What role did geographic location play in the history of Byzantium?
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<h2>55-5</h2><h2><em>
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Answer: A.) 8
Explanation:
Use u-substitution.
(1) Let u=x^3
By the power rule, du/dx=3x^2
Multiplying by dx and dividing by three, we have du/3=x^2dx
To find the new lower bound of integration, plug the old bound, -3, for x in equation (1). We get u=(-3)^3= -27
Similarly, when the upper bound 3 is plugged in, u=27
Now, replacing f(x^3) with f(u) and x^2dx with du/3:
since the value of the first integral of the question = 12, which is given. Although the variable is different than the given (u instead of x), it's still the same integral
Answer:
A) Molly can buy 60% of the available motorcycles.
B) The 30th percentile is $11920
C) $25,000 is considered an outlier because is greater than: $24792
Explanation:
Data:
mean, μ = $14,000
standard deviation, σ = $4,000.
A) Using standard normal distribution table (see first figure attached) we have to compute Z (the standard variable) for an x = $15,000 (x is the actual variable) as follows:
Z = (x - μ)/σ
Z = (15000 - 14000)/4000
Z = 0.25
From the table, that represent 60%, that is, Molly can buy 60% of the available motorcycles.
B) From the second figure attached, we can see that 30% of the results (here, the motorcycles prices) correspond to a value of Z = -0.52. That correspond to a price of:
x = μ + Z*σ
x = 14000 + (-0.52)*4000
x = $11920
C) The 1.5 x IQR rule states that any value bigger than 1.5 times the interquartile range (IQR) added to the third quartile is an outlier.
The third quartile is located at Z = 0.6745, in terms of the actual variable:
x = μ + Z*σ
x = 14000 + 0.6745*4000
x = $16698
The first quartile is located at Z = -0.6745, in terms of the actual variable:
x = μ + Z*σ
x = 14000 - 0.6745*4000
x = $11302
Then:
IQR = 16698 - 11302 = $5396
The third quartile value added to 1.5 x IQR is equal to 16698 + 1.5*5396 = $24792
