Consider a string consisting of a's, b's, and c's, where the number of b's is three times the number of a's and the number of c's is five times the number of a's. Prove that the length of the string is divisible by 3 Proof: Suppose s is a string of length n that consists of a's, b's, and c's, where the number of b's is times the number of a's, and the number of c's is | times the number of a's. Let x, y and z be the numbers of a's, b's, and c's in s, respectively. The length of s is the sum of the numbers of a's, b's and c's that are in s. Hence, n = x +y + = x+ 3x + by substitution by combining like terms by factoring out a common factor v Because x is an integer, so is x, and thus n equals 3· (an integer). Hence, by definition of divisibility, n is divisible by 3.

The number of measles cases decreased by 6% to 586 cases this year. What was the number of cases prior to the decrease?  Express your answer rounded correctly to the nearest whole number.

In general, most medical practices would hope to see a no show rate that is 3% or below.  As you have continued to monitor monthly schedules, the number of patient no shows have been alarming with 8,000 patients no showing of the 14,000 that were scheduled in August. Prior to determining initiatives to reduce missed appointments, you would like to determine the percentage of patients who no showed.  Calculate the no show rate for the medical practice:

The p-value is 0.0620, State the conclusion in terms of the claim and whether you would recommend shutting down the car factory with given p-value?