The work of a student to solve a set of equations is shown:
equation a: y = 4 − 2z
equation b: 4y = 2 − 4z
step 1: −4(y) = −4(4 − 2z) [equation a is multiplied by −4.]
4y = 2 − 4z [equation b]
step 2: −4y = 4 − 2z [equation a in step 1 is simplified.]
4y = 2 − 4z [equation b]
step 3: 0 = 6 − 6z [equations in step 2 are added.]
step 4: 6z = 6
step 5: z = 1
in which step did the student first make an error?
step 1
step 3
step 4
step 2

Astudy was interested in determining if eating milk chocolate lowered someone's cholesterol levels.ten people's cholesterol was measured. then, each of these individuals were told to eat 100g of milk chocolate every day and to eat as they normally did. after two weeks, their cholesterol levels were measured again. is there evidence to support that their cholesterol levels went down? how should we write the alternative hypothesis? (mud = the population mean difference= before - after)a. ha: mud = 0b. ha: mud > 0c. ha: mud < 0d. ha: mud does not equal 0

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?

Arestaurant offers delivery for their pizzas. the total cost the customer pays is the price of the pizzas, plus a delivery fee. one customer pays $23 to have 2 pizzas delivered. another customer pays $59 for 6 pizzas. how many pizzas are delivered to a customer who pays $86?