Consider the equation x^41 + 64x − 1=0 Which of the following statement is true?

a) The equation has a real root in the interval [-26,9]
b) The equation has a real root in the interval [-56,25]
c) The equation has a real root in the interval [-11,52]
d) The equation has a real root in the interval [-89,76]
e) All of the above
f) None of the above

If x=-3 is the only x-intercept of the graph of a quadratic equation, which statement best discribes the discriminant of the equation?

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?

Match the one-to-one functions with their inverse functions.