Two systems of equations are shown below: system a system b 2x + y = 5 −10x + 19y = −1 −4x + 6y = −2 −4x + 6y = −2 which of the following statements is correct about the two systems of equations? they will have the same solutions because the first equation of system b is obtained by adding the first equation of system a to 2 times the second equation of system a. they will have the same solution because the first equation of system b is obtained by adding the first equation of system a to 3 times the second equation of system a. the value of x for system b will be −5 times the value of x for system a because the coefficient of x in the first equation of system b is −5 times the coefficient of x in the first equation of system a. the value of x for system a will be equal to the value of y for system b because the first equation of system b is obtained by adding −12 to the first equation of system a and the second equations are identical.

How can you find the conditional probability of a given b as the fraction of b’s outcomes that also belong to a, and interpret the answer in terms of the model? i just need a good explanation

Which of the following is the shape of a cross section of the figure shown below

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?