An archaeologist is categorizing the artifacts he has discovered. two-thirds of the artifacts are shards of pottery. one-eighth of the artifacts are tools. the remaining artifacts are personal items, such as buttons, jewelry, and fragments of clothing. the archaeologist has discovered a total of 72 artifacts. how many of these are personal items?

Personal items=15

Step-by-step explanation:

We are given:

Total number of artifacts = 72.

We are told that 2/3 of total artifacts are shards of pottery.

We are also told that 1/8 of total artifacts are tools.

Now we will find out number of personal items by subtracting combined number of shards of pottery and tools from total number of artifacts.

Therefore, there are 15 personal items.

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.