We are looking for the value of \(n\) when the term's value is 49. Set up the equation: \(3n - 5 = 49\). Add 5 to both sides: \(3n = 54\). Divide by 3: \(n = 18\). So, the 18th term in the sequence has a value of 49. Distractor C is the intermediate value of \(3n\). Distractor D is the value of the 49th term (\(3(49) - 5 = 147 - 5 = 142\)). Distractor A is a result of an estimation or calculation error.

Let \(w\) be the width. The length \(l\) is \(2w + 3\). The formula for the perimeter of a rectangle is \(P = 2(l + w)\). Substitute the given values and expressions: \(54 = 2((2w + 3) + w)\). Simplify the expression inside the parentheses: \(54 = 2(3w + 3)\). Distribute the 2: \(54 = 6w + 6\). Subtract 6 from both sides: \(48 = 6w\). Divide by 6: \(w = 8\). The width is 8 cm. Distractor B (17) comes from using \(l + w = 54\) instead of \(2(l + w) = 54\). Distractor C (19) is the length. Distractor D (25.5) comes from solving \(2w + 3 = 54\) directly.

First, set up the equation to find \(k\): \(\frac{k}{4} + 9 = 15\). Subtract 9 from both sides: \(\frac{k}{4} = 6\). Multiply both sides by 4: \(k = 24\). The question asks for the value of \(k - 2\), not \(k\). So, substitute the value of \(k\): \(24 - 2 = 22\). Distractor B is the value of \(k\). Distractor C results from misinterpreting the order of operations as \(\frac{k+9}{4}=15\), which gives \(k+9=60\) and \(k=51\), so \(k-2=49\). Distractor D results from adding 9 instead of subtracting: \(\frac{k}{4}=15+9=24\), so \(k=96\) and \(k-2=94\).

Let the three consecutive odd integers be \(n\), \(n+2\), and \(n+4\). Their sum is \(n + (n+2) + (n+4) = 87\). Combining like terms gives \(3n + 6 = 87\). Subtracting 6 from both sides gives \(3n = 81\). Dividing by 3 gives \(n = 27\). This is the smallest of the three integers. The integers are 27, 29, and 31. The largest is 31. Distractor A is the smallest integer. Distractor B is the middle integer (which is also the average, \(87 \div 3 = 29\)). Distractor C is incorrect because the integer must be odd.

First, find the value of \(p\). The problem states \(\frac{p}{-6} = 8\). To solve for \(p\), multiply both sides by -6: \(p = 8 \times(-6) = -48\). Next, divide \(p\) by 4: \(\frac{-48}{4} = -12\). The final result is -12. Distractor C is the value of \(p\). Distractor A is the result of a sign error when finding \(p\) (if \(p=48\)) or when performing the final division. Distractor D does not follow from a likely calculation error.

The selling price is the original cost plus a 25% markup. This can be written as \(c + 0.25c = 300\), or \(1.25c = 300\). To find the original cost \(c\), divide the selling price by 1.25: \(c = 300 \div 1.25 = 240\). The original cost was $240. Distractor A is a common error where one finds 25% of the selling price (\(0.25 \times 300 = 75\)) and subtracts it from the selling price (\(300 - 75 = 225\)). Distractor D is another common error where one finds 25% of the cost and adds it to the selling price.

Substitute 86 for F in the formula: \(86 = \frac{9}{5}C + 32\). First, subtract 32 from both sides: \(86 - 32 = \frac{9}{5}C\), which simplifies to \(54 = \frac{9}{5}C\). To solve for C, multiply both sides by the reciprocal of \(\frac{9}{5}\), which is \(\frac{5}{9}\): \(C = 54 \times \frac{5}{9}\). This can be calculated as \((54 \div 9) \times 5 = 6 \times 5 = 30\). The temperature is 30°C. Distractor C is the intermediate result before multiplying by the reciprocal. Distractor D is the result of multiplying 54 by \(\frac{9}{5}\) instead of \(\frac{5}{9}\).

Let \(s\) be the length of each of the two equal sides. The base \(b\) is \(s + 6\). The perimeter is the sum of the three sides: \(s + s + b = 39\). Substitute the expression for \(b\): \(s + s + (s + 6) = 39\). Combine like terms: \(3s + 6 = 39\). Subtract 6 from both sides: \(3s = 33\). Divide by 3: \(s = 11\). This is the length of an equal side. The question asks for the length of the base, which is \(s + 6 = 11 + 6 = 17\) inches. Distractor A is the length of one of the equal sides. Distractors B and D are calculation errors.

First, set up the equation based on the information given: \(-3(n - 6) = 24\). To solve for \(n\), first divide both sides by -3: \(n - 6 = 24 \div(-3)\), which simplifies to \(n - 6 = -8\). Then, add 6 to both sides: \(n = -8 + 6\), which gives \(n = -2\). Therefore, the value in Column A is -2. The value in Column B is also -2. The two quantities are equal. A common mistake is a sign error in distribution (\(-3n - 18 = 24 \implies -3n = 42 \implies n = -14\), leading to B) or in solving (\(n - 6 = -8 \implies n = -14\), leading to B).

Let \(m\) be the total number of minutes. The cost is for the first minute plus the additional minutes. The cost of the additional minutes is \($1.24 - $0.20 = $1.04\). The number of additional minutes is the cost of additional minutes divided by the rate: \($1.04 \div $0.08 = 13\). These are the additional minutes. The total duration is the first minute plus the additional minutes: \(1 + 13 = 14\) minutes. Distractor B is the number of additional minutes, not the total duration. Distractor A is an estimation error. Distractor D is the result of dividing the total cost by the additional minute rate \($1.24 / 0.08 = 15.5\), which ignores the special rate for the first minute.