Grogg typed the following $1000$ expressions into his calculator, one by one: \[\sqrt{1}, \sqrt{2}, \sqrt{3}, \sqrt{4}, \dots, \sqrt{999}, \sqrt{1000}.\]How many times will Grogg's result be an integer?

Organisms that live in the alpine and taiga biomes have developed unique adaptations that aid in their survival. the douglas-fir is a conifer tree that grows in the taiga biome. it has an average height of about 70 feet, and its wood is an important source of lumber.

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.

Daniel expanded the expression as shown below -2(-8x-4y+3/4)=-10x-8y-11/4 what errors did he make? check all that apply