Emma measured the height of her laptop screen. She reported the height as 8 inches, accurate to the nearest inch. The actual height of the screen must be:
- A. at least 7.5 inches and less than 8.5 inches
- B. at least 7.9 inches and less than 8.1 inches
- C. at least 7.99 inches and less than 8.01 inches
- D. at least 8 inches
- E. exactly 8 inches
Correct Answer & Rationale
Correct Answer: A
When measuring to the nearest inch, values can range from halfway to the next whole number. For Emma's reported height of 8 inches, this means the actual height must be at least 7.5 inches (inclusive) and less than 8.5 inches (exclusive). Option B is too narrow, only allowing for heights between 7.9 and 8.1 inches, which does not encompass all possible values. Option C is even more restrictive, only allowing for heights between 7.99 and 8.01 inches, excluding valid measurements. Option D is incorrect as it suggests the height must be 8 inches or more, which is too limiting. Option E incorrectly states the height must be exactly 8 inches, disregarding the range of possible values.
When measuring to the nearest inch, values can range from halfway to the next whole number. For Emma's reported height of 8 inches, this means the actual height must be at least 7.5 inches (inclusive) and less than 8.5 inches (exclusive). Option B is too narrow, only allowing for heights between 7.9 and 8.1 inches, which does not encompass all possible values. Option C is even more restrictive, only allowing for heights between 7.99 and 8.01 inches, excluding valid measurements. Option D is incorrect as it suggests the height must be 8 inches or more, which is too limiting. Option E incorrectly states the height must be exactly 8 inches, disregarding the range of possible values.
Other Related Questions
The expression 6a + 4c represents the total price, in dollars, of admission to an air show for a adults and c children. On Saturday, 380 adults and 120 children paid admission to the air show. What was the total price of admission for those people?
- A. 524
- B. 2240
- C. 2760
- D. 5000
- E. 12000
Correct Answer & Rationale
Correct Answer: C
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
Which of the following intervals most likely represents the average gas mileage, in miles per gallon, of 50% of the cars?
- A. 20 to 32
- B. 24 to 32
- C. 29 to 32
- D. 30 to 44
- E. 32 to 44
Correct Answer & Rationale
Correct Answer: B
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.
Mallory loaded 200 digital pictures into a digital picture frame. 78 are pictures of family members, 26 are pictures of pets, the rest are pictures of friends. The frame displays one picture every 10 seconds. Which value is closest to the probability that the next picture the frame displays will be a picture of a friend?
- A. 0.33
- B. 0.43
- C. 0.48
- D. 0.52
- E. 0.96
Correct Answer & Rationale
Correct Answer: C
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
What are the solutions to (x-2)(x+4) = 0?
- A. -4 and 2
- B. -3 and 1
- C. -2 and 4
- D. -1 and 1
- E. -1 and 3
Correct Answer & Rationale
Correct Answer: A
To solve the equation (x-2)(x+4) = 0, we apply the zero product property, which states that if a product of factors equals zero, at least one of the factors must equal zero. Setting each factor to zero gives us the equations x - 2 = 0 and x + 4 = 0. Solving these yields x = 2 and x = -4, confirming that the solutions are -4 and 2. Options B, C, D, and E provide incorrect pairs of solutions that do not satisfy the original equation when substituted back in. Each of these pairs results in non-zero products for the factors, thus failing to meet the requirement of the equation.
To solve the equation (x-2)(x+4) = 0, we apply the zero product property, which states that if a product of factors equals zero, at least one of the factors must equal zero. Setting each factor to zero gives us the equations x - 2 = 0 and x + 4 = 0. Solving these yields x = 2 and x = -4, confirming that the solutions are -4 and 2. Options B, C, D, and E provide incorrect pairs of solutions that do not satisfy the original equation when substituted back in. Each of these pairs results in non-zero products for the factors, thus failing to meet the requirement of the equation.