A large plot of land is shaped like a trapezoid, ABCD, where AB is parallel to CD, AB = 12 km and CD = 8 km. The diagonal BD of the trapezoid is equal to 10 km. The internal angle ABD is equal to 58º. D 8 km С
D 10 km B
Angle B is 58
А 12 km B
Let a new point, H, be a point on AB closest to D.

(a) Calculate the distance from H to D.
(b) Calculate the length of AD.
(c) Calculate the size of the angle DÂB. A landowner estimates that the length of AD is equal to 11.5 km.
(d) Calculate the percentage error in the landowner's estimate.

The landowner decides to install cone-shaped concrete bollards along the perimeter of the plot of land. The bollards are to be installed at a distance of 100 m from each other. The radius of the base of each bollard is 20 cm and the height of each bollard is 40 cm.

(e) Calculate the volume of one of the bollards. (f) Calculate the total volume of concrete needed to install all the bollards.​

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.