
To find rational numbers between 3.1415 and 3.1416, extend the decimal places by appending digits. Three distinct rational numbers falling within this specific range are 3.14151, 3.14152, and 3.14153.