A project manager is evaluating the performance of two teams, Team A and Team B. Team A completes tasks at a rate of 'x' tasks per hour. Team B completes tasks at a rate of 'y' tasks per hour. When working together on a project of 100 tasks, they finish in 'T' hours. If Team A were to work alone, it would take them (T + 15) hours to complete the project. If x = 4, what is the value of y?
A marketing firm surveyed 500 consumers. 280 of them use social media platform A, 220 use platform B, and 150 use platform C. 80 use both A and B, 70 use both B and C, and 60 use both A and C. If 100 consumers use none of these platforms, how many consumers use all three platforms? Here is a visual representation of the problem: A(280) B(220) \ / \ / 80 X 70 | C(150) 60 Where X is the number of consumers who use all three.
For a positive integer n, the function f(n) is defined as the product of all even integers from 2 to n, inclusive. For example, f(8) = 2 * 4 * 6 * 8. What is the largest prime factor of f(20) + f(22)?
A company's stock price, P, is modeled by the equation P = -2t² + 28t + 60, where 't' is the number of months after a new product launch (t ≥ 0). Which of the following statements about the stock price are true? (Select TWO)
A data processing job consists of two sequential steps: validation and computation. A server farm has two types of servers: V-type for validation and C-type for computation. The time taken for each step is given in the table below. ``` ┌──────────┬─────────────┬──────────────┐ │ Server │ Validation │ Computation │ ├──────────┼─────────────┼──────────────┤ │ V-type │ 3 minutes │ 8 minutes │ │ C-type │ 7 minutes │ 2 minutes │ └──────────┴─────────────┴──────────────┘ ``` To minimize the total processing time for one job, the validation step should be assigned to a V-type server and the computation step to a C-type server.
A new product has a 20% chance of being defective. A quality control test correctly identifies a defective product 90% of the time, and correctly identifies a non-defective product 85% of the time. If a randomly selected product tests as defective, what is the probability that it is actually not defective?
A financial analyst is modeling a company's revenue growth. The model is R(t) = 500 * (1.05)^(2t), where R is the revenue in thousands of dollars and t is the number of years from the start. What is the approximate percentage increase in revenue from the end of year 2 to the end of year 3?
If integers x and y are chosen from the set {1, 2, 3, 4, 5, 6} with replacement, what is the probability that x² - y² is a multiple of 3?
A factory produces widgets in two shifts. The day shift produces 'd' widgets per hour for 8 hours. The night shift produces 'n' widgets per hour for 8 hours. The cost to produce a widget is $1.50 during the day and $2.00 during the night. If the total production for a day is 1200 widgets and the total cost is $2100, what is the value of 'd'?
## Case Study: E-Commerce Warehouse Optimization A logistics company, "ShipFast," operates a large warehouse. They are analyzing the efficiency of their packing department. The department has both expert and novice packers. An expert packer can pack a box in an average of 3 minutes, while a novice packer takes an average of 5 minutes. The department operates in 8-hour shifts. During a typical shift, there are 'E' expert packers and 'N' novice packers working. The total number of packers on any shift is always 24. The cost of an expert packer is $30 per hour, and a novice packer is $18 per hour. The company has a daily target of packing at least 3,500 boxes. The total daily labor budget for the packing department for one shift is $5,000. The company wants to find the optimal mix of packers to meet their targets while staying within budget. Which of the following combinations of expert (E) and novice (N) packers meets the production target of 3,500 boxes in an 8-hour shift?