The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.22. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 80% confidence level with an error of at most 0.03? Round your answer up to the next integer.

Will give brainliest sum of arithmetic series (sigma notation) find the numerical answer to the summation given below. (image shown below)

This is so hard and it’s for a test

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.