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Sagot :
Let's carefully analyze the problem step-by-step to identify if Mariah made a mistake and, if so, what that mistake is.
### Step 1: Identify the Numbers Greater Than 7
The spinner has the numbers 1 through 10. We need to figure out how many of these numbers are greater than 7. The numbers greater than 7 are:
- 8
- 9
- 10
Thus, there are 3 numbers greater than 7.
### Step 2: Calculate the Probability
Mariah needs to calculate the probability of the spinner landing on a number greater than 7. The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore,
[tex]\[ P(\text{number greater than 7}) = \frac{\text{Number of numbers greater than 7}}{\text{Total number of sections}} = \frac{3}{10} \][/tex]
### Step 3: Determine the Expected Number of Spins
Mariah wants to know how many times the spinner will land on a number greater than 7 out of 250 spins. The expected number of spins for a particular outcome is calculated using the formula:
[tex]\[ \text{Expected number of spins} = P(\text{number greater than 7}) \times \text{Total number of spins} \][/tex]
Substituting the numbers we have:
[tex]\[ \text{Expected number of spins} = \left(\frac{3}{10}\right) \times 250 = 0.3 \times 250 = 75 \][/tex]
### Analysis of Mariah's Work
Mariah's calculation is shown as:
[tex]\[ P(\text{number greater than 7}) = \frac{\text{Number of numbers greater than 7}}{\text{Total number of sections}} \times \text{Number of spins} = \frac{4}{10}(250) = 100 \][/tex]
### Step 4: Identify the Mistake
The correct number of numbers greater than 7 is 3, not 4. Mariah mistakenly used 4 as the numerator in her probability calculation. Therefore, her mistake is that she should have used 3 in the numerator because there are 3 numbers greater than 7: 8, 9, and 10.
### Conclusion
The correct options given the mistake analysis are:
- Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.
So, the correct identification of Mariah's mistake is:
Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.
### Step 1: Identify the Numbers Greater Than 7
The spinner has the numbers 1 through 10. We need to figure out how many of these numbers are greater than 7. The numbers greater than 7 are:
- 8
- 9
- 10
Thus, there are 3 numbers greater than 7.
### Step 2: Calculate the Probability
Mariah needs to calculate the probability of the spinner landing on a number greater than 7. The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore,
[tex]\[ P(\text{number greater than 7}) = \frac{\text{Number of numbers greater than 7}}{\text{Total number of sections}} = \frac{3}{10} \][/tex]
### Step 3: Determine the Expected Number of Spins
Mariah wants to know how many times the spinner will land on a number greater than 7 out of 250 spins. The expected number of spins for a particular outcome is calculated using the formula:
[tex]\[ \text{Expected number of spins} = P(\text{number greater than 7}) \times \text{Total number of spins} \][/tex]
Substituting the numbers we have:
[tex]\[ \text{Expected number of spins} = \left(\frac{3}{10}\right) \times 250 = 0.3 \times 250 = 75 \][/tex]
### Analysis of Mariah's Work
Mariah's calculation is shown as:
[tex]\[ P(\text{number greater than 7}) = \frac{\text{Number of numbers greater than 7}}{\text{Total number of sections}} \times \text{Number of spins} = \frac{4}{10}(250) = 100 \][/tex]
### Step 4: Identify the Mistake
The correct number of numbers greater than 7 is 3, not 4. Mariah mistakenly used 4 as the numerator in her probability calculation. Therefore, her mistake is that she should have used 3 in the numerator because there are 3 numbers greater than 7: 8, 9, and 10.
### Conclusion
The correct options given the mistake analysis are:
- Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.
So, the correct identification of Mariah's mistake is:
Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.
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