Question

6 a nonprofit foundation is hosting a pi day pi k running race. after the event, they report 45% of runners who registered for the pi day pi k race had never participated in a race before. of the runners who had participated in a race before, 90% completed the pi day pi k. of the runners who had never participated in a race before, 80% completed the pi day pi k. what percent of the runners who completed the pi day pi k had never participated in a race before?

Explanation:

Step1: Calculate the proportion of runners who had participated before and completed

Let the total number of registered runners be \(x\). The proportion of runners who had participated before is \((1 - 0.45)x=0.55x\). The number of those who had participated before and completed is \(0.55x\times0.9 = 0.495x\)

Step2: Calculate the proportion of runners who had never participated before and completed

The proportion of runners who had never participated before is \(0.45x\). The number of those who had never participated before and completed is \(0.45x\times0.8=0.36x\)

Step3: Calculate the total number of completed runners and the required proportion

The total number of completed runners is \(0.495x + 0.36x=0.855x\). The proportion of completed runners who had never participated before is \(\frac{0.36x}{0.855x}=\frac{360}{855}=\frac{24}{57}\approx 42\%\)

Answer:

Approximately \(42\%\)