Prove that there exists a positive integer $n$ such that the equation $x^2 + y^2 = n$ has at least 2005 solutions in non-negative integers $x$ and $y$.

Ageologist had two rocks on a scale that weighed 4.6 kilograms together.rock a was 0.5 of the total weight.how much did rock a weigh?

The sat and act tests use very different grading scales. the sat math scores follow a normal distribution with mean 518 and standard deviation of 118. the act math scores follow a normal distribution with mean 20.7 and standard deviation of 5. suppose regan scores a 754 on the math portion of the sat. how much would her sister veronica need to score on the math portion of the act to meet or beat regan's score?

Amajor grocery store chain is trying to cut down on waste. currently, they get peaches from two different distributors, whole fruits and green grocer. out of a two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. she then makes a confidence interval. is there a significant difference in the quality of the peaches between the two distributors? 95% ci for pw-pg: (0.064, 0.156)