According to the center for disease control (cdc), "measles is highly contagious and can be spread to others from four days before to four days after the rash appears. measles is so contagious that if one person has it, 90% of the people close to that person who are not immune will also become infected with the measles virus." if an individual has a contact rate of approximately 2 individuals per day, what percentage of the population needs to be vaccinated to prevent outbreaks of the disease?

Which of the expressions (on the photo document i inserted) together represent all solutions to the following equation? 8cos(12x)+4=-4 *the answer should be in degrees.* > i would like for someone to explain the process to find the solutions for this.

Combine the information in the problem and the chart using the average balance method to solve the problem.

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).