After a month-long survey, you collect 146 responses. You found that 83% of the customers indicated the life of the motor is greater than 10 years. You would like to understand what proportion of the motors last longer than 10 years. How many surveys would you need to collect in total in order to obtain a margin of error of /- 5% with 89.9% confidence

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

I'm at a bookstore with $\$35$ in my pocket and a $20\%$-off coupon. what is the cost of the most expensive book i can buy with my money and the coupon? (assume that there are books of every possible price in the bookstore. it's a large bookstore! )

Why is causation so much more difficult to prove than correlation?