(5) 1. One of the following hundred numbers is selected at random: 00 01 ... 09 10 11 ... 19 . . . . . . . . . . . . . . . 90 91 ... 99 Find the probabilities of the following events: a) The first digit is 6. b) The two digits are equal. c) The two digits are unequal. d) The second digit is larger than the first. e) The second digit is at least as large as the first. f) The second digit is 6. g) The sum of the two digits is 6. h) The sum of the two digits is 9. i) Neither digit exceeds 6. j) Both digits exceed 6. k) Only one of the digits exceeds 6. l) The first digit exceeds 6 and the second does not.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

At a constant it will take one hour to travel 32 mi.at that speed it will take 1/2 hr to travel the remaining 16 mi.it will take 1+1/2 hr to travel the 48mi @ 32mph.so 1 hr = 60 min& 1/2 hr = 30 min1+1/2 hr = 90 min.there are 60s in each 90 × 60 = 3600 seconds.the real question seriously is he why are they driving so slow? ! lol.