Which list shows the numbers arranged from least to greatest?
- A. -(2/9), -0.21, -0.2, -(2/11), -1
- B. -1, -(2/9), -0.21, -0.2, -(2/11)
- C. -1, -(2/11), -0.21, -0.2, -(2/9)
- D. -(2/11), -0.2, -0.21, -(2/9), -1
Correct Answer & Rationale
Correct Answer: C
To determine the correct order, it's essential to convert fractions and decimals to comparable values. In option C, the numbers arranged from least to greatest are: -1, approximately -0.1818 (for -(2/11)), -0.21, -0.2, and approximately -0.2222 (for -(2/9)). This sequence accurately reflects their values. Option A incorrectly places -1 at the end, misordering the fractions and decimals. Option B also misplaces -1, and the order of the decimals is incorrect. Option D incorrectly ranks -1 as the least value and misplaces the fraction values, leading to an inaccurate arrangement.
To determine the correct order, it's essential to convert fractions and decimals to comparable values. In option C, the numbers arranged from least to greatest are: -1, approximately -0.1818 (for -(2/11)), -0.21, -0.2, and approximately -0.2222 (for -(2/9)). This sequence accurately reflects their values. Option A incorrectly places -1 at the end, misordering the fractions and decimals. Option B also misplaces -1, and the order of the decimals is incorrect. Option D incorrectly ranks -1 as the least value and misplaces the fraction values, leading to an inaccurate arrangement.
Other Related Questions
Which equation represents the graphed line?
- A. y = -1/3x +3
- B. y = 3x - 7
- C. y = 3x + 7
- D. y = 1/3x + 1
Correct Answer & Rationale
Correct Answer: D
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually.
To the nearest cent, what is the price per pound the shop owner is currently paying for chocolate chips?
- A. $0.10
- B. $4.38
- C. $0.23
- D. $4.28
Correct Answer & Rationale
Correct Answer: D
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
The triangle shown in the diagram has an area of 24 square centimeters. What is h, the height in centimeters, of the triangle?
- A. 9
- B. 4
- C. 8
- D. 2
Correct Answer & Rationale
Correct Answer: C
To find the height \( h \) of the triangle, we use the area formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Given the area is 24 cm², we can rearrange the formula to solve for \( h \): \( h = \frac{2 \times \text{Area}}{\text{base}} \). Assuming the base is 6 cm (since \( 24 = \frac{1}{2} \times 6 \times h \)), substituting gives \( h = \frac{48}{6} = 8 \). - Option A (9) is too high, as it would yield an area greater than 24 cm². - Option B (4) results in an area of only 12 cm², which is insufficient. - Option D (2) yields an area of 6 cm², far below the required area. Thus, only option C (8) satisfies the area requirement.
To find the height \( h \) of the triangle, we use the area formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Given the area is 24 cm², we can rearrange the formula to solve for \( h \): \( h = \frac{2 \times \text{Area}}{\text{base}} \). Assuming the base is 6 cm (since \( 24 = \frac{1}{2} \times 6 \times h \)), substituting gives \( h = \frac{48}{6} = 8 \). - Option A (9) is too high, as it would yield an area greater than 24 cm². - Option B (4) results in an area of only 12 cm², which is insufficient. - Option D (2) yields an area of 6 cm², far below the required area. Thus, only option C (8) satisfies the area requirement.
The Great Pyramid at Giza in Egypt is a square pyramid that measures approximately 756 feet on each side. The height of the pyramid is approximately 450 feet. What is the approximate volume, in cubic feet, of the pyramid?
- A. 51,030,000
- B. 85,730,400
- C. 226,800
- D. 453,600
Correct Answer & Rationale
Correct Answer: B
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of the Great Pyramid, being a square, is calculated as \( 756 \times 756 = 571,536 \) square feet. Multiplying this by the height of 450 feet gives \( 571,536 \times 450 = 257,184,000 \). Dividing by 3 yields a volume of approximately 85,728,000 cubic feet, which rounds to 85,730,400. Option A (51,030,000) underestimates the height and base area. Option C (226,800) miscalculates the base area significantly. Option D (453,600) incorrectly applies the volume formula, failing to account for the correct base area and height.
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of the Great Pyramid, being a square, is calculated as \( 756 \times 756 = 571,536 \) square feet. Multiplying this by the height of 450 feet gives \( 571,536 \times 450 = 257,184,000 \). Dividing by 3 yields a volume of approximately 85,728,000 cubic feet, which rounds to 85,730,400. Option A (51,030,000) underestimates the height and base area. Option C (226,800) miscalculates the base area significantly. Option D (453,600) incorrectly applies the volume formula, failing to account for the correct base area and height.