When rolling a pair of dice, the roll should come up 11 once every 18 rolls, or 5.6% of the time. You decide to test this out, rolling 40 times a day every weekday, and using the weekend to analyze the data. As the table shows, with the exception of Friday, every day you rolled either double the expected number of 11s, half the expected number of 11s or no 11s at all. Yet the average for all the days is 5.5%, virtually identical with the theoretical number. How do you explain this?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Rewrite the following quadratic functions in intercept or factored form. show your work. f(x) = 3x^2 - 12

First work with stencil one. use a combination of reflections, rotations, and translations to see whether stencil one will overlap with the original pattern. list the sequence of rigid transformations you used in your attempt, noting the type of transformation, the direction, the coordinates, and the displacement in