Reagan will use a random number generator 1,200 times. Each result will be a digit from 1 to 6. Which statement best predicts how many times the digit 5 will appear among the 1,200 results?

Officer brimberry wrote 24 tickets for traffic violations last week, but only 9 tickets this week. what is the percent decrease? give your answer to the nearest tenth of a percent.

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

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?