The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6 matches. What is the mean for the number of matches that they win in the tournament?

The mean for the number of matches that they win in the tournament is 20.

Step-by-step explanation:

For each match, there are only two possible outcomes. Either they win, or they do not. The probability of winning a match is independent from other matches. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

The Stomping Elephants volleyball team plays 30 matches in a week-long tournament.

This means that

On average, they win 4 out of every 6 matches.

This means that

What is the mean for the number of matches that they win in the tournament?

The mean for the number of matches that they win in the tournament is 20.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).