15 athletes are assigned to one of three teams. Each team will have five athletes. The teams are different, so it matters who gets assigned to which team. How many ways are there to assign the athletes to the teams?

What is the value of ( ( 131 ) 39 + 11 ⋅ ( − 11 ) ) mod 13 ?

x = 2 3 ⋅ 5 2 ⋅ 7 ⋅ 13 3 y = 2 2 ⋅ 5 ⋅ 7 2 ⋅ 17 What is the prime factorization for lcm(x, y)?

A fair coin is flipped three times. Events A and B are defined as: A: there are at least two consecutive heads somewhere in the sequence B: at least one flip comes up tails What is p(A | B)?

  QUESTION 5.4     Show all your calculations in the text block below.     You have a 50 cm ribbon. You use 14 and 3/4 cm to tie around a gift and 5 and 1/4 cm to make a bow. How much ribbon do you have left? (3)

  QUESTION 4.3     Read the following descriptions of shapes and name them: A 2-D shape with 5 equal sides [ans1] A 2-D shape with 6 unequal sides [ans2] (2)

  QUESTION 2.4     How many more items were collected by the team Zizi  than the Blue team team? (1)

  QUESTION 2.5     Order the teams in ascending order by using their names: (1)

S and T are binary relations on the set {a, b, c, d} and are defined as follows: S = { (a, b), (a, c), (b, d), (d, c) } T = { (b, b), (c, a), (c, d), (a, d) } Select the set corresponding to T ∘ S .

Austin Manufacturing is considering three independent projects that each require an initial investment of $1.50 million. The estimated internal rate of return (IRR) and cost of capital for these projects are presented here:   Project 1:  cost of capital = 13%, IRR = 16% Project 2: cost of capital = 10%, IRR = 11% Project 3: cost of capital = 16%, IRR = 20%   Assume that Austin Manufacturing only pursues positive net present value projects. The company’s optimal capital structure calls for 45% equity.  Austin expects to have net income of $3,000,000.   a. If Austin establishes its dividend from the residual dividend model, what will be its payout ratio?   b. What would be the payout ratio if net income were only $2,250,000?