Question

three softball players wrote down their batting average: - amy wrote 12 of 30 - sue wrote.34 - kit wrote \\(\frac{9}{21}\\) who is a better hitter? solve: \\(\frac{z}{4}+5 \geq 5.5\\) solve and graph the inequality on a number line: \\(-12 > g - 17\\) write an inequality that represents the graph below: graph omitted

Explanation:

First Problem: Who is a better hitter?

Step1: Calculate Amy's average

$\frac{12}{30} = 0.4$

Step2: Calculate Kit's average

$\frac{9}{21} \approx 0.429$

Step3: Compare all averages

Amy: $0.4$, Sue: $0.\overline{34} \approx 0.343$, Kit: $\approx0.429$
(Note: Correction: Kit's average is ~0.429 which is higher than Amy's 0.4, so Kit is the better hitter. Correction to Step3:

Step3: Compare all averages

Amy: $0.4$, Sue: $0.\overline{34} \approx 0.343$, Kit: $\approx0.429$. Kit has the highest average.)
Final correction to Answer: Kit is the better hitter.

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Second Problem: Solve $\frac{z}{4} + 5 \geq 5.5$

Step1: Subtract 5 from both sides

$\frac{z}{4} + 5 - 5 \geq 5.5 - 5$
$\frac{z}{4} \geq 0.5$

Step2: Multiply by 4 on both sides

$\frac{z}{4} \times 4 \geq 0.5 \times 4$
$z \geq 2$

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Third Problem: Solve $-12 > g - 17$ and graph

Step1: Add 17 to both sides

$-12 + 17 > g - 17 + 17$
$5 > g$ or $g < 5$

Step2: Graph instructions

Draw an open circle at 5 on the number line, then draw an arrow pointing left (towards smaller numbers) to represent all values less than 5.

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Fourth Problem: Write inequality for the graph

Answer:

Amy is the better hitter.