Davindra made a paper box that is 8 in. Long, 5 in. Wide, and 1 in. High. It is shaped like a rectangular prism. What is the surface area of the box? *

106 in²

Step-by-step explanation:

Given that :

Davindra made a paper box that is 8 in. Long, 5 in. Wide, and 1 in. High.

Using the relation :

SA=2lw+2lh+2hw

Surface area :

2(lw + lh + hw)

l = 8 ; w = 5 ; h = 1

Surface area :

2(8*5 + 8*1 + 1*5)

Surface area :

2(40 + 8 + 5)

= 2(53)

= 106 in²

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)