A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x2=8y around its axis of symmetry (assume that x and y are in units of inches). In order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed?

Recall that the owner of a local health food store recently started a new ad campaign to attract more business and wants to know if average daily sales have increased. historically average daily sales were approximately $2,700. the upper bound of the 95% range of likely sample means for this one-sided test is approximately $2,843.44. if the owner took a random sample of forty-five days and found that daily average sales were now $2,984, what can she conclude at the 95% confidence level?

`if you have a set of parallel lines a and b cut by transversal x, if angle 1 = 167 degrees, what is angle 4 and why. also what is the measure of angle 5 and why? you need to use the names of the angle relationship and explain. ''.

Point r divides in the ratio 1 : 5. if the coordinates of e and f are (4, 8) and (11, 4), respectively, what are the coordinates of r to two decimal places?