Aneedle of length l is dropped on an infinite plane surface that is partitioned into rectangles by horizontal lines that are a apart and vertical lines that are b apart. suppose that the needle’s length l satisfies l < a and l < b. what is the expected number of rectangle sides crossed by the rectangle? what is the probability that the needle will cross at least one side of some rectangle?

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) step 1: 12 + (–3)·(–2x) + (–3)·(4) step 2: 12 + 6x + (–12) step 3: 12 + (–12) + 6x step 4: 0 + 6x step 5: 6x what property of real numbers was used to transition from step 3 to step 4? a. identity property of addition b. inverse property of addition c. associative property of addition d. commutative property of addition

What is f(3) for the quadratic functionf(x)=2x2 + x – 12? f -3g 3h 6i. 9

You’re giving a cube with a length of 2.5 cm and a width of 2.5 cm and a high of 2.5 cm you place it on a scale and it is 295 g calculate the density