Examine circle O, where chords AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are congruent. Point P lies on AB¯¯¯¯¯¯¯¯ and point Q lies on CD¯¯¯¯¯¯¯¯.
Angles APO and DQO are right angles.

The diagram as described in the problem.

Which congruence statement is true?
CD≅AP
QD≅QO
OP≅OQ
OP≅AB

During a bike challenge riders have to collect various colored ribbons each 1/2 mile they collect a red ribbon each eighth mile they collect a green ribbon and each quarter mile they collect a blue ribbion wich colors of ribion will be collected at the 3/4 markrer

Abag contains 4 red, 7 blue and 5 yellow marbles. event a is defined as drawing a yellow marble on the first draw and event b is defined as drawing a blue marble on the second draw. if two marbles are drawn from the bag, one after the other and not replaced, what is p(b|a) expressed in simplest form? a. 7/16 b. 7/15 c. 14/16 d. 14/15

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .