A farmer has a large field that is x feet in length. He wants to fence in a rectangular section in the middle of the field, leaving a length of 100 feet of open field beyond each end of the fenced rectangle. He also wants the width of the fenced-in space to be 100 feet less than its length, as shown in the diagram.

Find the equation in standard form for the area of the fenced-in section in terms of the length of the field.

What is the shape of the height and weight distribution

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.

A. the probability that a product is defective is 0.1. what is the probability that there will be 1 or less defective products out of the next 8 produced products b.the expected number of imperfections in the coating nylon for parachutes is 6 per 100 yards. what is the probability of finding 12 or fewer imperfections in 260 yards c.in a lot of 54 products there are 9 defective products. calculate the probability that not more than 1 is defective from a random sample of 17 products.