An invariant point is a point that remains fixed under a transformation. For the transformations described below, determine whether there will sometimes, always, or never exist at least one invariant point. If so, describe the invariant point(s). If not, explain why invariant points are not possible.

The first-serve percentage of a tennis player in a match is normally distributed with a standard deviation of 4.3%. if a sample of 15 random matches of the player is taken, the mean first-serve percentage is found to be 26.4%. what is the margin of error of the sample mean? a. 0.086% b. 0.533% c. 1.11% d. 2.22%

Agroup of randomly selected apple valley high school students were asked to pick their favorite gym class. the table below shows the results of the survey. there are 528 students at apple valley high school. gym class number of students racquet sports 1 team sports 9 track and field 17 bowling 13 based on the data, what is the most reasonable estimate for the number of students at apple valley high school whose favorite gym class is bowling? choose 1 answer a. 9 b. 13 c. 119 d. 172

Eliza wants to make $10,000 from her investments. she finds an investment account that earns 4.5% interest. she decides to deposit $2,500 into an account. how much money will be in her account after 14 years?