1. A Prom committee is to include 2 teachers and 6 students. How many different committees can be formed if there are 5 teachers and 9 students
available?

2. Steven asked 7 people if they want to go to the movies. Everyone said “maybe”. How many different groups of moviegoers are possible?

3. How many different batting orders are possible for a 9-player baseball team, if Sarah must bat last?

4. How many different 3-digit combinations are possible for a lock that has the
numbers 00 – 59 available if you already know the first digit?
5. A teacher has 9 questions she wants to put on a test. How many question orders
can she create if she insists that the easiest question and the hardest question are
side-by-side?

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

Idk i am in 5th grade lol

The answer is 76° i believe