Question 22 pts Use mathematical induction to prove the following statement: The sum of the first n even positive integers is (n2 + n). That is, 2 + 4 + 6 + 8 + + 2n = n2+ n. Use the space below to write your answer. You may use the symbol "^" for exponents. For example, n^2 is one way to write n2.

9.4.34  question   to estimate the height of a stone  figure, an observer holds a small square up to her eyes and walks backward from the figure. she stops when the bottom of the figure aligns with the bottom edge of the  square, and when the top of the figure aligns with the top edge of the square. her eye level is 1.811.81 m from the ground. she is 3.703.70 m from the figure. what is the height of the figure to the nearest hundredth of a  meter?

The circle below is centered at the point (3, 1) and has a radius of length 2. what is the equation?

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.