Math 3A Cycle 3 Variance

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Math 3A Cycle 3Variance

• Review Activity

2
Direct Variance
Inverse Variance
Whats that K Value?
In the REAL WORLD
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3

10 points
The table below is a direct variance between x
and y. What is the missing value?



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4
A N S W E R
10 points
Directly proportional means direct variance
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12

n
5
12n 90 n 7.5
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5

20 points
What is the general equation form for a direct
variance?
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6
A N S W E R
20 points
y kx for some constant, k.
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7

30 points
What is the equation of the direct variance
graphed below?
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8
A N S W E R
30 points
The slope of the line is ¾. This means k.75 and
the equation is y .75x

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9

10 points
What is the missing value for y in an inverse
variance relationship which passes through the
points (4,9) and (6,y)?
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10
A N S W E R
10 points
xy k xy 4 x 9 xy 36 This means if x6, 6y
36, so y must be 6.

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11

20 points
Which graph drawn below is most likely an inverse
variance. What is its name?
a b
c d
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12
A N S W E R
20 points

a Its name is a hyperbola
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13

30 points
True or False. Explain.
x
y
is an inverse variance.

4
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14
A N S W E R
30 points
False. This equation is the same as y .25x
since dividing by 4 is the same as multiplying by
.25. This is a direct variance with k.25.
Besides, as the values for x increase, the values
for y also increase, so it could not be an
inverse variance for this reason, too.
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15

10 points
Find the k value for the direct variance given by
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16
A N S W E R
10 points
x 6

x 6
Ans. k6
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17

20 points
What is k for the graph of the inverse variance
given below?
(2,8)
(4,4)
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18
A N S W E R
20 points
2 x 8 16 and 4 x 4 16

Since the equation must be xy16, this means k
16.
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19
30 points
x y - 6 3(x-2) is an equation which can be
re-written in the form of a direct variance.
What is the k value once this is completed?

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20
A N S W E R
30 points
x y - 6 3(x-2) x y 6 3x 6

6 6
x y 3x
-x -x
y 2x
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This direct variance has k2.
21

10 points
If you ride 9 mph for a 2 hour bike ride and then
increase your speed to 12 mph on the return trip,
then how long was the whole ride?
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22
A N S W E R
10 points
9 mph x 2 hours 18 miles 12 mph x H hours 18
miles (return trip) So H 1.5 hrs The whole rid
e took 2 hr. 1.5 hr. 3.5 hrs.

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23

20 points
As you climb up a mountain, the air pressure
becomes less and less, making it harder to
breathe.
What kind of relationship is there between the
altitude and the air pressure?
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24
A N S W E R
20 points
As the altitude (height) of the mountain gets
higher, the air pressure gets lower
proportionally. This makes it an inverse
variance relationship.

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25

30 points
As the number of agents protecting a target of an
assassin increase, the probability for success
and the cost will change according to the
following tables. What are the missing values in
each?
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26
A N S W E R
30 points
Cost varies directlyk7,500 per agent.
Probability varies inversely k48
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