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ahrayia [7]
3 years ago
6

Mrs.Stephan took her children to pick out pumpkins. Carter picked out a pumpkin priced $20,and Isabelle picked out a pumpkin pri

ced $13. How much did Mrs.Stephen pay for both pumpkins, including7% sales tax?
Mathematics
1 answer:
Fynjy0 [20]3 years ago
3 0
He paid 20 + 13, so 33 for the pumpkins and now you need to add the tax.

To compute the TAX ONLY, you would multiply 0.07 ( which is 7%) by 33, and you get $2.31. So the final cost with tax would be $33+ $2.31= $35.31

An easier way to compute total cost with the tax included would be to multiply $33 by 1.07, and you get the same answer as above, $35.31.

Do you see the difference? Some questions will ask for the amount of tax only, others will ask for the amount paid including tax.
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Step-by-step explanation:

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In convex optimization problems, a locally optimal solution is also globally optimal. These include LP problems; QP problems where the objective is positive definite (if minimizing; negative definite if maximizing); and NLP problems where the objective is a convex function (if minimizing; concave if maximizing) and the constraints form a convex set. But many nonlinear problems are non-convex and are likely to have multiple locally optimal solutions, as in the chart below. (Click the chart to see a full-size image.) These problems are intrinsically very difficult to solve; and the time required to solve these problems to increases rapidly with the number of variables and constraints.

GO Methods

Multistart methods are a popular way to seek globally optimal solutions with the aid of a "classical" smooth nonlinear solver (that by itself finds only locally optimal solutions). The basic idea here is to automatically start the nonlinear Solver from randomly selected starting points, reaching different locally optimal solutions, then select the best of these as the proposed globally optimal solution. Multistart methods have a limited guarantee that (given certain assumptions about the problem) they will "converge in probability" to a globally optimal solution. This means that as the number of runs of the nonlinear Solver increases, the probability that the globally optimal solution has been found also increases towards 100%.

Where Multistart methods rely on random sampling of starting points, Continuous Branch and Bound methods are designed to systematically subdivide the feasible region into successively smaller subregions, and find locally optimal solutions in each subregion. The best of the locally optimally solutions is proposed as the globally optimal solution. Continuous Branch and Bound methods have a theoretical guarantee of convergence to the globally optimal solution, but this guarantee usually cannot be realized in a reasonable amount of computing time, for problems of more than a small number of variables. Hence many Continuous Branch and Bound methods also use some kind of random or statistical sampling to improve performance.

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