Answer:
There is enough evidence to support the claim that the percent that the goalkeeper guessed correctly is less than 50%.
Step-by-step explanation:
We have to perform an hypothesis test on a proportion.
We have a sample of size n=138, a sample mean of p=0.41.
The standard error is SE=0.043.
We want to test the claim that the real proportion is below 50%.
Then, the null and alternative hypothesis are:

The significance level is α=0.05.
The z-statistic can be calculated as:

The P-value (left tail test) for this z-statistic is:

The P-value is smaller than the level of significance, so the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the percent that the goalkeeper guessed correctly is less than 50%.
Answer:

Step-by-step explanation:
Given
The attached graph
Required
The graph equation
Pick two points from the graph, we have:


Start by calculating the slope (a)

So, we have:



The equation is then calculated using:

So, we have:


Lets say that Williams current age is x, since it is currently unknown
From here we know that in 15 years (x+15) he will be 3 times his age 5 years prior (3x-5). Thus we can set these equations up as equal to one another
1) x + 15 = 3(x - 5)
2) x + 15 = 3x-15
3) 30= 2x
4) 15 = x
5) Now this age is his current age of 15 years, but they also want his age 15 years from now
The equation is x + 15 = 3(x - 5)
This should be correct now, sorry for the misconception. Good luck