On an average weekend, 7(4) people visit Times Square and 7(6) people visit the Great Wall of China. On an average weekend, how many times more people visit the Great Wall of China than Times Square?(1 point)

Responses

70 times more people visit The Great Wall
70 times more people visit The Great Wall

14 times more people visit The Great Wall
14 times more people visit The Great Wall

49 times more people visit The Great Wall
49 times more people visit The Great Wall

24 times more people visit The Great Wall

A student simplified this expression: 3(3)⋅3(−2)(3(6))(2)
using these steps:

Step 1: 3(−6)/3(12)

Step 2: 1/3(6)⋅3(12)

Step 3: 1/3(18)

Which of these steps contains a mistake from the previous step?

(1 point)
Responses

There are no mistakes. The answer is correct.
There are no mistakes. The answer is correct.

Step 1 had the mistake. Correct answer to this step is 31312
Step 1 had the mistake. Correct answer to this step is the fraction with numerator 3 to the 1th power and denominator 3 to the 12th power

Step 2 had the mistake. Correct answer to this step is 36
Step 2 had the mistake. Correct answer to this step is 3 to the 6th power

Step 3 had the mistake. Correct answer to this step is 136

1 answer

To solve the first question regarding the average number of visitors to Times Square and the Great Wall of China:

  1. Calculate the average number of visitors to Times Square: \[ 7(4) = 7 \times 4 = 28 \] So, 28 people visit Times Square on average.

  2. Calculate the average number of visitors to the Great Wall of China: \[ 7(6) = 7 \times 6 = 42 \] So, 42 people visit the Great Wall of China on average.

  3. To find out how many times more people visit the Great Wall than Times Square, we divide the number of visitors to the Great Wall by the number of visitors to Times Square: \[ \frac{42}{28} = 1.5 \]

  4. Since the question asks for how many times more people visit the Great Wall than Times Square, we can calculate: \[ \frac{42}{28} = 1.5 \text{ which is equivalent to saying } 1.5 = 1.5 \text{ times more than 28.} \] As "how many times more" typically asks for a count beyond the baseline, we state: \[ 1.5 - 1 = 0.5 + 1 = 1.5 \text{ or 50% more.} \]

  5. However, it appears the original phrasing and options do not align with the correct answer based on provided numbers. Thus the response may not be adequately listed. None of the provided options correctly represent the answer.

For the second question regarding the simplification of the expression \(3^{3} \cdot 3^{-2} \cdot 3^{6} \cdot 2\):

  1. Let's analyze Step 1: \[ 3^{3} \cdot 3^{-2} = 3^{3 - 2} = 3^{1} \] This step should be correct, but it seems it transformed into a fraction incorrectly.

  2. Step 2 contains: \[ \frac{1}{3^{6}} \cdot 3^{12} = 3^{12 - 6} = 3^{6} \] Which also seems to involve an error because the result should contain the powers of \(3\) without needing to go through excessive fractions.

  3. Step 3: \[ 1/3^{18} \text{ from } 3^{6} \] Is not accurate given the product seen before.

Conclusively:

The mistake occurred in Step 1 since it incorrectly turned the multiplication into a fraction rather than simplifying it directly. Thus:

Response: Step 1 had the mistake. Correct answer to this step is \(3^{1}\).