Which model represents a fraction less than Three-fifths? A circle divided into 5 equal parts. 4 parts are shaded. A circle divided into 5 equal parts. 2 parts are shaded. A circle divided into 5 equal parts. 6 parts are shaded. A circle divided into 10 equal parts. 8 parts are shaded.

The correct answer is:

A circle divided into 5 equal parts. 2 parts are shaded.

Step-by-step explanation:

To determine the fraction less than three-fifths, let us convert the word problems into figures and compare the values:

a) A circle divided into 5 equal parts. 4 parts are shaded (four-fifths)

b) A circle divided into 5 equal parts. 2 parts are shaded. (two-fifths)

c) A circle divided into 5 equal parts. 6 parts are shaded = (more than three-fifths)

d) A circle divided into 10 equal parts. 8 parts are shaded

Therefore, the fraction less than three-fifths = A circle divided into 5 equal parts. 2 parts are shaded. (two-fifths)

Amount of caffeine left after 5 hours = 36 mg

Step-by-step explanation:

We are told that the cup has 310 mg of caffeine originally.

Since it decreases by 35 percent or 0.35 each hour, it means that for each additional hour, the new amount of caffeine would be (1 - 0.35) x previous amount i.e. 0.65 x previous amount. Thus;

After 0 hour, we have; 310 mg

After 1 hour, we have; 310(0.65)

After 2 hours, we have; 310(0.65)(0.65)

After 3 hours, we have; 310(0.65)(0.65)(0.65)

We can see this follows a pattern of;

A(t) = 310(0.65)^(t)

Where;

A(t) is the amount left after t hours

And t is time t hours

Thus, amount left after 5 hours is;

A(5) = 310(0.65)^(5)

A(5) = 310 x 0.11603

A(5) ≈ 36 mg