Because 10 lies between two consecutive perfect squares (in increasing order), and
, 10‾‾‾√ is located between the square roots of these two numbers. This means that 10‾‾‾√ is located between
and
, so 10‾‾‾√ is less than 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?

If x varies directly as y, and x = 7.5 when y = 10, find x when y = 4

Jack has a rectangular piece of land, the area of which is represented by a1 = 9.5l. his brother has a different rectangular piece of land, the area of which is represented by a2 = l(14 − l). let a represent the area in square meters and l represent the length in meters of the pieces of land. the two equations plotted on a graph meet at a point as shown in the image