Thanks for uploading the image! I can help you solve the problems shown on the worksheet. Let me break them down and provide detailed solutions.

Problem 9:

A chemical dissolves at a rate of $0.984$ grams per second. The chemical has a weight of $18.75$ grams. Which equation represents $t$, the number of seconds it takes for the chemical to dissolve?

Solution: The chemical is dissolving at a constant rate of $0.984$ grams per second. To find the time $t$, you divide the total weight ($18.75$) by the rate ($0.984$): $t = \frac{18.75}{0.984}$ The equation that matches this is: $\boxed{D: \, 18.75 \div 0.984 = t}$

Problem 10:

Eriko wants to save $650. He has $125 and plans to save $17.50 each month. Write an equation to determine $x$, the number of months it will take Eriko to save $650.

Solution: Eriko starts with $125 and saves an additional $17.50 per month. The total amount saved is represented as: $125 + 17.5x$ We set this equal to $650 to find $x$: $125 + 17.5x = 650$ This is the required equation: $\boxed{125 + 17.5x = 650}$

Problem 11:

Armand is participating in a 7-day hike. The table shows the distance he travels over the first 4 days:

The entire hike is more than 50 miles. Write an inequality to represent $x$, the number of miles he must travel each day to finish the hike.

Solution: First, calculate the total distance Armand has already traveled in the first 4 days: $5.8 + 12.1 + 8.9 + 10.5 = 37.3 \, \text{miles.}$ He needs to hike more than 50 miles total, so the remaining distance he must hike is: $50 - 37.3 = 12.7 \, \text{miles.}$ If $x$ is the number of miles he must travel each of the remaining 3 days, the inequality is: $3x > 12.7$ Divide both sides by 3 to solve for $x$: $x > 4.23 \, \text{miles.}$ The inequality is: $\boxed{x > 4.23}$

Problem 12:

Yesenia wants to run more than 15 miles in 6 days. On the first day, she ran 2.5 miles. Write an inequality to represent how many more miles ($x$) Yesenia needs to run each day.

Solution: Yesenia already ran 2.5 miles, so the remaining distance she needs to run is: $15 - 2.5 = 12.5 \, \text{miles.}$ If $x$ is the number of miles she runs per day for the next 5 days, the inequality is: $5x > 12.5$ Divide both sides by 5: $x > 2.5$ The inequality is: $\boxed{x > 2.5}$

Let me know if you'd like a step-by-step breakdown of any solution or if you have more questions!

Follow-Up Questions:

1. Can you solve Problem 9 by plugging in values to confirm the correct equation?
2. How would the equation in Problem 10 change if Eriko already had $200 instead of $125?
3. What would happen to Armand’s inequality in Problem 11 if the total hike was 60 miles instead of 50?
4. In Problem 12, how would the inequality change if Yesenia ran 5 miles on the first day instead of 2.5?
5. Can you graph the inequality $5x > 12.5$ from Problem 12 on a number line?

Tip:

When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number!