Final answer:
To determine if each statement is true or false, we substitute the given values of w into the expression 7 x w and evaluate the products. The first statement is true, the second is false, and the last two statements are true.
Step-by-step explanation:
The expression is 7 x w. To evaluate whether each statement is true or false, we need to substitute the given values of w into the expression and determine if the product is between the given ranges. Let's go through each statement:
- Statement: The product is between 0 and 7 when w = , because is greater than 0 and less than 1.
- Substituting w = into the expression, we have 7 x = . Since is greater than 0 and less than 1, the product is indeed between 0 and 7. Therefore, the statement is true.
- Statement: The product is between 0 and 7 when w = , because is greater than 1 and less than 2.
- Substituting w = into the expression, we have 7 x = . Since is greater than 1 and less than 2, the product is not between 0 and 7. Therefore, the statement is false.
- Statement: The product is between 7 and 14 when w = , because is greater than 1 and less than 2.
- Substituting w = into the expression, we have 7 x = . Since is greater than 1 and less than 2, the product is indeed between 7 and 14. Therefore, the statement is true.
- Statement: The product is between 7 and 14 when w = , because is greater than 1 and less than 2.
- Substituting w = into the expression, we have 7 x = . Since is greater than 1 and less than 2, the product is indeed between 7 and 14. Therefore, the statement is true.