Give an algebraic proof for the triangle inequality vw v w +≤+ . draw a sketch. [hint: expand 2 vw vw vw + ≤+ ⋅+ ( )( ) . then use the cauchy-schwartz inequality ( vw v w ⋅ ≤ ).]

At least two people have the same birthday in a school of 150 students

Tracy solved the following problem. which of the statements is true? 9 ÷ 3 + 6 × 2 3 + 6 × 2 9 × 2 18 her answer is correct. her answer is incorrect. she should have multiplied before dividing. her answer is incorrect. she should have multiplied before adding. her answer is incorrect. she should have added before dividing.

If the dimensions of a rectangular prism are 5 ft x 3.5 ft x 2 ſt, what is the surface area?