Red tides is a form of harmful algae that release toxins as it breaks down in the environment. A marine biologist is testing a new spray, composed of clay and water, hoping to kill the red tide that almost completely covers a beach in southern Floride. He applies the spray to a representative sample of 200 square feet of the beach. By thhe end of the week, 184 square feet of the beach is free of the red tide. Based on these results, and assuming the same general conditions, how much of the 10,000-squarefoot beach would still be covered by red tide if the spray had been used on the entire area?

Options

A. 800 sq ft
B. 920 sq ft
C. 8,000 sq ft
D. 9,200 sq ft

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the percentage of the area that is free of red tide.
The marine biologist applied the spray to a sample area of 200 square feet, and by the end of the week, 184 square feet was free of red tide.

\[ \text{Percentage of area free of red tide} = \left(\frac{184}{200}\right) \times 100 \]

### Step 2: Perform the calculation.
Calculating the percentage:

\[ \frac{184}{200} = 0.92 \]

Now, converting to percentage:

\[ 0.92 \times 100 = 92\% \]

### Step 3: Calculate the area free of red tide on the entire beach.
Now, we need to apply this percentage to the entire beach area of 10,000 square feet.

\[ \text{Area free of red tide} = 92\% \text{ of } 10,000 = \left(\frac{92}{100}\right) \times 10,000 \]

### Step 4: Perform the calculation.
Calculating the area:

\[ \left(\frac{92}{100}\right) \times 10,000 = 9200 \text{ square feet} \]

### Step 5: Calculate the area still covered by red tide.
To find out how much of the beach is still covered by red tide, we subtract the area that is free from red tide from the total area of the beach.

\[ \text{Area still covered by red tide} = 10,000 - 9200 \]

### Step 6: Perform the calculation.
Calculating the area still covered:

\[ 10,000 - 9200 = 800 \text{ square feet} \]

### Final Answer:
The area still covered by red tide is **800 square feet**.

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