Abus and a train leave the same station at the same time and travel in the same direction along parallel routes. the train runs twice as fast as the bus. they are from 12 1/2 to 15 miles apart at the end of half an hour. find the smallest and largest possible value of each rate.

Smallest rate for the train is 50 mph and largest is 60 mph.

For the bus it is 25 and 30 mph.

Step-by-step explanation:

If the speed of the train is 2x then speed of the bus is x mph, and the train travels twice as far as the bus in a given time.

Distance = speed * time

For the largest rate:

d =  2x * 0.5   for the train

x = d

0.5d  =  x       for the bus

d - 0.5d = 15

0.5d = 15

d = 30

So the rate for the train =  30 / 0.5 = 60 mph.

In a similar fashion we can show that the smallest rate for the train is

25/ 0.5 = 50 mph.

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%

step-by-step explanation:

f(gx)=f(1/x+2)

=(1/x+2)+2

=(1+2x)/2+2

=(1+2x+4)/2

= (2x+5)/2