Tarush is a landscape architect. For his first public project he is asked to create a small scale drawing of a garden to be placed in the corner of a city park. The garden is a right triangle with base 10 m10\text{ m} 10 m 10, start text, space, m, end text and height 15 m15\text{ m} 15 m 15, start text, space, m, end text . Draw the garden such that 11 1 1 unit on the grid below represents 2 m 2\text{ m} 2 m 2, start text, space, m, end text . ≈8.2\approx 8.2 ≈8.2 ≈8.9\approx 8.9 ≈8.9

If f(x) = x+8 and g(x) = 4x- 3, find (f+g)(x)

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?

Jeremy wants to determine the number of solutions for the equation below without actually solving the equation. which method should jeremy use?