The pulse rates, in beats per minute, for some students of a class are shown below:

82, 88, 67, 88, 85, 67, 79, 76, 79, 67, 88, 67, 85, 79, 67, 88, 79, 88, 76, 67

midge created the following incorrect dot plot to represent the data:

dot plot showing 6 dots over 67, 2 dots over 76, 3 dots over 79, 1 dot over 82, 2 dots over 85, and 5 dots over 88

what should midge do to make the dot plot correct?

put another dot on 79
put another dot on 76
delete one dot on 88
delete one dot on 67

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