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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.
Draw the standard normal distribution, label the axis, locate both z-scores on the axis (z7 = -1.5, z15 = 2.5), and shade an area equal to the probability that a randomly chosen croaker fish will be b/t 7 and 15 inches.
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.
Use the mean, median, and mode to make a statement about the difference in performance for city and highway driving.
The director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.
Analysis of variance- One way classification - Are there differences among these 3 drugs with respect to how long they are retained in the body?
Suppose the sample variance for 30 parts turns out to be s 2 = .0005. Use α = .05 to test whether the population variance specification is being violated.
Base on a survey of over 10,000 households, the number of televisions in the home was recorded as given in the table below. Based on the data, find the expected number of televisions in a home.
He will then compare the season batting averages of group A (those with ballet training) and group B (those without ballet training) by comparing the mean of group A with the mean of group B.
For the 20 test scores shown, find the percentile rank for a score of 86.
The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.
Dating In Chances- Risks and Odds in Everyday Life, James Burke claims that about 70 percent of all single men would welcome a woman taking the initiative in asking for a date. A random sample of 20 single men was asked if they would welcome the woma..
What does it mean for two random variables to be uncorrelated?
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