The first step is to square root both sides to get the exponent out. that actually is the only step :)
Answer:
Explanation:
Number the sides of the decagon: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, from top (currently red) clockwise.
- The side number one can be colored of five different colors (red, orange, blue, green, or yellow): 5
- The side number two can be colored with four different colors: 4
- The side number three can be colored with three different colors: 3
- The side number four can be colored with two different colors: 2
- The side number five can be colored with the only color left: 1
- Each of the sides six through ten can be colored with one color, the same as its opposite side: 1
Thus, by the multiplication or fundamental principle of counting, the number of different ways to color the decagon will be:
- 5 × 4 × 3 × 2 ×1 × 1 × 1 × 1 × 1 × 1 = 120.
Notice that numbering the sides starting from other than the top side is a rotation of the decagon, which would lead to identical coloring decagons, not adding a new way to the number of ways to color the sides of the figure.
Answer:
1/12
Step-by-step explanation:
He has a 1/4 pan left and wants to divide that into 3 equal pieces. So in night he will eat 1/3 of what he has left from the 1/4 pan. To figure out how much one slice is from an entire pan:
1/4 * 1/3 = 1/12
One bag of popcorn would cost $6.50
To solve this, we can set up equations:
28p+40c=$282
17p+20c=$160.50
To solve this system, we would need to make either the candy bars the same or the bags of popcorn the same. Since we are solving for bags of popcorn, we will make the candy bars the same:
20(28p+40c=$282)
40(17p+20c=$160.50)
Which would give you:
560p+800c=$5,640
680p+800c=$6,420
Subtract them:
(680p+800c=$6,420)
-(560p+800c=$5,640)
_________________
120p=$780
Now divide by 120 to get the price of one bag of popcorn:
120p=$780
_________
120
p=$6.50
