the circumference of a circle is 120 millimeters. Which of the following inqualities is true for d, the diameter of the circle measured in millimeters? A. 10<d<20

B. 30<d<40
C. 50<d<60
D. 70<d<80

pi is about 3, so d is about 120/3 or 40.

But, pi is slightly larger than 3, so d is slightly smaller than 40.

(B)

To determine the correct inequality for the diameter of the circle, we need to use the formula for the circumference of a circle in terms of its diameter:

C = πd,

where C is the circumference and d is the diameter.

Given that the circumference is 120 millimeters:

120 = πd.

Now, let's solve for d by dividing both sides of the equation by π:

d = 120/π.

To approximate this value, we need to use an estimation for the value of π. Let's use the commonly used approximation, π ≈ 3.14:

d ≈ 120/3.14.

Calculating this, we find:

d ≈ 38.22.

Therefore, the value of d, the diameter of the circle, is approximately 38.22 millimeters.

Now let's evaluate the given inequalities to find which one is true:

A. 10 < d < 20

Substituting our value of d, we have:

10 < 38.22 < 20

This statement is false.

B. 30 < d < 40

Substituting the value of d, we have:

30 < 38.22 < 40

This statement is true.

C. 50 < d < 60

Substituting the value of d, we have:

50 < 38.22 < 60

This statement is false.

D. 70 < d < 80

Substituting the value of d, we have:

70 < 38.22 < 80

This statement is false.

Therefore, the correct inequality for d, the diameter of the circle, is:

B. 30 < d < 40.