Question

for each scenario, choose the best statement.
scenarios\tstatements
(a) the company loses 13 employees and then gains 0 employees.\tthe company’s size is larger.
\tthe company’s size is smaller.
\tthe company’s size is the same.
(b) the temperature rises 5 °f and then drops 5 °f.\tthe temperature is higher than its beginning value.
\tthe temperature is lower than its beginning value.
\tthe temperature is 0 °f from its beginning value.
(c) a hot air balloon goes down 30 feet and then up 30 feet.\tthe balloon is above its initial height.
\tthe balloon is below its initial height.
\tthe balloon is at its initial height.

Explanation:

Part (a)

Step 1: Analyze the change

The company loses 13 employees (a decrease) and then gains 0 employees (no change). So the net change is \(-13 + 0=- 13\) (or we can think in terms of size: losing employees makes the size smaller, and gaining 0 doesn't change that).

Step 2: Evaluate the statements

• "The company’s size is larger" is wrong because we lost employees.
• "The company’s size is smaller" is correct as we lost 13 employees and gained none.
• "The company’s size is the same" is wrong because we had a loss.

Part (b)

Step 1: Analyze the temperature change

The temperature rises \(5^{\circ}\text{F}\) (an increase) and then drops \(5^{\circ}\text{F}\) (a decrease). The net change is \(+ 5-5 = 0\) from the beginning value.

Step 2: Evaluate the statements

• "The temperature is higher than its beginning value" is wrong because the rise and drop cancel.
• "The temperature is lower than its beginning value" is wrong for the same reason.
• "The temperature is \(0^{\circ}\text{F}\) from its beginning value" is correct (net change is 0).

Part (c)

Step 1: Analyze the height change

The balloon goes down 30 feet (a decrease) and then up 30 feet (an increase). The net change is \(-30 + 30=0\) from the initial height.

Step 2: Evaluate the statements

• "The balloon is above its initial height" is wrong because the down and up cancel.
• "The balloon is below its initial height" is wrong for the same reason.
• "The balloon is at its initial height" is correct (net change is 0).

Answer:

(a) The company’s size is smaller.
(b) The temperature is \(0^{\circ}\text{F}\) from its beginning value.
(c) The balloon is at its initial height.