Final answer:
The lower and upper bounds of the product of two numbers x and y, when each is rounded to the nearest integer, can be found by multiplying the lower and upper bounds of the individual numbers. The lower bound of xy is 101.75, and the upper bound is 126.75.
Step-by-step explanation:
To calculate the lower and upper bound of the product of two numbers x and y, when each is rounded to the nearest integer, we first must determine the ranges of x and y.
The number x, rounded to the nearest integer, is 6. This means the possible range for x is 5.5 to 6.5 because 5.5 rounds up to 6 and anything below would round down to 5, and 6.5 rounds down to 6, while anything above would round up to 7.
Similarly, for y which rounds to 19, the range is 18.5 to 19.5.
To find the lower bound of the product xy, we multiply the lower bounds of x and y, which gives us 5.5 × 18.5.
For the upper bound, we multiply the upper bounds of x and y: 6.5 × 19.5.
Thus, the lower bound for the product xy is 101.75, and the upper bound is 126.75.