If an item regularly costs d dollars and is discounted 12 percent, which of the following represents the discounted price in dollars?
- A. 0.12d
- B. 0.88d
- C. 1.12d
- D. d-0.12
Correct Answer & Rationale
Correct Answer: B
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
Other Related Questions
Which of the following is a factor of u²+uv-2v²?
- A. (u-v)
- B. (2u-v)
- C. (u-2v)
- D. (u+v)
Correct Answer & Rationale
Correct Answer: C
To determine the factors of \( u^2 + uv - 2v^2 \), we can factor the expression. Option C, \( (u - 2v) \), is a valid factor. When we perform polynomial long division or synthetic division using \( (u - 2v) \), we find that it divides evenly, confirming it as a factor. Option A, \( (u - v) \), does not satisfy the factorization, as substituting \( v \) does not yield a zero remainder. Option B, \( (2u - v) \), also fails to factor the expression correctly, leading to a non-zero remainder upon division. Option D, \( (u + v) \), similarly does not yield a zero remainder, confirming it is not a factor. Thus, only \( (u - 2v) \) is a valid factor of the expression.
To determine the factors of \( u^2 + uv - 2v^2 \), we can factor the expression. Option C, \( (u - 2v) \), is a valid factor. When we perform polynomial long division or synthetic division using \( (u - 2v) \), we find that it divides evenly, confirming it as a factor. Option A, \( (u - v) \), does not satisfy the factorization, as substituting \( v \) does not yield a zero remainder. Option B, \( (2u - v) \), also fails to factor the expression correctly, leading to a non-zero remainder upon division. Option D, \( (u + v) \), similarly does not yield a zero remainder, confirming it is not a factor. Thus, only \( (u - 2v) \) is a valid factor of the expression.
If the combined amount of donations collected by Kevin, Fran, and Brooke exceeded the amount Lamar collected by $250, what was the total amount of donations collected by all five club members?
- A. $500
- B. $1,200
- C. $2,500
- D. $3,200
Correct Answer & Rationale
Correct Answer: C
To determine the total amount of donations collected by all five club members, we start with the information that the combined donations of Kevin, Fran, and Brooke exceeded Lamar's by $250. If we denote Lamar's donations as \( L \), then the amount collected by Kevin, Fran, and Brooke is \( L + 250 \). Thus, the total donations from all five members can be expressed as \( L + (L + 250) = 2L + 250 \). To find a plausible total, we consider the options. - A: $500 is too low, as it doesn't allow for both \( L \) and the excess amount. - B: $1,200 also falls short since it would imply \( L \) is negative. - D: $3,200 would require \( L \) to be too high, exceeding reasonable donation limits. C: $2,500 fits perfectly, allowing \( L \) to be $1,125, which is a feasible figure. Therefore, the total amount is logically $2,500.
To determine the total amount of donations collected by all five club members, we start with the information that the combined donations of Kevin, Fran, and Brooke exceeded Lamar's by $250. If we denote Lamar's donations as \( L \), then the amount collected by Kevin, Fran, and Brooke is \( L + 250 \). Thus, the total donations from all five members can be expressed as \( L + (L + 250) = 2L + 250 \). To find a plausible total, we consider the options. - A: $500 is too low, as it doesn't allow for both \( L \) and the excess amount. - B: $1,200 also falls short since it would imply \( L \) is negative. - D: $3,200 would require \( L \) to be too high, exceeding reasonable donation limits. C: $2,500 fits perfectly, allowing \( L \) to be $1,125, which is a feasible figure. Therefore, the total amount is logically $2,500.
Which equation is a correct way to calculate x?
- A. sin x=5,000 /7,000
- B. sin x= 7,000 /5,000
- C. tan x= 5,000/7,000
- D. tan x=7,000/5,000
Correct Answer & Rationale
Correct Answer: C
To solve for \( x \), the correct relationship involves the tangent function, as \( \tan \) is defined as the ratio of the opposite side to the adjacent side in a right triangle. Option C, \( \tan x = \frac{5,000}{7,000} \), accurately represents this ratio. Option A misapplies the sine function, which should represent the ratio of the opposite side to the hypotenuse, not the adjacent side. Similarly, option B incorrectly uses sine but with the sides reversed, leading to an inaccurate representation. Option D misuses tangent, suggesting the opposite and adjacent sides are swapped, which does not align with the definition of tangent. Thus, only option C correctly applies the tangent function to find \( x \).
To solve for \( x \), the correct relationship involves the tangent function, as \( \tan \) is defined as the ratio of the opposite side to the adjacent side in a right triangle. Option C, \( \tan x = \frac{5,000}{7,000} \), accurately represents this ratio. Option A misapplies the sine function, which should represent the ratio of the opposite side to the hypotenuse, not the adjacent side. Similarly, option B incorrectly uses sine but with the sides reversed, leading to an inaccurate representation. Option D misuses tangent, suggesting the opposite and adjacent sides are swapped, which does not align with the definition of tangent. Thus, only option C correctly applies the tangent function to find \( x \).
What is the range of her scores?
- A. 100
- B. 120
- C. 440
- D. 2,250
Correct Answer & Rationale
Correct Answer: B
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.