A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is ninety six feet and its width from left to right is eighteen feet.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.

If the perimeter of the garden is 37 ft. the width is x and the length is 15 ft. what is the width of the garden in feet?

Exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on october 4. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (d) compute the probability that a randomly selected person was not born in january. (type an integer or a decimal rounded to three decimal places as needed.)