7kg of soybean oil which costs $4/kg was combined with 14kg of canola which costs $1/kg. find the cost per kg of mixture.

Arectangle has a width of 5 cm and a length of 10 cm. if the width is increased by 3, how does the perimeter change?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

David leaves his house to go to school. he walks 200 meters west and 300 meters north. how far is david from his original starting point?