Review: Proportions, Significant Figures, And Velocity Problems

Explanation
To convert minutes to seconds, we multiply the number of minutes by 60 since there are 60 seconds in a minute. In this case, 2.6 minutes multiplied by 60 gives us 156 seconds.

Explanation
To find the number of minutes in 744 seconds, we divide 744 by 60 (since there are 60 seconds in a minute). This gives us 12.4, so the answer is 12.4 minutes.

Explanation
To find the number of seconds in 2.4 hours, we multiply 2.4 by the number of seconds in 1 hour, which is 3600. Therefore, 2.4 hours is equal to 2.4 x 3600 = 8640 seconds. The answer is 8640 seconds or 8,640 seconds.

Explanation
To find the number of hours in 44,640 seconds, we divide the total number of seconds by the number of seconds in an hour. Since there are 3600 seconds in an hour, we divide 44,640 by 3600. This gives us 12.4, which represents the number of hours. Therefore, the correct answer is 12.4 hours.

Explanation
To find out how many cups of milk are needed when using 9.6 cups of flour, we can set up a proportion based on the given ratio of milk to flour. The ratio is 2 cups of milk for every 3 cups of flour.

We can set up the proportion as follows:

2 cups of milk / 3 cups of flour = x cups of milk / 9.6 cups of flour

Cross-multiplying, we get:

3 cups of flour * x cups of milk = 9.6 cups of flour * 2 cups of milk

Simplifying, we have:

3x = 19.2

Dividing both sides by 3, we find:

x = 6.4

Therefore, when using 9.6 cups of flour, you will need 6.4 cups of milk.

Explanation
The number 0.002 has only one significant figure, which is the non-zero digit 2. The leading zeros in the number are not considered significant because they are simply placeholders and do not contribute to the precision of the measurement. Therefore, the correct answer is 1.

Explanation
The number 120 has two significant figures because both the digits 1 and 2 are non-zero digits and are known with certainty.

Explanation
The number 120 has three significant figures because all non-zero digits are considered significant, and any zeros between non-zero digits are also significant. In this case, the digits 1, 2, and 0 are all non-zero, so they are all significant.

Explanation
The number 202 has three significant figures because all non-zero digits are considered significant and any zeros between non-zero digits are also significant. In this case, all three digits (2, 0, and 2) are non-zero, so they are all significant.

Explanation
The number 202.00 has 5 significant figures because all the digits, including the zeros, are non-zero and contribute to the precision of the number. The zeros in between the non-zero digits are also significant, indicating that the measurement was made to a high degree of accuracy.

Explanation
The velocity of the car can be calculated by dividing the distance traveled by the time taken. The distance traveled is given as 12.0 kilometers, which is equal to 12.0 x 1000 = 12000 meters. The time taken is given as 7.0 minutes, which is equal to 7.0 x 60 = 420 seconds. Therefore, the velocity of the car is 12000 meters / 420 seconds = 28.6 meters/second. The direction of the velocity is specified as East.

Explanation
The motorcycle maintains a constant velocity of 10.0 meters per second West for 2.20 minutes. To calculate the distance traveled, we can use the formula distance = velocity * time. Therefore, the distance traveled is 10.0 meters/second * 2.20 minutes * 60 seconds/minute = 1320 meters.