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20b(4b3)3
How to find the initial and the future population based on today's data?A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 27,000.(A) - What was the initial size of the bird population? (Round your answer to the nearest whole number.) n (initial) = 27 , 000 2 ( 25 / 10 ) ⟹ [ n ] (initial) = 4773 - correct.(B) - Estimate the bird population 8 years from now. (Round your answer to the nearest whole number.) n (8 years later) = 4773 × 2 ( 8 / 10 ) ⟹ [ n ] (8 years later) = 8310 - wrong.
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The definition of a linear program is following:Find a vector x such that: min c T x, subject to A x = b and x ≥ 0.Generally, b is assumed to be a fixed constant. However is it possible to construct a program where values of b are part of the optimization? Could I included b in the optimization by changing A x = b to A x − b = 0. If so, would I also be able to place constraints upon b like ∑ b = 1 and 1 > b > 0? Finally, would such a program be possible to solve efficiently?I am trying to solve the linear program for Wasserstein Distance between two discrete distributions. In the standard case, b represents the marginals for each datapoint. I know the marginals for the target distribution but the marginals from my source distribution are unknown. I am wondering if there is an efficient way to optimize the marginals for my source distribution such that the Wasserstein distance is minimized.
Qeustion about inscribed angle in a circle.I have a circle as shown in the figure. In my text book, the angle BAD is the sum of angles ACD and angle ADC. There might be a theorem that shows this in the book but I cannot find it. Why is this true?
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The manufacturer of a certain type of product claims that the machine that fills packages of these products is set up in such a way that the average net weight of the packages is 32 grams with a variance of 0.015 square grams. A consumer agency took a random sample of 25 packages from the production line, obtained a sample variance of 0.029 square grams and constructed a 95% confidence interval for the population variance. It is known that the machine is stopped and adjusted if either both or one of the two limits of the confidence interval is not in the interval 0.008 to 0.030. Based on the agent’s sample information, does the machine need an adjustment? Assume that the product net weights in all packages are normally distributed.I know the confidence interval is defined by: [ x ¯ − c s n , x ¯ + c s n ] I'm just not sure which mean or standard deviation to use.
Prove an inequality involving a root of a quadratic equationIf x=ρis a solution to: x2+bx+c=0Prove that |ρ|−1<|b|+|c|
How do you solve x3−1=0?
Use the two second-order multi-step methods ω i + 1 = ω i + h 2 ( 3 f i − f i − 1 )and ω i + 1 = ω i + h 2 ( f i + 1 + f i )as a pblackictor-corrector method to compute an approximation to y ( 0.3 ), with stepsize h = 0.1, for the IVP; y ′ ( t ) = 3 t y , y ( 0 ) = − 1.Use Euler’s method to start.I do not understand how to use these methods to approximate y ( 0.3 ). Moreover I am not sure how Euler's method fits into this question. Could someone clarify this question please?
Angular momentum is defined from linear momentum via L → = r → × p → , and is conserved in a closed system. Since energy is the time part of the linear four-momentum, is there a quantity defined from energy that's also conserved?
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