Trains headed for destination a arrive at the train station at 15-minute intervals starting at 7 a. m., whereas trains headed for destination b arrive at 15-minute intervals starting at 7: 05 a. m. (a) if a certain passenger arrives at the station at a time uniformly distributed between 7 and 8 a. m. and then gets on the first train that arrives, what proportion of time does he or she go to destination a

  2/3

Step-by-step explanation:

In the 5-minute interval between 7:00 and 7:05, a train to B is the first to arrive. In the 10-minute interval between 7:05 and 7:15, a train to A is the first to arrive. That is, in any 15-minute interval, the probability is 10/15 = 2/3 that a train to A is the first to arrive.

The 1-hour interval between 7 A.M. and 8 A.M. is an integer number of such intervals, so ...

  2/3 of the time, he or she will go to destination A.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°