Hugo took these steps to solve the system of equations.

2 x minus 3 y = negative 11. 3 x + 2 y = negative 5.

step 1 4 x minus 6 y = negative 11. 9 x + 6 y = negative 15.
step 2 13 x = negative 26
step 3 x = negative 2
step 4 3 (negative 2) + 2 y = negative 5. negative 6 + 2 y = negative 5. 2 y = 1. y = one-half.
step 5 the solution is (negative 2, one-half).

is hugo’s solution to the system of equations correct? explain why or why not.
yes, hugo’s solution is correct.
no, hugo should have gotten positive 2 in step three.
no, hugo forgot to multiply both sides of the first equation in step one.
no, hugo should have subtracted the equations instead of adding them in step 2.

On a piece of paper graft y+2> -3x-3 then determine which answer matches the graph you drew

Solve the triangle. a = 21°, c = 105°, c = 5

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?