A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to difference between the radius of the hole and the radius of the shaft. Let the random variable X denote the clearance, in millimeters. The probability density function of X is

F(x) =1.25(1 - x4) if 0 < x < 1
F(x) = 0 otherwise

A. Components with clearances larger than 0.8 mm must be scrapped. What proportion of components are scraped?
B. Find the cumulative distribution function F(x) and plot it.
C. Use the cumulative distribution to find the probability that the shaft clearance is less than 0.5 mm.
D. Find the mean clearance and the variance of the clearance.

Iam stuck on one problem. my mind is in absoloute vacation mode. i literallty just need to finish this to be done will give brainliest and all my points if i have to! 1- point free throw and 2- point feild goal. he made 35 shots, and scored 62 points how many of each shot did he make in 1 minute? (i already did the math. he made 8 1-point free throws and 27 2-point feild goals.) 1. write two equations for the problem. (i had a major brain fart.)

Solve each quadratic equation by factoring and using the zero product property. x^2 - 8x + 30 = 3x

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.