What is the average rate of change for this exponential function for the interval from x=1 x=3

In a timed typing test lara typed 63 words per minute. estimate the number of words she should be able to type in half in hour show your work

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)

Tom and lilly rented a house for $12,000 last year. at the start of the year they bought the house they had been renting directly from the owner for $250,000. they believe they could rent it for $12,000 this year, but stay in the house. how much does tom and lilly’s decision to buy the house change gdp? a. it reduces gdp by $12,000 b. it does not change gdp c. it raises gdp by $238,000 d. it raises gdp by $250,000