Algebra Review

A statistician is reviewing a dataset of the ages of a random sample of 500 people. The ages are normally distributed, with a mean of 35 and a standard deviation of 10. The statistician is interested in the proportion of the sample that falls between the ages of 25 and 45. Use the standard normal distribution to answer this question. Additionally, the statistician is looking for the roots of the quadratic equation \(x^2 - 5x + 6 = 0\). Factor the equation and find the roots.

A statistics student collects data for a project and determines the variance of his data set to be 49. If he represents the variance as a difference of squares, what are the two numbers he can use?

Given a set of data \(x = \{2, 4, 6, 8, 10\}\), calculate the sum of cubes and then factorize the result.

Given the set of data points \( \{ (2,5), (4,10), (6,15), (8,20) \} \), find the equation of the line of best fit. Then, factor out the greatest common factor (GCF) from each term in the equation.

Given the statistical data set \(\{3x+2, 4x-3, 5x+1, 6x-5\}\), where x is a positive integer, find the mean (average) of the data set after factoring by grouping.

If the mean of the data set \(x^2 - 7x + 10\), \(x^2 - 5x + 6\), and \(x^2 - 3x + 2\) is \(x^2 - 5x + 6\), what is the value of \(x\)?

Given the quadratic equation \(x^2 - 2sx + n = 0\) where \(s\) is the sample mean of a dataset \(a, b, c\) and \(n\) is the perfect square trinomial. Find the value of \(n\) if the dataset is \(3, 5, 7\).

Given a line with the equation \(3x - 4y = 12\). Find the equation of the line that passes through the point (1,2) and is perpendicular to the given line.

Given the data points (2,5) and (6,14), find the slope of the line that passes through these points.

The line \( y = 3x - 2 \) has a slope of 3. Find the equation of the line that is parallel to this line and passes through the point (2, -1).