Acertain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: blue, green, yellow, or pink. the store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. if the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
a. 6.
b. 8.
c. 16.
d. 24.
e. 32.

Option C. 16

Step-by-step explanation:

Number of differents colors = 4

Number of differents sizes = 2

Case 1: 3 notepads of the same size and the same color:

If we have a package with the same size and the same color, the number of possible packages is:

N° packages = 4(colors)*2(sizes) = 8

Case 2: 3 notepads of the same size and different colors:      

In this case, to calculate the number of possible permutations of packages without repetitions we need to use the following equation:    

where p: is the number of colors for each package = 3, and n: is the total number of colors = 4.

This number calculated is for one size, if the have two different sizes the number of possible packages is:

N° packages = 4(colors)*2(sizes) = 8    

Therefore, the total number of different possible packages is:

N° packages = case 1 + case 2 = 8 + 8 = 16

So, the correct answer is option C = 16.

I hope it helps you!

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!