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1. What is (-1/2)! x (-1/2)!
2. Write the complex form (a + bi) for: Sqrt ( i )
3. Find the Limit as n goes to infinity for: (1^n + 2^n + 3^n + 4^n....+ n^n) ---------------------over--------------------- (n^1+ n^2 + n^3 + n^4 ... + n^n)
4. I agree that it will vary but we can bound the area.
5. Suppose you have a triangle that has 2-1 inch lengths. Divide this triangle into half by drawing a line from vertex between the two identical sides, choose one of the sides randomly and shade it. The non-shaded side is cut in half again. Choose one of these sides randomly and cut it in half again shading one random piece. If this pattern of cut, shade, cut, cut, shade, cut, cut, shade cut, cut,.... was to be continued forever, what would be the area of the shaded region?
6. Maybe one of you answered this question: :) I should have included this pic though...
7. Suppose i have a circle. I cut off its arcs such that it became the biggest possible square i could make from that circle. What's the ratio of the edge of the circle to the middle of the edge of the square (assume minimum length) to the radius of the circle.
8. No they just need to be distinguishable.
9. Imagine you have several distinguishable rows composed of several distinguishable columns The intersection of the rows and columns either have a 1 or a 0. Each row sums to the same value and the question is how many of the columns can you eliminate assuming the the 1's in each row are randomly distributed across the columns Example, there are 30 rows and 20 columns with each row containing 7 randomly dispersed 1's. How many columns can be eliminated reducing the total in each row by no more than 2.
10. I meant them to be fractions so five in each
11. Mining gold in a particular region is hard work. The metal only appears in 1% of rocks in the mine. But your friend Old Joe created a detector he’s been perfecting for months and it is finally ready. To your astonishment it always detect gold if gold is present. Otherwise it will have a 90% accuracy rate in detecting that a particular rock does not have gold. Working with Old Joe, You guys scan a large rock and determine that it gives a positive result. In loading it up, Old Joe realizes that both of you can't fit into the vehicle. He offers to sell his share to you for \$200. You know that a rock of gold that size is worth easily \$1000. Is that a fair price? Assume the vehicle remains with the proper owner.
12. There are two bowls that you and a challenger must eat from. After flipping a coin you were selected to pick the bowl that each would eat from. In the first bowl there are three out of five poisonous apples. In the second bowl, there are two out of five poisonous apples. Whoever eats from the first bowl must eat two apples at random from the bowl. Whoever eats from the second bowl must eat three random apples from the second bowl. Which bowl should you pick to eat?
13. If I am not mistaken, you found a way to calculate the area every time; which is wonderful, However, I wanted to know if it could be extended to know the amount of nxn squares that were defined within the shape not the precise area.
14. nails are 12 perimeter are the side lengths, 8+sqrt(2) Forgive my english, i think i see the confusion. When I say the number of nails in the perimeter what I am really trying to say is the number of nails throughout the shape.
15. Hmmm, I only considered convex figures when making this problem. Let us first solve the simple case (only convex) then we could consider the more complex case with the relaxed condition.
16. Imagine a piece of plywood with an array of evenly spaced nails forming small squares and consider that each square has side lengths of 1 unit. A simple closed shape is formed with a rubber band. If you knew the number of nails used in the perimeter and the perimeter itself, how could you predict how many squares can be counted inside this rubber band shape? for example say the rubber band shape is outlining these nails: * - * - * - * - * | / * * * * | / * - * - * Perimeter = 8 + 2*sqrt(2) Nails = 12 Squares: 6 squares (5 - 1x1 and 1 - 2x2) --- the result of 6, at a minimum, is what we are trying to predict.
17. excellent work as always bonanova but should
18. Alas, English.... But I am confused. From your interviewing you know for a fact that this family has A boy. So regardless of their birth order all we don't know is the probability that the other child is a boy. And the other child could be a boy or girl, so I still believe it is 1/2.
19. If it is given that they already have one boy then... I get 1/2. Since the second child could either be a boy or a girl. Note: The spoiler buttons seems to be missing on mobile again.
20. Assume we have a circle and a rectangle. The circumference of the circle is the same as the perimeter of the rectangle and the areas of each shape is also the same. Write the ratio of the circle's circumference to the diagonal of the rectangle as a function in terms of the width of the rectangle.
21. I hope there is a nuanced way of solving this besides brute force.
22. The first case
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