Question Solved1 Answer Find the topological sorting for the given graph. The rule of the sort is: remove the source with the largest outdegree first, and then remove the source with the smallest value. 20 36 18 34 73 67 78 56 19 41 43 57 28 37 62 95 81 82

6. Let S be the set of perfect binary trees, defined as: • Basic step: a single vertex v with no edges is a perfect binary tree T.. Recursive step: if T is a perfect binary tree, then a new perfect binary tree T' can be constructed by taking two copies of T, adding a new vertex v, and adding edges between v and the roots of each copy of T Prove that h(T) = log2(n(T) + 1) – 1 for any perfect binary tree T, where n(T) is the number of vertices of T and h(T) is the height of T.

Identify each variable as quantitative or qualitative.a) ethnic origin of a candidate for public officeb) score (0-100) on a placement examinationc) fast-food establishment preferred by a student(McDonald's, Burger King, or Carl's Jr.)d) mercury concentration in a sample of tuna

•• An infinite slab of charge of thickness 2zo lies in the xy-plane between z = -zo and 46. z = +z0. The volume charge density p (C/m³) is a constant. a. Use Gauss's law to find an expression for the electric field strength inside the slab (-zo zo). c. Draw a graph of E from z = 0 to z = 3z0.

Exercise 5 : Two particles in a potential well Consider two noninteracting particles, both of mass m, in a quadratic potential well (i.e. har- monic oscillator potential). For the case with one particle in the single-particle state [n) and the other in state k) (n + k), calculate the expectation value of the squared interparticle spacing ((21 – 222) assuming: 5.1 The particles are distinguishable 5.2 The particles are identical spin-o bosons 5.3 The particles are identical spin-1/2 fermions in a spin triplet state. Hint: use bra-ket notation as much as possible. Remember that for the harmonic oscillator it is easiest to use, whenever possible, raising and lowering operators to evaluate expectation values (i.e. to evaluate integrals).

Problem 4 A new test is developed for cancer detection with sensitivity 0.80 and specificity 0.91. Assume this cancer affects 6% of the population. (a) Sketch the probability tree for this test and label each branch appropriately. (b) Calculate the Bayes probability that an individual has cancer if their test result is posi- tive. (c) Calculate the Bayes probability that an individual does not have cancer if their test result is negative. (d) Compute a naive Bayes estimate for either b or c. Your choice! Then, briefly explain why is this referred to as "naive".

Activity #2 6. Using the chart provided in Lecture Module 2/Slide 71, what star would have been the North Star in 1000 BC? pts 7. (a) Bailey's beads occur during what type of eclipse? (Hint: There are 3 types of solar eclipses and 3 types of lunar eclipses. or these 6 types of eclipses, Bailey's beads can be seen only during 1 of them.] Part 10 pts (b) What Activity #2 6. Using the chart provided in Lecture Module 2/Slide 71, what star would have been the North Star in 1000 BC? pts 7. (a) Bailey's beads occur during what type of eclipse? (Hint: There are 3 types of solar eclipses and 3 types of lunar eclipses. or these 6 types of eclipses, Bailey's beads can be seen only during 1 of them.] Part 10 pts (b) What causes Bailey's beads to form? Part b = 10 pts 8. During an annular eclipse of the Sun, we see a bright annulus or "ring of fire." During a total solar eclipse we see the corona during totality. In both events, the Moon is directly in line with the Sun and Earth. What differentiates these two types of solar eclipses? That is what aspect of the eclipse geometry has changed to create an annular eclipse rather than a total eclipse? 115 pts