The U.S. Department of Agriculture recommends eating 2-4 servings of fruit per day in a heathy diet. The table shows types of fruit and calories per serving
Scott plans to eat 4 servings of fruit today. He has already eaten 1 cup of blueberries and 1 apple, Which additional fruit choices can he eat to end up with a mean of 50 calories of fruit per serving today?
- A. 1 plum and 1 tangerine
- B. 1 banana and 1 mandarin orange
- C. 1 cup of blueberries and 1 banana
- D. 1 apple and 1 plum
Correct Answer & Rationale
Correct Answer: A
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
Other Related Questions
What is the value of x^3 - 2y + 3 if x = -5 and y = -2?
Correct Answer & Rationale
Correct Answer: A
To find the value of \( x^3 - 2y + 3 \) when \( x = -5 \) and \( y = -2 \), substitute the values into the expression. Calculating \( x^3 \): \[ (-5)^3 = -125 \] Calculating \( -2y \): \[ -2(-2) = 4 \] Now, substituting these values into the expression: \[ -125 + 4 + 3 = -118 \] Thus, the value of the expression is \(-118\), corresponding to option A. Other options are incorrect due to miscalculations in either \( x^3 \), \( -2y \), or the final sum, leading to values that do not match the correct result of \(-118\).
To find the value of \( x^3 - 2y + 3 \) when \( x = -5 \) and \( y = -2 \), substitute the values into the expression. Calculating \( x^3 \): \[ (-5)^3 = -125 \] Calculating \( -2y \): \[ -2(-2) = 4 \] Now, substituting these values into the expression: \[ -125 + 4 + 3 = -118 \] Thus, the value of the expression is \(-118\), corresponding to option A. Other options are incorrect due to miscalculations in either \( x^3 \), \( -2y \), or the final sum, leading to values that do not match the correct result of \(-118\).
What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?
- A. y=5x+3
- B. y=5x-3
- C. y=5x-17
- D. y=5x+17
Correct Answer & Rationale
Correct Answer: C
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
Tina Is designing a cabin. One of her plans for the cabin is a rectangle twice as long as it is wide, with 10 feet (ft) of the length reserved for the Kitchen and the bathroom. The diagram shows this basic plan. Tina wants the area of the main room to be 300 square feet. Which equation can be used to find x, the width, in feet, of the main room?
- A. 2x^2 + 10x - 300 = 0
- B. 2x^2 - 10x - 300 = 0
- C. 2x^2 - 20x - 300 = 0
- D. 2x^2 + 20x - 300 = 0
Correct Answer & Rationale
Correct Answer: B
To determine the width \( x \) of the main room, we start with the area formula for a rectangle: Area = Length × Width. The cabin's length is twice the width, so it can be expressed as \( 2x \). Since 10 ft is allocated for the kitchen and bathroom, the length of the main room is \( 2x - 10 \). The equation for the area of the main room is therefore \( (2x - 10)x = 300 \), which simplifies to \( 2x^2 - 10x - 300 = 0 \), matching option B. Option A incorrectly adds \( 10x \) instead of subtracting, leading to an incorrect area calculation. Option C miscalculates the length by subtracting 20 instead of 10, while option D incorrectly adds 20, which does not reflect the reserved space. Thus, only option B accurately represents the relationship between length, width, and area.
To determine the width \( x \) of the main room, we start with the area formula for a rectangle: Area = Length × Width. The cabin's length is twice the width, so it can be expressed as \( 2x \). Since 10 ft is allocated for the kitchen and bathroom, the length of the main room is \( 2x - 10 \). The equation for the area of the main room is therefore \( (2x - 10)x = 300 \), which simplifies to \( 2x^2 - 10x - 300 = 0 \), matching option B. Option A incorrectly adds \( 10x \) instead of subtracting, leading to an incorrect area calculation. Option C miscalculates the length by subtracting 20 instead of 10, while option D incorrectly adds 20, which does not reflect the reserved space. Thus, only option B accurately represents the relationship between length, width, and area.
How many more tickets did Larry buy than Jim?
- A. 3
- B. 12
- C. 6
- D. 1
Correct Answer & Rationale
Correct Answer: C
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.