Aset of 48 cards is numbered with positive integers from 1 to 48. if the cards are shuffled and one is chosen at random, what is the probability that the number on the card is a multiple of both 6 and 8?

The probability of randomly drawing a card that is a multiple of both 6 and 8 is:

P = 1/24 = 0.42

Assuming that all the cards have the same probability of being randomly drawn, we can conclude that the probability of randomly drawing a number that is multiple of both 6 and 8 is equal to the quotient between the number of cards that are multiples of both 6 and 8, and the total number of cards on the deck.

The multiples of 6 are:

6*1 = 6

6*2 = 12

6*3 = 18

6*4 = 24

6*5 = 30

6*6 = 36

6*7 = 42

6*8 = 48

The multiples of 8 are:

8*1 = 8

8*2 = 16

8*3 = 24

8*4 = 32

8*5 = 40

8*6 = 42

The common multiples are: 24 and 42.

Then out of 48 cards, there are only two that are multiples of both 6 and 8, then the probability of randomly choosing one of these two is:

P = 2/48 = 1/24 = 0.042

If you want to learn more about probability, you can read:

link

multiples of 6 = 6, 12, 18, 24 , 30, 36 ,42 , 48

multiples of 8 = 8, 16, 24,32,40,48

 24 & 48 are the common multiples

so there is a 2 out of 48 chance which is 2/48 which reduces to 1/24 probability

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: