Question

If 4 < a <5 and 5 < b < 8, what are the possible values for a/b (a) between 5 and 8 (b) between 1 and 2 (c) between 0 and 2 4 5 (d) between - and 1 2 (e) cannot be determined

Answer 1

The possible values for a/b are between 0.5 and 1.

Step-by-step explanation:

The possible values for a/b within the given range can be found by substituting the values of a and b into the expression a/b. Given that 4 < a < 5 and 5 < b < 8, we can consider the extreme cases to determine the range of possible values.

(a) If a is at its maximum value (a = 5) and b is at its minimum value (b = 5), then the maximum value of a/b is 5/5 = 1.

(b) Similarly, if a is at its minimum value (a = 4) and b is at its maximum value (b = 8), then the minimum value of a/b is 4/8 = 0.5.

(c) For a/b to be between 0 and 2.45, both a and b must be within the range (0,2.45). As the given ranges for a and b do not intersect with this range, there are no possible values of a/b in this range.

(d) Similarly, for a/b to fall between -∞ and 1.2, both a and b must be within the range (-∞,1.2). Again, as the given ranges for a and b do not intersect with this range, there are no possible values of a/b in this range.

(e) Therefore, the possible values of a/b are between 0.5 and 1.