A random survey of seventh and eighth grade students was conducted to find out how many hours are spent doing homework each nigh
t. Of the two sets of data, which has the greater median?
A: seventh graders
B: eighth graders
C: they have the same median
D: impossible to determine from the box plot
A: seventh graders
B: eighth graders
C: they have the same median
D: impossible to determine from the box plot
1 answer:
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Answer:
- penny object: 5
- quarter object: 10
- circle object: 20
Step-by-step explanation:
The first thing to realize is that the penny object is <em>not</em> worth 1, and the quarter object is <em>not</em> worth 25. Once you realize <em>the values are not what they seem</em>, but are consistent throughout, it becomes a different problem than it first appears to be.
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Let p, q, c represent the values of the penny object, the quarter object, and the circle object, respectively. The trick is to find 3 independent equations describing their values.
The middle two rows of the matrix shown give rise to the equations ...
2p +c +q = 40
p +2c +q = 55
The leftmost column adds a third independent equation ...
p + c + 2q = 45
We can subtract the last equation from the middle one.
(p +2c +q) -(p +c +2q) = 55 -45
c - q = 10 . . . . . simplify . . . [eq4]
And we can subtract the first equation from twice the last one.
2(p +c +2q) -(2p +c +q) = 2(45) -40
c +3q = 50 . . . . simplify . . . [eq5]
Subtracting eq4 from eq5 gives ...
(c +3q) -(c -q) = (50) -(10)
4q = 40 . . . . simplify
q = 10 . . . . . .divide by 4
The eq4 tells us
c = 10 + q = 10 + 10 = 20
and the third equation tells us
p = 45 - 2q - c = 45 -2·10 -20 = 5
The object values are: penny, 5; quarter, 10; circle, 20.
