It takes lacey 3 hours to knit a stocking cap and 5 hours to knit a pair of mittens. she has at most 20 hours of spare time in a week and knits at least one pair of mittens each week. let x stand for the number of stocking caps and let y stand for the number of pairs of mittens. write a system of linear inequalities that models the number of stocking caps and pairs of mittens that lacey can knit in a week. graph the solution. a. 5x+3y≤1x≤1 b. 3x+5y≤20y≥1 c. 3x+5y≥20y≥1 d. 3x+5y≤20x≥1

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

Awater truck is filling a swimming pool. the equation that represents this relationship is y=19.75x where y is the number of gallons of water in the pool and x is the number of minutes the truck has been filling the pool.

What is the least common multiple for 6 and 8? what is the least common multiple for 4 and 12 ? what is the least common multiple for 11 and 12? what is the least common multiple for 3 and 6?