The union of sets p = {5, 6, 7, 8, 9} q = {1, 2, 3, 4, 5} is given by which of the following?

The $x$-intercepts of the parabola $y = x^2 + bx + c$ are $(-3,0)$ and $(5,0).$ find the equation of the parabola, and submit your answer in $y = ax^2 + bx + c$ form.

The lengths of nails produced in a factory are normally distributed with a mean of 4.91 centimeters and a standard deviation of 0.05 centimeters. find the two lengths that separate the top 4% and the bottom 4%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial