Which of the four labeled points on the number line above has coordinate-?
- A. A
- B. B
- C. C
- D. D
Correct Answer & Rationale
Correct Answer: B
Point B is positioned at the coordinate -2 on the number line, making it the accurate choice. Point A is located at -1, which is not the specified coordinate. Point C is at 0, representing the origin, and thus does not match the target coordinate. Point D is found at 1, clearly outside the negative range required. Each of these points is distinctly marked, confirming that only Point B aligns with the coordinate of -2. This clarity in placement reinforces the understanding of negative values on a number line.
Point B is positioned at the coordinate -2 on the number line, making it the accurate choice. Point A is located at -1, which is not the specified coordinate. Point C is at 0, representing the origin, and thus does not match the target coordinate. Point D is found at 1, clearly outside the negative range required. Each of these points is distinctly marked, confirming that only Point B aligns with the coordinate of -2. This clarity in placement reinforces the understanding of negative values on a number line.
Other Related Questions
At the Crest Coffee Shop, the cost of a plain bagel was $0.75 last year. This year the cost of a plain bagel is $0.90. By what percent did the cost of a plain bagel increase from last year to this year?
- A. 10%
- B. 15%
- C. 17%
- D. 20%
Correct Answer & Rationale
Correct Answer: D
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
Alexia bought a book that is 252 pages long. She read the book in 3 days. The first day, she read 1/2 of the book's pages, the second day, she read 1/3 of the book's pages, and the third day she read all the remaining pages. How many pages did Alexia read the third day?
- A. 3200%
- B. 3600%
- C. 4000%
- D. 4200%
Correct Answer & Rationale
Correct Answer: D
To determine how many pages Alexia read on the third day, we first calculate the pages read on the first two days. On the first day, she read half of 252 pages, which is 126 pages. On the second day, she read one-third, totaling 84 pages. Adding these gives 210 pages read over the first two days. Thus, the remaining pages for the third day are 252 - 210 = 42 pages. Options A, B, and C do not relate to the total pages read, as they present percentages rather than the actual number of pages. The correct choice reflects the accurate calculation of pages read on the final day.
To determine how many pages Alexia read on the third day, we first calculate the pages read on the first two days. On the first day, she read half of 252 pages, which is 126 pages. On the second day, she read one-third, totaling 84 pages. Adding these gives 210 pages read over the first two days. Thus, the remaining pages for the third day are 252 - 210 = 42 pages. Options A, B, and C do not relate to the total pages read, as they present percentages rather than the actual number of pages. The correct choice reflects the accurate calculation of pages read on the final day.
50.50 ÷ 0.25
- A. 202
- B. 2.2
- C. 2.02
- D. 0.22
Correct Answer & Rationale
Correct Answer: A
To solve 50.50 ÷ 0.25, converting the division into a simpler form is helpful. Dividing both numbers by 0.25 effectively transforms the problem into 50.50 ÷ 0.25 = 50.50 × 4, which equals 202. Option B (2.2) is incorrect as it misrepresents the scale of the division, resulting from a misunderstanding of decimal placement. Option C (2.02) also miscalculates the division, likely stemming from incorrect multiplication or division steps. Option D (0.22) is far too low, indicating a significant error in understanding the relationship between the dividend and divisor.
To solve 50.50 ÷ 0.25, converting the division into a simpler form is helpful. Dividing both numbers by 0.25 effectively transforms the problem into 50.50 ÷ 0.25 = 50.50 × 4, which equals 202. Option B (2.2) is incorrect as it misrepresents the scale of the division, resulting from a misunderstanding of decimal placement. Option C (2.02) also miscalculates the division, likely stemming from incorrect multiplication or division steps. Option D (0.22) is far too low, indicating a significant error in understanding the relationship between the dividend and divisor.
The large square above has sides of length 1. It is divided into smaller squares by dividing each side into 10 equal parts. In the figure, 3 full rows and 4 smaller squares in the next row are shaded. What is the area of the shaded region?
- A. 0.34
- B. 0.37
- C. 0.43
- D. 0.7
Correct Answer & Rationale
Correct Answer: A
To determine the area of the shaded region, first note that the large square has a side length of 1, resulting in a total area of 1 square unit. Each side is divided into 10 equal parts, creating a grid of 100 smaller squares, each with an area of 0.01 (1/100). In the figure, 3 full rows of squares are shaded, which accounts for 30 squares (3 rows x 10 squares per row). Additionally, 4 squares are shaded in the fourth row, bringing the total shaded squares to 34. Thus, the area of the shaded region is 34 squares x 0.01 = 0.34. Option B (0.37) incorrectly suggests 37 squares shaded. Option C (0.43) implies 43 squares, which is not possible given the shading described. Option D (0.7) overestimates the shaded area, miscounting the total squares shaded.
To determine the area of the shaded region, first note that the large square has a side length of 1, resulting in a total area of 1 square unit. Each side is divided into 10 equal parts, creating a grid of 100 smaller squares, each with an area of 0.01 (1/100). In the figure, 3 full rows of squares are shaded, which accounts for 30 squares (3 rows x 10 squares per row). Additionally, 4 squares are shaded in the fourth row, bringing the total shaded squares to 34. Thus, the area of the shaded region is 34 squares x 0.01 = 0.34. Option B (0.37) incorrectly suggests 37 squares shaded. Option C (0.43) implies 43 squares, which is not possible given the shading described. Option D (0.7) overestimates the shaded area, miscounting the total squares shaded.