A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to
make the maximum profit.
y = -3x^2 + 239x – 2268

The sum of the speeds of two trains is 720.2 mph. if the speed of the first train is 7.8 mph faster than the second train, find the speeds of each.

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?

In physics, if a moving object has a starting position at so, an initial velocity of vo, and a constant acceleration a, the the position s at any time t> o is given by: s = 1/2 at ^2 + vot+so solve for the acceleration, a, in terms of the other variables. for this assessment item, you can use^to show exponent and type your answer in the answer box, or you may choose to write your answer on paper and upload it.