Here are the answers to your questions:
Question 1: To find how many slices of the blueberry pie they ate, we can set up a proportion. They ate 3/5 of the apple pie. The same fraction of the blueberry pie, which has 10 slices, can be calculated:
\[ \text{Slices of blueberry pie eaten} = \frac{3}{5} \times 10 = 6 \text{ slices} \]
Correct Response: 6 slices
Question 2: We are looking for fractions equivalent to 27, which can be written as 27/1. The two equivalent fractions would be those that have the same ratio:
- \(\frac{8}{28} = \frac{2}{7} \rightarrow \text{not equivalent}\)
- \(\frac{4}{7} \rightarrow \text{not equivalent}\)
- \(\frac{10}{35} = \frac{2}{7} \rightarrow \text{not equivalent}\)
- \(\frac{2}{14} = \frac{1}{7} \rightarrow \text{not equivalent}\)
None of these are equivalent fractions to 27. Please check for a possible missing fraction.
Question 3: To find which type of candle has the greatest ratio of fragrance to wax, you would need the actual ratios provided in the tables. As this information is not provided, I'm unable to determine the answer.
Correct Response: (Need data to confirm)
Question 4: The ratios can be calculated based on the given data. The only one that seems out of line given the progression would be 80 servings = 8 pounds because:
- 20/2 = 10, 40/6 = 6.67, 80/8 = 10, but 120/12 = 10 indicating it’s consistent.
The potential error is with the 40 servings.
Correct Response: 40 servings
Question 5: This question references a table that is missing from your request, which is needed to determine which table has 70 as the missing value of x. Please provide that table.
Question 6: To solve this, we can establish a ratio between kilometers and miles. The given ratios are:
- 2 km = 1.2 miles
- 7 km = 4.2 miles
- Thus, 20 km = x miles, needs calculation through a scaling method or direct ratio setup.
Using the earlier ratio:
- \(\frac{2}{1.2} = \frac{20}{x} \rightarrow x = \frac{20*1.2}{2} = 12\)
- For 30 km: \(\frac{2}{1.2} = \frac{30}{y} \rightarrow y = \frac{30*1.2}{2} = 18\)
Correct Values:
- 20 km: 12 miles
- 30 km: 18 miles
Question 7: If 200 students are 40% of the total, we can set up the equation: Let x be the total number of students. \[ 0.4x = 200 \Rightarrow x = \frac{200}{0.4} = 500 \]
Correct Response: 500 students
Question 8: If 120 shirts represent 30% of the total, the total sales can be calculated by: \[ \frac{120}{0.3} = 400 \] The total sales will be greater than 120 shirts.
Correct Responses:
- The band sold 400 shirts.
- The total sales will be greater than 120 shirts.
Question 9: If 13% of the plates arrive broken and 117 plates arrived broken, we set up the equation: Let x = total plates shipped. \[ 0.13x = 117 \Rightarrow x = \frac{117}{0.13} = 900 \]
Correct Response: 900 plates
Question 10: Using the progression of feet from miles:
- 1 mile = 5280 feet
- 5 miles = 5280 * 5 = 26,400 feet
- 15 miles = 5280 * 15 = 79,200 feet
- 42,240 feet would be 8 miles.
Correct Values:
- 5 miles: 26,400 feet
- 15 miles: 79,200 feet
- 8 miles: 42,240 feet
Question 11: To identify the relationship, let's check the stitches and length: The consistent relationship appears to be that the number of stitches increases by a factor of 5 for every increase in length of 1 cm.
Correct Response: The number of stitches is 5 times the length.
Question 12: Let's check the ratios:
- Row 1: 5/2, Row 2: 10/4 (5/2), Row 3: 15/7 (not in the same pattern), Row 4: 20/8 (5/2).
Row 3 does not fit the pattern. To maintain the ratio of 5/2, you would need:
- \(\frac{15}{x} = \frac{5}{2} \rightarrow 5x = 30 \rightarrow x = 6\) cups of oats.
Correct Response: Row 3, 6 cups of oats.
Question 13: Comparing shaded areas can determine equivalent fractions—based on how many sections are shaded compared to total sections. If the fractions in the diagrams do not reflect equality, the statement indicating the difference is true based on the values given.
Correct Response: The fractions are not equivalent. The top diagram represents 1 third, and the bottom diagram represents 2 thirds.
Make sure to verify or provide additional information for the questions that required more context or data!
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