Type the correct answer in each box. Use numerals instead of words. A steel company is making flat rectangular frames as a part of a new product they are launching. Each frame will be cut out of a piece of steel and will have a final area as close to 28 cm2 as possible. The width of the frame needs to be uniform throughout. The inside dimensions of the frame must be 11 cm by 6 cm.

Complete the equation that models the above situation, and find the width of the frame, x.

The area of the steel frame can be modeled by the following equation.

__x2 + __ x -28=0
x - 28 = 0

The width of the frame, x, rounded to the nearest hundredth, is approximately ___
cm.

Questions 7-8. use the following table to answer. year 2006 2007 2008 2009 2010 2011 2012 2013 cpi 201.6 207.342 215.303 214.537 218.056 224.939 229.594 232.957 7. suppose you bought a house in 2006 for $120,000. use the table above to calculate the 2013 value adjusted for inflation. (round to the nearest whole number) 8. suppose you bought a house in 2013 for $90,000. use the table above to calculate the 2006 value adjusted for inflation. (round to the nearest whole number)

Write an equation of the line that passes through the point (2, 3) and is perpendicular to the line x = -1. a) y = 1 b) y = 3 c) y = 0 eliminate d) y = -3

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.