Question2. (1 point) Debbie gathered the following evidence. $4(33)=132$ $5(33)=165$ $6(33)=198$ Which conjecture, if any, is Debbie most likely to make from this evidence? a. When you multiply a two-digit number by 33 , the first and last digits of the product form a number that is twice the original number. b. When you multiply a one-digit number by 33 , the first and last digits of the product form a number that is three times the original number. c. When you multiply a one-digit number by 33 , the sum of the digits in the product is equal to the original number. d. None of the above conjectures can be made from this evidence.

Studdy Solution

STEP 1

1. We are given three multiplication results involving the number 33.
2. We need to determine which conjecture, if any, is supported by the evidence provided.
3. Each conjecture involves a specific relationship between the digits of the product and the original number.

STEP 2

1. Analyze each conjecture to understand what it claims.
2. Verify each conjecture using the given multiplication results.
3. Determine which conjecture is supported by the evidence.

STEP 3

Analyze each conjecture:
a. When you multiply a two-digit number by 33, the first and last digits of the product form a number that is twice the original number.
b. When you multiply a one-digit number by 33, the first and last digits of the product form a number that is three times the original number.
c. When you multiply a one-digit number by 33, the sum of the digits in the product is equal to the original number.
d. None of the above conjectures can be made from this evidence.

STEP 4

Verify each conjecture using the given multiplication results:
- For $4 \times 33 = 132$ : - First and last digits: 1 and 2, forming the number 12. - Sum of the digits: $1 + 3 + 2 = 6$ .
- For $5 \times 33 = 165$ : - First and last digits: 1 and 5, forming the number 15. - Sum of the digits: $1 + 6 + 5 = 12$ .
- For $6 \times 33 = 198$ : - First and last digits: 1 and 8, forming the number 18. - Sum of the digits: $1 + 9 + 8 = 18$ .

STEP 5

Check each conjecture:
- Conjecture a: Involves two-digit numbers, but all given numbers are one-digit. - Conjecture b: Check if the first and last digits form a number that is three times the original number: - For 4: $12 \neq 3 \times 4$ - For 5: $15 \neq 3 \times 5$ - For 6: $18 = 3 \times 6$
- Conjecture c: Check if the sum of the digits equals the original number: - For 4: $6 \neq 4$ - For 5: $12 \neq 5$ - For 6: $18 = 6$

STEP 6

Determine which conjecture is supported:
- Conjecture b is partially supported but not consistently. - Conjecture c is supported for the number 6.
Given the evidence, Conjecture c is most likely to be made from this evidence since it holds true for one of the examples.
The conjecture that Debbie is most likely to make from this evidence is: c. When you multiply a one-digit number by 33, the sum of the digits in the product is equal to the original number.

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