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. Debbie is examining the results of multiplying a one-digit number by 33.
2. We are looking for a pattern or conjecture based on the products given.
3. The conjecture should be consistent with all provided evidence.

STEP 2

1. Analyze the given products.
2. Evaluate each conjecture option.
3. Determine which conjecture, if any, matches the evidence.

STEP 3

Analyze the given products:
1. $4 \times 33 = 132$
2. $5 \times 33 = 165$
3. $6 \times 33 = 198$

STEP 4

Evaluate each conjecture option:
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.
- Check for $4 \times 33 = 132$ : First and last digits form 12, which is not twice 4. - Check for $5 \times 33 = 165$ : First and last digits form 15, which is not twice 5. - Check for $6 \times 33 = 198$ : First and last digits form 18, which is not twice 6. - This conjecture does not hold for any case.
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.
- Check for $4 \times 33 = 132$ : First and last digits form 12, which is not three times 4. - Check for $5 \times 33 = 165$ : First and last digits form 15, which is three times 5. - Check for $6 \times 33 = 198$ : First and last digits form 18, which is three times 6. - This conjecture holds for two cases.
c. When you multiply a one-digit number by 33, the sum of the digits in the product is equal to the original number.
- Check for $4 \times 33 = 132$ : Sum of digits is $1 + 3 + 2 = 6$ , which is not 4. - Check for $5 \times 33 = 165$ : Sum of digits is $1 + 6 + 5 = 12$ , which is not 5. - Check for $6 \times 33 = 198$ : Sum of digits is $1 + 9 + 8 = 18$ , which is not 6. - This conjecture does not hold for any case.

STEP 5

Determine which conjecture, if any, matches the evidence:
- Conjecture b holds for two out of three cases, which is more than any other option. - Conjecture a and c do not hold for any cases. - Therefore, the most likely conjecture Debbie might make is b.
Debbie is most likely to make conjecture $\boxed{b}$ .

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