bulletin board border
please help me. i would like to make a geometry bulletin board that has a a border of circles, triangles and squares. i know that 20 shapes will fit across the board and that 12 shapes will fit down the board . if i start in the top left hand corner with a circle, followed by a triangles, then a square, and repeat this pattern all around the board, how many of each shape will i pattern all around the board, how many of each shape will i need? explain your solution using words and pictures.
sorry, no pictures here.
If 20 fit across top and bottom, that's 40.
The sides hold 12, but top and bottom are already taken at the corners, leaving room for 10 more along the sides. That makes 20 more for both sides.
So, you will have 60 pictures in all.
Since you have 3 different pictures, I guess you can figure how many of each you will need . . .
you could also have figured this out by spending 5 minutes drawing the border . . .
Three letters are chosen at random from the letters P, A, N, S, O, L. What is the size of the sample space of this experiment? Assume that the order of the letters matters. That is, PAN is different from APN.
To determine how many of each shape you will need for the bulletin board, we first need to calculate the total number of shapes that fit on the board.
Given that 20 shapes fit across the board and 12 shapes fit down the board, we can calculate the total number of shapes using the formula:
Total number of shapes = Number of shapes across × Number of shapes down
Total number of shapes = 20 × 12 = 240
Now, since you want to create a pattern of circles, triangles, and squares around the board, let's break down the total number of shapes into quantities of each shape.
To determine the number of circles, triangles, and squares needed, we need to find the least common multiple (LCM) of the respective shapes in the pattern – in this case, 3 shapes (circle, triangle, and square).
The LCM of 3 shapes is equal to the product of the maximum multiplicities of each shape within the pattern. In this scenario, the maximum number of circles, triangles, and squares that repeat continuously in the pattern is 1.
Therefore, the LCM of 3 is 1.
Now, we divide the total number of shapes (240) by the LCM (1) to find the quantity of each shape needed:
Number of circles = Total number of shapes ÷ LCM = 240 ÷ 1 = 240
Number of triangles = Total number of shapes ÷ LCM = 240 ÷ 1 = 240
Number of squares = Total number of shapes ÷ LCM = 240 ÷ 1 = 240
So, you will need 240 circles, 240 triangles, and 240 squares to complete the pattern all around the board.
Here's an example representation of the pattern:
```
C T S C T S C T S C T S ...
C T S C T S C T S C T S ...
C T S C T S C T S C T S ...
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
```
In this diagram:
C represents a circle
T represents a triangle
S represents a square
The pattern continues horizontally and vertically across the bulletin board.