The rule for a repeating pattern is "circle, diamond, sphere, circle, square." Use the drop-down menus to complete the phrase.

To find the thirty-second shape of the pattern,
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32 by
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. The remainder is
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making the thirty-second shape a
Choose
.

1 answer

To find the thirty-second shape of the pattern, we first need to understand the repeating sequence: "circle, diamond, sphere, circle, square." This sequence has 5 shapes in total.

  1. To find the thirty-second shape of the pattern, we divide 32 by the number of shapes in the repeating sequence, which is 5.

  2. So, we calculate 32 divided by 5:

    \( 32 \div 5 = 6 \) with a remainder.

  3. To find the remainder, we multiply the whole number part of the division (which is 6) by the number of shapes (5):

    \( 5 \times 6 = 30 \).

    Then, we subtract this from 32:

    \( 32 - 30 = 2 \).

Thus, the remainder is 2.

  1. Now, we look at the position of the remainder in the repeating pattern:
    • 1 = circle
    • 2 = diamond
    • 3 = sphere
    • 4 = circle
    • 5 = square

Since the remainder is 2, the thirty-second shape corresponds to the second shape in our pattern, which is a diamond.

Putting it all together:

To find the thirty-second shape of the pattern, choose 32 by 5. The remainder is choose 2, making the thirty-second shape a choose diamond.