Jess has a storage bin that is 3 ft. High, 4 ft. Long, and 2 ft. Wide. If each box is one cubic foot in volume, how many will fit into the storage bin?

The number of boxes that will fit into the storage bin is 24 boxes

Step-by-step explanation:

Here we have the the dimensions of the bin given as

Height of bin = 3 ft

Length of bin = 4 ft

Width of bin = 2 ft

Volume of bin is given by

Volume of bin = Length of bin × Width of bin × Height of bin

The size of the box is also given as 1 ft³

Therefore since the volume of the bin = 3 ft × 2 ft × 4 ft =24 ft³

There is enough room for;

The number of boxes that will fit into the storage bin is therefore, 24.

24 boxes

Step-by-step explanation:

First we need to calculate the volume of the storage bin.

This volume can be calculated multiplying all the 3 dimensions of the storage bin:

V = H * L * W

Where V is the volume, H is the height, L is the length and W is the width of the storage bin.

So, its volume is:

V = 3 * 4 * 2 = 24 ft3

If each box has 1 ft3 in volume, we divide the volume of the storage bin by the volume of the box to find how many box will fit in the bin:

number of boxes = 24 / 1 = 24 boxes

1.5%

step-by-step explanation:

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24