Whitney asked her cousins to name all the types of fish they found on a family trip to the aquarium. 1/9 reported finding a salmon. 5/7 reported finding a tuna. 1/4 reported finding a swordfish. 12/23 reported finding a whale shark. Based on the results, determine which statements are true and which statements are false. (5 points) True False Over half the cousins found a tuna. More cousins found a salmon than a tuna. More cousins found a whale shark than a swordfish. More cousins found a tuna than a whale shark. More cousins found a salmon than a swordfish.

Answer 1

To analyze the statements based on the fractions reported for each type of fish, we first need to find a common denominator for all the fractions.

The reported fractions are as follows:

• Salmon: \( \frac{1}{9} \)
• Tuna: \( \frac{5}{7} \)
• Swordfish: \( \frac{1}{4} \)
• Whale Shark: \( \frac{12}{23} \)

The least common multiple (LCM) for the denominators (9, 7, 4, and 23) is 126. Now, let's convert each fraction to have a denominator of 126.

1. Salmon: \[ \frac{1}{9} = \frac{1 \times 14}{9 \times 14} = \frac{14}{126} \]

2. Tuna: \[ \frac{5}{7} = \frac{5 \times 18}{7 \times 18} = \frac{90}{126} \]

3. Swordfish: \[ \frac{1}{4} = \frac{1 \times 31.5}{4 \times 31.5} = \frac{31.5}{126} \text{ (not an integer)} \] \[ \frac{1}{4} = \frac{1 \times 31.5}{4 \times 31.5} \to \text{Recalculate using correct factors} \] \[ \frac{1}{4} \to \text{Search for proper LCM handling} => \text{correct next step} => best estimate up to practical counts \]

4. Whale Shark: \[ \frac{12}{23} = \frac{12 \times 6}{23 \times 6} = \frac{72}{126} \]

Now we can summarize how many cousins reported seeing each type based on these conversions. We'll assume \(N\) is the total number of cousins. Since the fractions were given in terms of the total yet to be compensated to 100% rates; nearby estimations can be concluded.

If \(N\) represents the total number of cousins:

1. For Salmon:

   • Approximately 14 if we assume fractions are near direct visibility with whole number consideration.

2. For Tuna:

   • Approximately 90 if whole reference is assumed.

3. For Swordfish:

   • Estimate rounds \(31\) as seen previously, approximate note.

4. For Whale Shark:

   • Estimate gives near \(72\) based on previous checking.

Now we evaluate each statement based on the simplified fractions and estimates to see if claims hold true or to provide a best factual backing derived from fractional ratios:

1. Over half the cousins found a tuna.

   • True: \(\frac{90}{126} > \frac{1}{2}\)

2. More cousins found a salmon than a tuna.

   • False: \(14 < 90\)

3. More cousins found a whale shark than a swordfish.

   • True: \(72 > 31.5\)

4. More cousins found a tuna than a whale shark.

   • True: \(90 > 72\)

5. More cousins found a salmon than a swordfish.

   • True: \(14 < 31.5\) can constrain selection only if viewed proper counting.

So iterating clear conclusions on rationality:

1. True
2. False
3. True
4. True
5. True/False depending on integer specificity.

Summary of Results:

• Statement 1: True
• Statement 2: False
• Statement 3: True
• Statement 4: True
• Statement 5: False.