Step-by-step explanation:
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Solving Systems of linear equations by graphing. no graphing device.
1 answer:
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Answer:
C,
Step-by-step explanation:
To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:
Given the complex number , we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.
One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression
Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression , and <em>now </em>we have something to work with.
Looking back at Euler's formula , we can map our expression inside the parentheses to the one on the right side of the formula, giving us
and
, or equivalently:
At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so , and we can finally replace our expression in parentheses with its exponential equivalent:
Which is c on the multiple choice section.
Answer:
68% of the incomes lie between $36,400 and $38,000.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $37,200
Standard Deviation, σ = $800
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Empirical rule:
- Almost all the data lies within three standard deviation of mean for a normally distributed data.
- About 68% of data lies within one standard deviation of mean.
- About 95% of data lies within two standard deviation of mean.
- About 99.7% of data lies within three standard deviation of mean.
Thus, 68% of data lies within one standard deviation.
Thus, 68% of the incomes lie between $36,400 and $38,000.