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Question: Use mathematical induction, prove the given statements.
Part 1: There exists a positive integers k, so that for every integer n > k, 2^n > n3.
Part 2: \(\sum_{i=1}^{n} 8i-5 = 4n^2 -n\)
You have to use mathematical induction to prove these statements.
If the box is to have a volume of 72 cubic inches, find the length and width of the cardboard that must be used.
Explain the statistical analysis that you completed in Part I. Be sure to explain where the data came from, what analysis was done, and what the results were.
If one gallon of paint has a volume of approximately 4000 cubic cm, what is the maximum number of whole gallons of paint that can be poured into the bucket?
Let S be the part of the plane 3x + 1y + z = 4 which lies in the first octant, oriented upward. Find the flux of the vector field F = 1I + 2J + 2K across the surface S.
Math: Linear Transformation of the Space of Polynomials, Which of the following is a linear transformation T of the space of polynomials? Circle the letters corresponding to correct answers.
Find the height of the flag pole from the word problem and determine the total number of student-tickets sold from given word problem
A student and a professor each choose a number between 1 and 5 (1 and 5 are both possible choices). What is the probability that the two choose the same number?
Explain why it fits the definition of an observational study rather than a randomized experiment
Assume season-ticket prices in the lower bowl for the Buffalo Bills will rise from $495 for a 10-game package to $770. Fans sitting in the best seats in the upper deck will pay an increase from $310 to $555. Don Manning plans to purchase 4 season ..
what does the shadow price reflect in a maximization problem? explain. how do the graphical and computer-based methods
A Diner served 15 salads during lunch and 27 during dinner.
Suppose that a car normally sells for $16,500 and is now on sale for $14,000. What is the percent of discount? If necessary, round your answer to the nearest tenth.
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