Question

The temperature at 6 A.M. is -14. The temperature increase an average of 3/4 each hour until noon, and then it drops an average of -1 1/4 each hour until 5 P.M.

Answer 1

The temperature starts at -14°F at 6 A.M., increases by 3/4°F per hour until noon, then decreases by -1 1/4°F per hour until 5 P.M. Statements (a), (b), and (c) are true; statements (d) and (e) are false.

Let's analyze each statement:

a. The change in the temperature from noon to 5 P.M. is -6 1/4°F.

- The temperature decreases by
`\(-1 (1)/(4)\)^\circ F` each hour from noon to 5 P.M.

- The total change is
`\(-1 (1)/(4) * 5 = -6 (1)/(4)\)^\circ F.`

- So, statement (a) is true.

b. At noon, the temperature is -9 1/2°F.

- The temperature increases by
`\((3)/(4)\)^\circ F` each hour from 6 A.M. to noon.

- The total increase is
`\((3)/(4) * 6 = 4 (1)/(2)\)^\circ F.`

- So, at noon, the temperature is
`\(-14 + 4 (1)/(2) = -9 (1)/(2)\)^\circ F.`

- Therefore, statement (b) is true.

c. The temperature at 5 P.M. is -15 3/4°F.

- The temperature decreases by
`\(-1 (1)/(4)\)^\circ F` each hour from noon to 5 P.M.

- The total decrease is
`\(-1 (1)/(4) * 5 = -6 (1)/(4)\)^\circ F.`

- So, the temperature at 5 P.M. is
`\(-9 (1)/(2) - 6 (1)/(4) = -15 (3)/(4)\)^\circ F.`

- Statement (c) is true.

d. The total change in the temperature from 6 A.M. to 5 P.M. is -2 1/4°F.

- The temperature increases by
`\((3)/(4)\)^\circ F` each hour from 6 A.M. to noon.

- The total increase is
`\((3)/(4) * 6 = 4 (1)/(2)\)^\circ F.`

- The temperature decreases by
`\(-1 (1)/(4)\)^\circ F` each hour from noon to 5 P.M.

- The total decrease is
`\(-1 (1)/(4) * 5 = -6 (1)/(4)\)^\circ F.`

- The net change is
`\(4 (1)/(2) - 6 (1)/(4) = -1 (3)/(4)\)^\circ F.`

- So, statement (d) is false.

e. The change in the temperature from 6 A.M. to noon is
`\((1)/(8)\)^\circ F`.

- The temperature increases by
`\((3)/(4)\)^\circ`F each hour from 6 A.M. to noon.

- The total increase is
`\((3)/(4) * 6 = 4 (1)/(2)\)^\circ`F.

- So, statement (e) is false.

In summary, statements (a), (b), and (c) are true, while statements (d) and (e) are false.

The probable question may be:

The national weather service is recording the temperatures on a cold day. The temperature at 6 A.M. is -14°F. The temperature increases an average of 3/4F each hour until noon, and then it drops an average of -1 1/4F each hour untlil . 5 P.M. Which of the following statements are true? Select all that apply.

a. The change in the temperature from noon to 5 P.M. is -6 1/4F.

b. At noon, the temperature is -9 1/2F.

c. The temperature at 5 P.M. is -15 3/4F.

d. The total change in the temperature from 6 A.M. to 5 P.M. is -2 1/4F.

e. The change in the temperature from 6 A.M. to noon is 1/8F.