In what case the Gaussian quadratures can be applied to the improper integrals?

6. In what case the Gaussian quadratures can be applied to the improper integrals? Analyze whether the following integral is convergent and evaluate it by the appropriate method 7. Find numerically the derivative of y = sin x at x = 0.2. Compare to the exact value and to the theoretically predicted error. 8. Solve the following initial value problem by the Euler’s method using h = 0.1; and by the Runge-Kutta method. Compare results. Obtain the exact solution. Find an error at x = 1. 9. Find the following determinant. 10. Use the LU-factorization to solve the following system of linear equations if possible. If a solution doesn’t exist, explain why.

Ensco Lighting Company has fixed costs of $100,000, sells its units for $28, and has variable costs of $15.50 per unit.

Ensco Lighting Company has fixed costs of $100,000, sells its units for $28, and has variable costs of $15.50 per unit. a. Compute the break-even point. b. Ms. Watts comes up with a new plan to cut fixed costs to $75,000. However, more labor will now be required, which will increase variable costs per unit to $17. The sales price will remain at $28. What is the new break-even point? c. Under the new plan, what is likely to happen to profitability at very high volume levels (compared to the old plan)?

Ensco Lighting Company has fixed costs of $100,000, sells its units for $28, and has variable costs of $15.50 per unit.

Ensco Lighting Company has fixed costs of $100,000, sells its units for $28, and has variable costs of $15.50 per unit. a. Compute the break-even point. b. Ms. Watts comes up with a new plan to cut fixed costs to $75,000. However, more labor will now be required, which will increase variable costs per unit to $17. The sales price will remain at $28. What is the new break-even point? c. Under the new plan, what is likely to happen to profitability at very high volume levels (compared to the old plan)?

Prove the Dedekind cut theorem.

The problem did not appear in the box, so please see attachment.

An organization uses a spam filtering software to distinguish legitimate messages from spam messages.

Please see attached. Also note that we need to specify an optimal strategy here. An organization uses a spam filtering software to distinguish legitimate messages from spam messages. The spam filter tags messages as High-Risk (H), Moderate-Risk (M), or Low-Risk (L). Extensive experimentation with the software indicates that it tags 80% of spam messages as H, 15% of spam messages as M, and the remaining 5% of spam messages as L. Similarly, experiments with legitimate messages indicate that the software tags 6% of legitimate messages as H, 18% as M, and the remaining 76% as L. The organization estimates that 90% of the messages that it receives are spam while the remaining 10% a... click for more