The accompanying stem-and-leaf plot represents Kiko's test scores this year. What is the median score for this set of data?
1 answer:
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To model this situation, we are going to use the exponential function: 
where
is the initial number of cars
is the growing rate in decimal form
is number of tames the growing rate is increasing per year
is the time in years
To convert the growing rate to decimal form, we are going to divide the rate by 100%
Since the growing rate is increasing quarterly,
. We also know that the initial number of cars is 920, so 
. Lets replace all those values in our function:
We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03
where
To convert the growing rate to decimal form, we are going to divide the rate by 100%
Since the growing rate is increasing quarterly,
We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03
Answer:
CD ≠ EF
Step-by-step explanation:
Using the distance formula
d =
with (x₁, y₁ ) = C(- 2, 5) and (x₂, y₂ ) = D(- 1, 1)
CD =
=
= =
Repeat using (x₁, y₁ ) = E(- 4, - 3) and (x₂, y₂ ) = F(- 1, - 1)
EF =
=
= =
Since ≈
, then CD and EF are not congruent
This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:
See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result:
Now, the
This means that we get the result 7i for the numerator.
In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely:
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.
See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how
I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product
You should know from your classes that i^2 = -1, thefore the numerator simplifies to
You can do it as a curious thing, but simplifying yields the result: