How many variations in the first-, second-, and third-place finishes are possible in a 100-yd dash with 6 runners?

Can you answer these problems and show work. 1. How many variations in the first-, second-, and third-place finishes are possible in a 100-yd dash with 6 runners? 2. Suppose a family plans 6 children, and the probability that a particular child is a girl is ½. Find the probabilities that the 6-child family has at least ...continues

In the game Over-and-Under, a pair of dice is rolled and one bets $1 whether the sum of dots showing on the two dice

11 Questions on probability, Mean, Median etc. 1. In the game Over-and-Under, a pair of dice is rolled and one bets $1 whether the sum of dots showing on the two dice is over 7, under 7, or exactly 7 with payoffs of $2, $2, and $5, respectively. Determine a person's expected net winnings if the bet is as indicated. ... ...continues

Linear equations as matrices

1. In Example 3 of Section 2.5, the text shows how to write a system of linear equations using matrix notation. You can similarly write a linear programming problem in matrix notation. Find matrices A, B, C, and X such that the maximization problem Maximize z = 3x1 + 2x2 + x3 ...continues

Onto or One-to-one

let f(s) = string s with 01100 concatenated. Example: f(0000) = 000001100 Show: a) the range of f b) f is onto c) f is one-one

Sets

let A= {n element of Z : n=4q+1 for q element of Z} B= {m element of Z : m=8r-3 for r element of Z} Prove: a) A is in B b) B is in A C) A=B in set notation.

Floor and ceiling functions

Let F(x): R -> Z be the floor function and C(x): R -> Z be the ceiling function. Select which of the following function equations are true (select zero or more answers). a. C(x) - F(x) = 1 for all x. b. C(F(x)) = F(x) for all x c. C(F(x)) = F(C(x)) - 1 for all x d. F(F(x)) = F(x) for all x

One-to-one, onto matching

All of the functions below follow the equation f(x) = x^2. However, they have different domains and co-domains. Match each to its properties. Remember, Z = the set of integers, R = the set of real numbers, R+ is the set of positive real numbers, R(nonneg) is the set of nonnegative real numbers. Match: * f: Z -> Z ...continues

Smallest positive value

Suppose n = (2^5)(3^7)(5^9)(7^4) m where n and m are integers. What is the smallest positive value of m that makes n a perfect cube (multiply the number out, please).

Big-O Big-Theta

Given the algorithm below, suppose the number of times the "beep" instruction is executed is f(n). Choose all true statements below, and no false ones... for i := 1 to n for j : = 1 to i for k := 1 to 18 BEEP next k next j next i a. f(n) is big-Theta (n^2) b. f( ...continues

Introduction to Statistics

Having trouble comprehending the attached questions. Need to complete these tasks for a study guide to final exam. 1 of 9 A medical research team studied the ages of patients who had strokes caused by stress. The ages of 34 patients who suffered stress strokes were as follows. Use 8 intervals starting with 25-29. 29 30 3 ...continues