A psychiatrist believes that 80% of all people who visit doctors have problems of a psychosomatic nature. 25 patients at random are selected to test the theory. Assuming that the psychiatrist's theory is true, if X be the number of the 25 patients who have psychosomatic problems, what is the mean value of X?

Here’s a look at a map of the east side of Dubuque, Iowa. It shows a driving path from a casino on the river to a golf course on the other side. According to the maps app on my phone, the driving distance is 3.0 miles. We’re most interested in the graphic at the bottom left, which indicates that 1 inch on the map (measure if you don’t believe me) corresponds to 2,000 feet in real life.   If a 50-foot boat were on the river, how big would it appear on the photo? Round to three decimal places.

Donna wants to give her child some cough medicine. However, she is unsure about the dosage, so she reads the directions. She notices that the dosage differs based on age. Determine the independent variable and the dependent variable.

Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap.Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? The answer to this question should be the amount of time in seconds rounded to four decimal places that it takes for Bob to run a complete lap around the circular track.