Question Solved1 Answer Do n to 17. The decay of a certain substance is modelled by the function N(t) = 100(3+ e ), where the number of particles is represented by N in a time of t hours. a. What is the initial number of particles? b. Determine the rate of change in the number of particles at time t. c. How fast is the number of particles changing when t = 3 hours? %3D

5. (8 marks ) For each of the following, determine it is always "true (T)" or "false (F)". Expla- nation is NOT required. (a) Example: 1+1=2. (b) A homogeneous system of equations can be inconsistent. (c) If A and B are n x n matrices, then (A - B)2 = A - 2AB + B2. (d) If A and B are nonsingular n x n matrices, then A+B is also nonsingular. (e) If A and B 5. (8 marks ) For each of the following, determine it is always "true (T)" or "false (F)". Expla- nation is NOT required. (a) Example: 1+1=2. (b) A homogeneous system of equations can be inconsistent. (c) If A and B are n x n matrices, then (A - B)2 = A - 2AB + B2. (d) If A and B are nonsingular n x n matrices, then A+B is also nonsingular. (e) If A and B are nonsingular matrices, then det((ATB)-°) = (det(A) det(BT)]-. Answer: Statement (a) Example (b) (c) () (e) True or not FT nin

Write a C++ program to find first and follow of any grammar in C++ language

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".