Answer:
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.
The hypothesis illustrates that the males in the group don't follow a same distribution as all the males that are in the United States.
<h3>How to illustrate the information?</h3>
Based on the information given, it should be noted that the degree of freedom given in this case will be:
= 4 - 1
= 3
By using the Excel function, the p-value is given as 0.0002. In this case, we've to reject the null hypothesis if the p value is less than 0.1.
Therefore, we will reject the null hypothesis in this case. In inferential statistics, the null hypothesis is that two possibilities are the same. It is observed difference is due to chance alone. Using statistical tests, it is possible to calculate the likelihood that the null hypothesis is true
Therefore, the hypothesis illustrates that the males in the group don't follow the same distribution as all the males that are in the United States.
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Let's deconstruct the equation.
K x (1/8) = 7
You want to isolate K, so you multiply by 8 for both sides (since 8 x 1/8 = 1)
So, K = 7 x 8
K=56
2)
P(4,-4) -->(-4, 7)
4 - 8 = -4 -------->left 8
-4 + 11 = 7 -------->up 11
Answer: left 8; up 11
3)
C(3,-1) , left 4 up 1
3 - 4 = -1 -------->left 4
-1 + 1 = 0 -------->up 1
a)
(x , y) -->(x - 4 , y +1)
C(3, -1) -->C'(-1 , 0)
b)
(x , y) --> (x - 4, y + 1); (-1 , 0)