A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How many different sandwiches are possible? Breads: Italian, white, wheat Proteins: Tuna, ham, turkey, beans Cheese: Provolone, Swiss, American, none Vegetables: Lettuce, tomatoes, peppers, onions, pickles

480 different sandwiches

Step-by-step explanation:

To find how many sandwiches can be made, we need to find the number of possibilities for each choice: bread, protein, cheese, vegetables.

Bread: 3 types -> combination of 3 choose 1 -> 3

Protein: 4 types -> combination of 4 choose 1 -> 4

Cheese: 4 types -> combination of 4 choose 1 -> 4

Vegetables: 5 types -> combination of 5 choose 2 -> 5!/(3!*2!) = 5*4/2 = 10

So the number of different sandwiches is:

3 * 4 * 4 * 10 = 480

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)