Morse code uses "dots" and "dashes," which are known to occur in the proportion of 3: 4. this means that for any given symbol, p(dot sent) = 3/7 and p(dash sent) = 4/7. unfortunately, when coded messages are sent, there are sometimes errors in transmission. suppose there is interference on the transmission line, and with probability 1/8 a dot is mistakenly received as a dash, and vice versa. a) what is the probability that the received symbol is a dot?

Which ordered pair (c,d) is a solution to the given system of linear equations- c+2d=13 -9c-4d=-15

Suppose you just purchased a digital music player and have put 8 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 8 songs is played once in random order. find the probability that among the first two songs played (a) you like both of them. would this be unusual? (b) you like neither of them. (c) you like exactly one of them. (d) redo () if a song can be replayed before all 8 songs are played.

The median am of triangle ∆abc is half the length of the side towards which it is drawn, bc . prove that triangle ∆abc is a right triangle, and find angle mac and abm