A researcher is estimating the mean income of residents in a large city. She collects a random sample of 25 people. The resulting 95% confidence interval is ($26700,$35400). Which of the following conclusions are valid? (i) We are 95% confident that the mean income for all residents of this city is between $26700 and $35400. (ii) 95% of the residents of this city have an income between $26700 and $35400. (iii) No conclusion can be drawn.

Josh has a rewards card for a movie theater he receives 15 points for becoming a rewards card holder he earns 3.5 points for each visit to the movie theater he needs at least 55 points to earn a free movie ticket which inequality can josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket.

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

The krasnapolski is a top-of-the-line hotel in amsterdam, the netherlands. among their many services, they rent bicycles to guests. the bicycle checkout is open 24 hours per day 7 days per week and has 50 bicycles on hand. on average, 10 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. guests keep bicycles for four days on average, with a standard deviation of two days. how long does a guest on average have to wait for a bike? a. approximately 24 hours b. approximately 0.033 hours c. approximately 4 days d. approximately 47 minutes