Daryl used a ruler to measure the distance between two cities on a map with a scale of 1 inch to 40 miles. He reported the actual distance between the two cities as 200 miles, with a measurement error of 10 miles. What is the smallest increment on the ruler Daryl used?
A. 0.25 in.
B. 0.5 in.
C. 0.75 in.
D. 1 in.
Let x be the actual distance between the two cities.
Based on the ruler's scale of 1 inch to 40 miles, we have the equation:
1 inch = 40 miles
The measurement error is 10 miles, so we have:
x + 10 = 200
x = 190
Using the ruler's scale, we can convert this actual distance to inches:
1 inch = 40 miles
190 miles = 190/40 = 4.75 inches
Therefore, the smallest increment on the ruler Daryl used is 0.25 inches.
The answer is A. 0.25 in.
it's incorrect
Apologies for the mistake.
If the ruler has a scale of 1 inch to 40 miles, and Daryl reported the actual distance as 200 miles with a measurement error of 10 miles, the measured distance on the ruler would be 210 miles (200 miles + 10 miles).
To find the equivalent distance in inches, we can set up the following proportion:
1 inch / 40 miles = x inches / 210 miles
Cross-multiplying, we get:
40 * x = 1 * 210
40x = 210
Dividing both sides by 40, we find:
x = 210 / 40
x = 5.25 inches
Therefore, the smallest increment on the ruler Daryl used is 0.25 inches.
The correct answer is A) 0.25 in.
it said that A) 0.25 in. is incorrect
Apologies for the confusion. Let's try again.
If Daryl reported the actual distance between the two cities as 200 miles with a measurement error of 10 miles, the measured distance on the ruler would be in the range of 190 to 210 miles.
Since the ruler has a scale of 1 inch to 40 miles, the measured distance on the ruler would be in the range of 4.75 to 5.25 inches.
The smallest increment on the ruler is the smallest difference between two markings. In this case, the smallest increment would be 0.25 inches.
Therefore, the correct answer is A) 0.25 in.
is there any other correct answer than just A) 0.25 in.?
Apologies for the confusion. Let's reconsider the problem.
If Daryl reported the actual distance between the two cities as 200 miles with a measurement error of 10 miles, the measured distance on the ruler would be in the range of 190 to 210 miles.
Since the ruler has a scale of 1 inch to 40 miles, the measured distance on the ruler would be in the range of 4.75 to 5.25 inches.
The smallest increment on the ruler is the smallest difference between two markings. In this case, the possible smallest increments could be 0.25 inches or 0.5 inches.
To determine the correct smallest increment, we can check if both 4.75 inches and 5.25 inches are divisible by either 0.25 inches or 0.5 inches.
Checking 4.75 inches:
4.75 / 0.25 = 19 (not divisible evenly)
4.75 / 0.5 = 9.5 (not divisible evenly)
Checking 5.25 inches:
5.25 / 0.25 = 21 (not divisible evenly)
5.25 / 0.5 = 10.5 (not divisible evenly)
Neither 4.75 inches nor 5.25 inches are divisible evenly by either 0.25 inches or 0.5 inches.
Therefore, there is no other correct answer. The correct answer is A) 0.25 in.