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Please help me with the attached pre-calculus questions.
1. Use mathematical induction to prove that 6 is a factor of n (n + 1)(n + 2).
2. Use mathematical induction to prove 1^2 + 3^2 + 5^2 + . . . + (2n - 1)^2 = n (4n^2 - 1) / 3.
3. Expand (2x - y)^6 using binomial coefficients and then evaluate each coefficient.Example: the first term is 6 chose 0 (2x)^6 (-y)^0 = 64x^6
4. Interpret what the result in problem 3 tells us about construction the next row of the Pascal triangle:11 11 2 11 3 3 11 4 6 4 1
5. Find the equation of the circle that has its center at the focus of the parabola X^2 - 4x + 6y - 20 = 0 and that is tangent to the parabola at its vertex. Also sketch both curves.
6. Find the equation of the Ellipse whose foci coincide with the foci of the hyperbola x^2 - 3y^2 - 2x - 12y + 1 = 0 and whose eccentricity is the reciprocal of that of the hyperbola.
Critically discuss the general characteristics of a research study for which an independent-measures t would be the appropriate test statistics
A supervisor has noticed that sales for all departments world wide has been averaging $12,000 a month for a number of years. For the last 18 review periods the average sales figure has dropped to $11,500 with a standard deviation of $4,000. Manage..
he population consists of all 15 year olds living in the attendance district of a local high school. You plan to obtain a simple random sample of 200 such residents by using the roster of the high school as the sampling frame.
Construct appropriate control charts for before and after introduction of the new pathway. Discuss process stability and the results.
Sally wanted to build a multiple regression model based on advertising expenditures and A coffee business price index. Based on the selection of all normal values she obtained the following:
Four young children were monitored closely over a period of several weeks to measure how much they watched violent television programs and their amount of violent behavior toward their playmates.
Formulate the hypotheses that can be used to determine whether the mean of all account balances is significantly different from $1,150
Comparison of paired and unpaired samples test - Prepare a brief conclusion statement summarizing your results. What can you tell this MHMR about client satisfaction? What could you suggest they do to improve?
The McBurger restaurant chain claims that the waiting time of customers for service is normally distributed with a mean of 3 minutes and a standard deviation of 1 minute.
Determine the standard error of students that favoured the move.
Give an example of how you may use multiple regression to answer a question related to the impact of leadership change on employee attitudes scores, teambuilding training and performance outcomes.
After a logarithmic transformation, we obtain the following regression result of Cobb-Douglas production formula for a firm:
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