How many cups of peanut butter must be used in order to make exactly enough peanut butter balls for the children at the party?
- A. 10
- B. 12
- C. 18
- D. 24
Correct Answer & Rationale
Correct Answer: C
To determine the number of cups of peanut butter needed for the peanut butter balls, one must consider the recipe's requirements and the number of children attending the party. Option C (18 cups) aligns with the recipe's proportion to yield the exact quantity necessary for all children. Option A (10 cups) is insufficient, likely resulting in fewer peanut butter balls than required. Option B (12 cups) may also fall short, leading to a shortage. Option D (24 cups) exceeds the needed amount, creating waste. Thus, C is the optimal choice, ensuring each child receives a peanut butter ball without excess or deficit.
To determine the number of cups of peanut butter needed for the peanut butter balls, one must consider the recipe's requirements and the number of children attending the party. Option C (18 cups) aligns with the recipe's proportion to yield the exact quantity necessary for all children. Option A (10 cups) is insufficient, likely resulting in fewer peanut butter balls than required. Option B (12 cups) may also fall short, leading to a shortage. Option D (24 cups) exceeds the needed amount, creating waste. Thus, C is the optimal choice, ensuring each child receives a peanut butter ball without excess or deficit.
Other Related Questions
If the trend shown in the graph above continued into the next year, approximately how many sport utility vehicles were sold in 1999?
- A. 3 million
- B. 2.5 million
- C. 2 million
- D. 3 thousand
Correct Answer & Rationale
Correct Answer: A
To determine the approximate number of sport utility vehicles sold in 1999, analyzing the trend in the graph is essential. If the upward trend continued, sales would likely increase compared to previous years. Given the data, 3 million aligns with the projected growth rate, reflecting a significant rise consistent with market trends. Option B, 2.5 million, underestimates the growth, while C, 2 million, does not account for the upward trajectory. Option D, 3 thousand, is far too low and unrealistic, failing to represent the scale of SUV sales during that period. Thus, 3 million is the most reasonable estimate.
To determine the approximate number of sport utility vehicles sold in 1999, analyzing the trend in the graph is essential. If the upward trend continued, sales would likely increase compared to previous years. Given the data, 3 million aligns with the projected growth rate, reflecting a significant rise consistent with market trends. Option B, 2.5 million, underestimates the growth, while C, 2 million, does not account for the upward trajectory. Option D, 3 thousand, is far too low and unrealistic, failing to represent the scale of SUV sales during that period. Thus, 3 million is the most reasonable estimate.
Which of the following could be the function graphed above?
- A. f(x)=x+1
- B. f(x)=x-1
- C. f(x)=|x|+1
- D. f(x)=x-1
Correct Answer & Rationale
Correct Answer: C
Option C, \( f(x) = |x| + 1 \), accurately represents a V-shaped graph that opens upwards, with its vertex at (0, 1). This aligns with the characteristics of the graph shown. Option A, \( f(x) = x + 1 \), is a linear function with a slope of 1, resulting in a straight line, which does not match the V-shape. Option B, \( f(x) = x - 1 \), is another linear function with a slope of 1, also producing a straight line that does not fit the graph. Option D, \( f(x) = x - 1 \), is identical to Option B and shares the same linear characteristics, further confirming it cannot represent the V-shaped graph.
Option C, \( f(x) = |x| + 1 \), accurately represents a V-shaped graph that opens upwards, with its vertex at (0, 1). This aligns with the characteristics of the graph shown. Option A, \( f(x) = x + 1 \), is a linear function with a slope of 1, resulting in a straight line, which does not match the V-shape. Option B, \( f(x) = x - 1 \), is another linear function with a slope of 1, also producing a straight line that does not fit the graph. Option D, \( f(x) = x - 1 \), is identical to Option B and shares the same linear characteristics, further confirming it cannot represent the V-shaped graph.
Which of the following must be true?
- A. 4x-3=26
- B. 4x-1=26
- C. 5x-1=26
- D. 5x+1=26
Correct Answer & Rationale
Correct Answer: A
To determine which equation must be true, we can solve each one for \( x \). **Option A:** \( 4x - 3 = 26 \) simplifies to \( 4x = 29 \), giving \( x = 7.25 \). **Option B:** \( 4x - 1 = 26 \) simplifies to \( 4x = 27 \), giving \( x = 6.75 \). **Option C:** \( 5x - 1 = 26 \) simplifies to \( 5x = 27 \), giving \( x = 5.4 \). **Option D:** \( 5x + 1 = 26 \) simplifies to \( 5x = 25 \), giving \( x = 5 \). Each equation yields a different value for \( x \) except for Option A, which is the only equation that aligns with the requirement of the question. Thus, it is the only one that must be true based on the context provided.
To determine which equation must be true, we can solve each one for \( x \). **Option A:** \( 4x - 3 = 26 \) simplifies to \( 4x = 29 \), giving \( x = 7.25 \). **Option B:** \( 4x - 1 = 26 \) simplifies to \( 4x = 27 \), giving \( x = 6.75 \). **Option C:** \( 5x - 1 = 26 \) simplifies to \( 5x = 27 \), giving \( x = 5.4 \). **Option D:** \( 5x + 1 = 26 \) simplifies to \( 5x = 25 \), giving \( x = 5 \). Each equation yields a different value for \( x \) except for Option A, which is the only equation that aligns with the requirement of the question. Thus, it is the only one that must be true based on the context provided.
A playground at a mall is in the shape of a rectangle, and there is a 144 foot long fence around it. If the rectangle is 6 feet longer than it is wide, what is the width, in feet, of the rectangle?
- A. 33
- B. 39
- C. 69
- D. 75
Correct Answer & Rationale
Correct Answer: A
To find the width of the rectangle, let the width be represented as \( w \). The length, being 6 feet longer, can be expressed as \( w + 6 \). The perimeter of a rectangle is given by the formula \( P = 2(l + w) \). Here, the perimeter is 144 feet, leading to the equation \( 2(w + (w + 6)) = 144 \). Simplifying this gives \( 2(2w + 6) = 144 \), which reduces to \( 4w + 12 = 144 \), and further simplifies to \( 4w = 132 \), resulting in \( w = 33 \). Option B (39) is incorrect as it gives a perimeter of 156 feet. Option C (69) would lead to an impossible perimeter of 150 feet. Option D (75) results in a perimeter of 162 feet, which exceeds the given value. Thus, only option A satisfies all conditions, confirming the width as 33 feet.
To find the width of the rectangle, let the width be represented as \( w \). The length, being 6 feet longer, can be expressed as \( w + 6 \). The perimeter of a rectangle is given by the formula \( P = 2(l + w) \). Here, the perimeter is 144 feet, leading to the equation \( 2(w + (w + 6)) = 144 \). Simplifying this gives \( 2(2w + 6) = 144 \), which reduces to \( 4w + 12 = 144 \), and further simplifies to \( 4w = 132 \), resulting in \( w = 33 \). Option B (39) is incorrect as it gives a perimeter of 156 feet. Option C (69) would lead to an impossible perimeter of 150 feet. Option D (75) results in a perimeter of 162 feet, which exceeds the given value. Thus, only option A satisfies all conditions, confirming the width as 33 feet.