Part of a train timetable is shown. Aberystwyth

Shrewsbury

Birmingham

08 30

10 17

12 30

14 19

13 55

16 05

17 20

a)

Bob catches the 12 30 train from Aberystwyth. He arrives in Shrewsbury 8 minutes late. What time does he arrive in Shrewsbury?

b) How long is Bob's journey from Aberystwyth to Shrewsbury? Give your answer in minutes.

minutes

11 30

15 30

Judy catches the 12 30 train from Aberystwyth.

She arrives in Shrewsbury on time.

She attends a job interview.

She gets back to Shrewsbury station 1 hour and 50 minutes later. Is she back in time to catch the 16 05 train to Birmingham?

You must show your working.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

The graph of y x3 is translated so that the point (1. 1) is moved to (1, 4). what is the equation of the new graph?

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )