You order a fruit smoothie made with 2 liquid ingredients and 3 fruit ingredients from the menu shown. How many different fruit smoothies can you order?

Write the system of equations represented by the matrix. 0 1 2 4 -2 3 6 9 1 0 1 3

Question part points submissions used suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a party. of these 100 tickets, only 12 are winning tickets. the generalized pigeonhole principle guarantees that there must be a streak of at least l losing tickets in a row. find l.

What is the missing step in this proof ?