Newton’s law of cooling states that for a cooling substance with initial temperature t0 , the temperature t(t) after t minutes can be modeled by the equation t(t)=ts+(t0−ts)e−kt , where ts is the surrounding temperature and k is the substance’s cooling rate. a liquid substance is heated to 80°c . upon being removed from the heat, it cools to 60°c in 25 min. what is the substance’s cooling rate when the surrounding air temperature is 50°c ? round the answer to four decimal places.

The length of an intercepted arc of a central angle of a circle is 4 cm. if the radius of the circle is 5 cm what is the measurement of the central angle to the nearest whole degree

(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?

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