A rectangular paperboard measuring 31 in long and 24 in wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.

Marcus built a model car that is 4 inches wide. what scale was used to build the car if the actual width of the car is 6 feet? a. 1 in. = 2 ftb. 1 in. = 2.5 ftc. 1 in. = 1.5 ftd. 1 ft = 1.5 in.

The upcoming championship high school football game is a big deal in your little town. the problem is, it is being played in the next biggest town, which is two hours away! to get as many people as you can to attend the game, you decide to come up with a ride-sharing app, but you want to be sure it will be used before you put all the time in to creating it. you determine that if more than three students share a ride, on average, you will create the app. you conduct simple random sampling of 20 students in a school with a population of 300 students to determine how many students are in each ride-share (carpool) on the way to school every day to get a good idea of who would use the app. the following data are collected: 6 5 5 5 3 2 3 6 2 2 5 4 3 3 4 2 5 3 4 5 construct a 95% confidence interval for the mean number of students who share a ride to school, and interpret the results. part a: state the parameter and check the conditions. part b: construct the confidence interval. be sure to show all your work, including the degrees of freedom, critical value, sample statistics, and an explanation of your process. part c: interpret the meaning of the confidence interval. part d: use your findings to explain whether you should develop the ride-share app for the football game.

The weights of soy patties sold by a diner are normally distributed. a random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard deviation of 0.5 ounces. at the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is < 4 ounces. what is the correct conclusion at the 0.05 level of significance?