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Why are quadratics factored into 2 brackets?
2x(x+4+3×1x) or 2x(x+4+3x)?
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Why do we integrate along the whole length while finding the gravitational force between a object of mass (m) and a rod of length L and mass M? Can't we simply use F = G m M r 2 ??
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Simplify the expression 1-sin2x
Expressing ln 54 3 in terms of ln 2 and/or ln 3I know that 54 3 = 54 1 / 3 but otherwise I don't know how to address these types of problems. How do I solve this, and is there a general way of tackling these problems? Like, if I had ln .75 or ln 8 9 , for example. These types of problems that I have are all different and I don't understand a general way of looking at them.thanks.
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Solve the simultaneous Linear equations using matrix inverse Method.
Find ∑i=1i=4 ∏j=2j=3(i+⌈j+0.5⌉)
Probability vs ConfidenceMy notes on confidence give this question:An investigator is interested in the amount of time internet users spend watching TV a week. He assumes σ=3.5 hours and samples n=50 users and takes the sample mean to estimate the population mean μ.Since n=50 is large we know that X―−μσn approximates the Standard Normal. So, with probability α=0.99, the maximum error of estimate is E=zα2×σn≈1.27 hours.The investigator collects that data and obtain X―=11.5 hours. Can he still assert with 99% probability that the error is at most 1.27 hours?With the answer that:No he cannot, because the probability describes the method/estimator, not the result. We say that "we conclude with 99% confidence that the error does not exceed 1.27 hours."I am confused. What is this difference between probability and confidence? Is it related to confidence intervals? Is there an intuitive explanation for the difference?
The volume of a cube is increasing at a rate of 1200 cm^3/min at the moment the lengths of the sides are 20 cm. How fast are the lengths of the sides increasing at the moment?
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