Let z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by:
alpha o k = [[alpha]].k for all k in z

where [[alpha]] denotes the greatest integer less than or equal to alpha, for example,
2.25 o 4 = [[2.25]].4 =2..4 = 8
show that z, together with these operations, is not a vector space. which axioms fail to hold?

Cody was 165cm tall on the first day of school this year, which was 10% taller than he was on the first day of school last year.

Time (minutes) amount of water (gallons) practice 1. jin fills up a 510-gallon pool in the backyard for her children. she fills it with the garden hose at a rate of 17 gallons per minute. after it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. the children then get in and have fun for an hour. the pool loses about 5 gallon of water each minute due to their splashing and playing. at the end of the hour, they tear the pool while getting out, which causes a leak the pool then begins to lose water at a rate of 2 gallons per minute. a. complete the table to show the amount of water in the pool after each minute. b. create a graph to model the problem situation. include when the pool will be empty. c. write a piecewise function that models this problem situation. explain your reasoning for each piece of the function. d. identify the x- and y-intercept. explain what they mean in terms of the problem situation, atamantha a cul 80 100 120 150 200 ning, inc

Do xuan nam isgoing to invest $1000 at a simple interest rate of 4% how long will it take for the investment to be worth $1040?