Question 11 (5 points) Solve the problem. Among all pairs of numbers whose difference is 58,...
Among all pairs of numbers whose difference is 22, find a pair whose product is as small as possible. What is the minimum product? . The pair of numbers whose difference is 22 and whose product is as small as possible is (Use a comma to separate answers.) The minimum product is 1.
Among all pairs of numbers with a sum of 139, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.
8. Find all pairs of numbers whose sum of squares is 14 and whose difference of squares is 4.
1.
First find all the closest pairs of points among this set of
points.
Then choose a pair of points below such that the first point is
in a closest pair, and the second point is NOT in a closest
pair.
a)
(12,8) and (12,1)
b)
(20,7) and (1,3)
c)
(1,3) and (27,8)
d)
(8,10) and (1,3)
(4.7)(8,10) (12.8) (16,10) (20,7) (27,8) (1,3) (8,4) (12,1) (16, 3) (20,1) (24,4)
Solve the problem using a system of equations in two variables. Find two positive numbers whose squares have a sum of 25 and a difference of 7. h The two numbers are 1 (Use a comma to separate answers.)
Problem 5(4 points): Solve following LP problem by Simplex Algorithm Mar = 11 +12 subject to 2r1tr2 29 ri +2r2 25
Problem 5(4 points): Solve following LP problem by Simplex Algorithm Mar = 11 +12 subject to 2r1tr2 29 ri +2r2 25
Problem 11. (5 points) Roberto finishes a triathlon in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among all women in the race, the mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better in relation to their gender?
4.39 Exercise. Find all pairs of numbers a and b in {2,3,...,11) such that ab = 1 (mod 13). The preceding theorems and examples are giving us a perspective about numbers and their multiplicative inverses modulo a prime p. One conse- quence of this picture is that when we multiply all the numbers from 2 up to (p - 2), we get a number congruent to 1 modulo the prime p.
Problem 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers 1 to 4 without replacement. Let A,δΊ§(1,2,3,41, be the event that the first number is . 1. Find the probability of the event B that the second number chosen is 3. 2. What is the probability that the first number is 1 given that the second number is 3?
Problem 4: Please use the paired difference test to solve this problem given the following conditions (5 points). Employee # Before (1) After (2) Difference Di 1 8 11 2 7 5 3 11 19