36 pencils in equal groups? Select THREE.
- A. 3
- B. 4
- C. 5
- D. 6
- E. 8
Correct Answer & Rationale
Correct Answer: A,B,D
To determine how many equal groups can be formed from 36 pencils, we need to identify the factors of 36. Option A (3) is valid because 36 ÷ 3 = 12, resulting in 12 pencils per group. Option B (4) is also correct since 36 ÷ 4 = 9, yielding 9 pencils per group. Option D (6) works as well, as 36 ÷ 6 = 6, giving 6 pencils per group. Options C (5) and E (8) are incorrect because 36 is not divisible by 5 (36 ÷ 5 = 7.2, which is not a whole number) and 8 (36 ÷ 8 = 4.5, also not a whole number). Thus, only 3, 4, and 6 are valid factors of 36.
To determine how many equal groups can be formed from 36 pencils, we need to identify the factors of 36. Option A (3) is valid because 36 ÷ 3 = 12, resulting in 12 pencils per group. Option B (4) is also correct since 36 ÷ 4 = 9, yielding 9 pencils per group. Option D (6) works as well, as 36 ÷ 6 = 6, giving 6 pencils per group. Options C (5) and E (8) are incorrect because 36 is not divisible by 5 (36 ÷ 5 = 7.2, which is not a whole number) and 8 (36 ÷ 8 = 4.5, also not a whole number). Thus, only 3, 4, and 6 are valid factors of 36.
Other Related Questions
(2x+3y-7)-(2x-3y-8)?
- A. 1
- B. -15
- C. 6y+1
- D. 6y-15
Correct Answer & Rationale
Correct Answer: C
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
Square side 5(1/2)cm. Area?
Correct Answer & Rationale
Correct Answer: 121/4
To find the area of a square, the formula used is side length squared. Here, the side length is 5(1/2) cm, which converts to 5.5 cm or 11/2 cm. Squaring this value gives (11/2)² = 121/4 cm², confirming the correct area. The other options are incorrect because: - If calculated as 5 cm, the area would be 25 cm², neglecting the fractional part. - If 5.5 cm is incorrectly squared as 30.25 cm², it miscalculates the area. - Any other value derived from misinterpretation of the side length will not yield the correct area.
To find the area of a square, the formula used is side length squared. Here, the side length is 5(1/2) cm, which converts to 5.5 cm or 11/2 cm. Squaring this value gives (11/2)² = 121/4 cm², confirming the correct area. The other options are incorrect because: - If calculated as 5 cm, the area would be 25 cm², neglecting the fractional part. - If 5.5 cm is incorrectly squared as 30.25 cm², it miscalculates the area. - Any other value derived from misinterpretation of the side length will not yield the correct area.
Which student wrote the estimate closest to 1,592 + 8?
- A. Isabella
- B. Jayden
- C. Michael
- D. Sarah
Correct Answer & Rationale
Correct Answer: A
Isabella's estimate of 1,592 + 8 is 1,600, which is closest to the actual sum. This estimation rounds 1,592 to 1,590 and adds 10 for simplicity, yielding 1,600. Jayden likely underestimated or rounded incorrectly, resulting in a less accurate estimate. Michael may have rounded too far or added an incorrect value, leading to a larger discrepancy. Sarah's estimate might not have accounted properly for the addition, causing it to stray further from the actual result. Thus, Isabella’s approach demonstrates the most accurate estimation strategy.
Isabella's estimate of 1,592 + 8 is 1,600, which is closest to the actual sum. This estimation rounds 1,592 to 1,590 and adds 10 for simplicity, yielding 1,600. Jayden likely underestimated or rounded incorrectly, resulting in a less accurate estimate. Michael may have rounded too far or added an incorrect value, leading to a larger discrepancy. Sarah's estimate might not have accounted properly for the addition, causing it to stray further from the actual result. Thus, Isabella’s approach demonstrates the most accurate estimation strategy.
Measure changed?
- A. Mean
- B. Median
- C. Mode
- D. Range
Correct Answer & Rationale
Correct Answer: A
The mean is sensitive to changes in data values, as it considers all values in a dataset. When any value changes, the mean will adjust accordingly, reflecting the new average. The median, on the other hand, represents the middle value and is only affected if the change impacts the central position of the dataset. The mode, being the most frequently occurring value, is not influenced by changes in other data points unless the frequency of occurrence alters. Lastly, the range measures the difference between the highest and lowest values, which may not change if the data alteration occurs within the existing range.
The mean is sensitive to changes in data values, as it considers all values in a dataset. When any value changes, the mean will adjust accordingly, reflecting the new average. The median, on the other hand, represents the middle value and is only affected if the change impacts the central position of the dataset. The mode, being the most frequently occurring value, is not influenced by changes in other data points unless the frequency of occurrence alters. Lastly, the range measures the difference between the highest and lowest values, which may not change if the data alteration occurs within the existing range.