A parabolic arch sculpture is on top of a city bank. A model of the arch is y = −0.005x2 + 0.3x where x and y are in feet. The image is of a rectangle which represents the building of a Bank and its height is 30 feet. On top of it a semi circle is placed whose diameter is equal to the width of the rectangle.

a. What is the distance from the highest point of the arch to the ground?
b. What is the width of the bank?

A. a. 34.5 feet
b. 60 feet
B. a. 4.5 feet
b. 60 feet
C. a. 4.5 feet
b. 30 feet
D. a. 34.5 feet
b. 30 feet

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

How many square centimeters of wrapping paper will be used to wrap the shoe box?

Taina went to the toy store and spent $21.05 on a board game, $2.75 on coloring books, and $13.22 on a model airplane. about how much money did taina spend in the toy store?