Solve the equation, keeping the value for x as an improper fraction. 2 3 x = − 1 2 x + 5 1. Isolate the variable by adding 1 2 x to both sides: 1 2 x + 2 3 x = 5 2. Use the common denominator to add terms: 3 6 x + 4 6 x = 5 7 6 x = 5 3. Multiply by the reciprocal: 6 7 (7 6 )x = 5(6 7 ) x =

Find all the values of x that make 0.1x + 0.25(102 - x) < 17.10 true.

Which of the following parabolas opens down?

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?