To find the thirty-second shape of the pattern, we first need to determine the length of the repeating sequence:
The repeating pattern is: "circle, diamond, sphere, circle, square". This has 5 shapes.
Now, we can find the thirty-second shape by calculating:
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Divide 32 by 5: \[ 32 \div 5 = 6 \text{ remainder } 2 \] This means that when we divide 32 by 5, we get 6 complete cycles of the pattern with a remainder of 2.
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The remainder tells us which shape corresponds to the thirty-second position in the sequence:
- A remainder of 1 corresponds to the first shape: circle
- A remainder of 2 corresponds to the second shape: diamond
- A remainder of 3 corresponds to the third shape: sphere
- A remainder of 4 corresponds to the fourth shape: circle
- A remainder of 5 corresponds to the fifth shape: square
Since the remainder is 2, the thirty-second shape is a diamond.
Final answer: To find the thirty-second shape of the pattern, choose 32 by 5. The remainder is 2 making the thirty-second shape a diamond.