Question

Hedly gathered the following evidence. 5(22) = 110 5(33) = 165 5(44) = 220 Which conjecture might Hedly make from this evidence? Is the conjecture valid? Select one:

a. When you multiply 11 by a multiple of 5, the first and last digits of the product will sum to the middle digit; this conjecture is valid.

b. When you multiply 11 by a multiple of 11, the first and last digits of the product will sum to the middle digit; this conjecture is valid.

c. When you multiply 5 by a multiple of 11, the first and last digits of the product will sum to the middle digit; this conjecture is valid.

d. When you multiply 5 by a multiple of 11, the first and last digits of the product will sum to the middle digit; this conjecture is not valid.

Answer 1

The valid conjecture from the given evidence is that a) when you multiply 11 by a multiple of 5, the first and last digits of the product will sum to the middle digit.

Step-by-step explanation:

a. When you multiply 11 by a multiple of 5, the first and last digits of the product will sum to the middle digit; this conjecture is valid.

To determine which conjecture is valid, we can analyze the given evidence. In each equation, the first and last digits of the product are double the middle digit. For example, in 5(22) = 110, the first digit (1) plus the last digit (0) equals the middle digit (1) doubled.

This pattern is consistent in all three equations, indicating that the conjecture that the first and last digits of the product will sum to the middle digit when multiplying 11 by a multiple of 5 is valid.