Deirdre is buying plastic mugs to send to her cousin. She made a table of the various heights of stacks of different numbers of mugs.
Number of Plastics Mugs Stack Height (in inches)
1 6
2 6.75
3 7.5
4 8.25
5 9
6 9.75
Which equation represents the height, h, of a stack of mugs in terms of the number of mugs, t, in the stack?
A. H= 6+ 0.75 (T - 1)
B. H= 6+ 0.75T
C. H= 0.75 + T(T- 1)
D. H= 0.75+ T- 6
Number of Plastics Mugs
1
2
3
4
6
Stack Height (in inches)
6
6.75
7.5
8.25
9
9.75
Well, Deirdre seems to be stacking those mugs quite efficiently. I suppose she's mastered the art of the mug tower. Anyway, let's take a look at those options.
A. H= 6+ 0.75 (T - 1) - Well, this equation seems to be accounting for the initial height of 6 inches and adding 0.75 inches for each mug after the first one. So, if you consider the first mug to be the base, this equation makes sense.
B. H= 6+ 0.75T - Ah, a simple equation that adds 0.75 inches for each mug in the stack. No funny business here, just straightforward math.
C. H= 0.75 + T(T- 1) - Wait a minute, this equation has a "T(T-1)" term in it. Unless Deirdre's mugs are secretly multiplying when stacked, I don't think this equation is accurate.
D. H= 0.75+ T- 6 - This equation seems to be subtracting 6 inches from the height. I'm not sure why, but maybe it represents the height difference between Deirdre's cousin's house and Deirdre's house. That's quite a height difference, if you ask me.
So, after all the mug stacking analysis, I'd say the correct equation is B. H= 6+ 0.75T. Deirdre sure knows how to stack those mugs!
To determine the equation that represents the height of a stack of mugs in terms of the number of mugs in the stack, we need to analyze the given table.
Looking at the table, we can observe that the stack height increases by 0.75 inches for each additional mug. This means that for every extra mug added to the stack, the height increases by 0.75 inches.
Since the initial height of the stack with one mug is 6 inches, we know that the starting point of the stack height is 6 inches.
Putting this information together, the equation that represents the height, h, of a stack of mugs in terms of the number of mugs, t, in the stack is:
h = 6 + 0.75t
Therefore, the correct answer is B. H = 6 + 0.75t.
To find the equation that represents the height, h, of a stack of mugs in terms of the number of mugs, t, in the stack, we need to analyze the given table to identify the pattern.
Looking at the table, we can see that the height of the stack increases by 0.75 inches as the number of mugs increases by 1. In other words, for each additional mug in the stack, the height increases by 0.75 inches.
We can also observe that when there are no mugs in the stack (t=0), the height is 6 inches. This gives us a starting point for the equation.
Based on these observations, the equation that represents the height, h, of a stack of mugs in terms of the number of mugs, t, in the stack can be written as:
H = 6 + 0.75t
Now, let's check which answer choice matches this equation.
A. H= 6+ 0.75 (T - 1)
This option is incorrect because the 0.75 is multiplied by (T - 1) instead of just T.
B. H= 6+ 0.75T
This option matches the equation we derived and is the correct answer.
C. H= 0.75 + T(T- 1)
This option does not match the pattern observed in the table.
D. H= 0.75+ T- 6
This option does not match the pattern observed in the table.
Therefore, the correct answer is B. H= 6+ 0.75T, which represents the height, h, of a stack of mugs in terms of the number of mugs, t, in the stack.