A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of the trip-length to be normally distributed.

a. If the office opens at 9:00am and he leaves his house at 8:40 am daily, what percentage of the time is he late for work? You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number.
b. Find the length of time above which we find the longest 20% of the trips. You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number.
c. Find the probability that two of the next three trips will take at least 30 minutes.

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Three times the sum of a number and seven is negative thirty-six. what is the number?

Determine the domain and range of the given function. the domain is all real numbers all real numbers greater than or equal to –2{x: x = –2, –1, 0, 1, 2}{y: y = –2, –1, 0, 1, 2}. the range is all real numbers all real numbers greater than or equal to –2{x: x = –2, –1, 0, 1, 2}{y: y = –2, –1, 0, 1, 2}.