a. 0.5 mL
b. 8 mL
c. 14.5 mL
d. Yes; the slope of the line would be 0.5x (x = number of marbles dropped into the water) and it means that for every one marble dropped, the volume of water will rise by 0.5 mL.
Step-by-step explanation:
a:
We know that after dropping in 4 marbles the water rose to 10 mL. After dropping in 6 marbles the water rose to 11 mL.
Therefore we can infer that every 2 marbles rises the water by 1 mL.
Since we know this then we can infer that the volume of one marble would be 1 mL divided by 2, because it takes two marbles to rise one milliliter.
1/2 = 0.5, so the volume of one marble is 0.5 mL.
b:
Since two marbles rise the water level by a milliliter, then if we have added 4 marbles at the start then we can multiply 4 marbles by 0.5 mL to find the volume of water that 10 mL increased from.
4 times 0.5 is 2, so we can subtract 2 mL from 10 mL to find the amount of water (in mL) there was in the graduated cylinder before Jada dropped the marble.
10 mL - 2 mL = 8 mL
This means that there were 8 milliliters of water in the g. cylinder before Jada added the four marbles.
c:
There are 6 marbles in the g. cylinder and the water level is at 11 mL. If we have 13 marbles in total, this means that 7 marbles have been added (13 - 6).
Multiply 7 marbles by 0.5 mL (the marble's volume) to get 3.5 mL.
The water level is at 11 mL with 6 marbles, so at 13 marbles the water level will be 3.5 mL added on to 11 mL.
3.5 mL + 11 mL = 14.5 mL
The height of the water after 13 marbles are dropped in should be 14.5 mL.
d:
The volume of water is a linear relationship with the number of marbles dropped in the graduated cylinder.
This is because the marbles are all the same volume, 0.5 mL, and every 2 marbles raise the water level by 1 mL.
The number of marbles in the water in proportional to the volume of the water because we can calculate the volume of water after x amount of marbles are dropped in.
The slope of the line would be 0.5x, where x represents the number of marbles dropped into the water in the graduated cylinder.
The slope of the line would mean that it is a linear relationship and that the more marbles added into the water, the higher the volume of water will become.
