Below we give the overall dining experience ratings (Outstanding, Very Good, Good, Average, or Poor) of 30 randomly selected patrons at a restaurant on a Saturday evening. DS RestRating Outstanding Good Very Good Outstanding Outstanding Outstanding Very Good Outstanding Outstanding Outstanding Good Very Good Good Very Good Outstanding Very Good Outstanding Good Very Good Very Good Average Outstanding Outstanding Very Good Outstanding Very Good Outstanding Very Good Good Outstanding a Find the frequency distribution and relative frequency distribution for these data. b Construct a percentage bar chart for these data. c Construct a percentage pie chart for these data.

Kindly check explanation

Step-by-step explanation:

Relative frequency = frequency / total frequency

Total frequency = 30

Outstanding = 14 / 30 = 0. 467 = 46.7%

Very good = 10/30 = 0.333 = 33.3%

Good = 5 / 30 = 0.167 = 16.7%

Average = 1 / 30 = 0.0333 = 3.3%

Poor = 0

_______Rating : frequency : R/ frequency

Outstanding _____ 14 _______0.467

Very good _______10 _______0.333

Good ___________ 5 _______ 0.167

Average _________ 1 _______ 0.033

Poor ____________ 0 _______ 0

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