What is the average (arithmetic mean) of the first 90 measurements in a certain list of 92 measurements? (1) the average of the 92 measurements is 7.0 centimeters. (2) the average of the last 2 measurements is 7.2 centimeters?

The sum of all the measurements is just the average times the number.





So if the average of all 92 is 7 the sum of those is 

The average of the last two is 7.2 so their sum is

That means the sum of the first 90 is

so the average of the first 90 is

  cm

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