PLEASE HELP AND EXTRA POINTS. what method (factoring, using square roots, complete the square, and quadratic formula) would i use for solving this quadratic equation 6x^2+13x+2=0. justify your answer

Asimple random sample of size nequals14 is drawn from a population that is normally distributed. the sample mean is found to be x overbar equals 70 and the sample standard deviation is found to be sequals13. construct a 90% confidence interval about the population mean

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.