Given that a point P (1, 3) lies on the circumference of the circle from the centre (4, 7): Find the gradient of the line from the centre to point P (1, 3)
Hence, find the equation of the normal to the circle at P (1, 3)
find the equation of the tangent to the circle at P (1, 3)
Find the Radius of this circle.

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.

Sam is picking fruit from a basket that contains many different kinds of fruit. which set of events is independent?

How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid in order to get a 40% solution of acid?