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.
Answer:
C
Step-by-step explanation:
A triangle always consists of it being 180 degrees. The box on the triangle on angle A depicts that it is a right angle, 90 degrees. And since Angle B is given at 45, angle C must be 45 degrees as well, since 180-45-90 (triangle angles=given angles for A and B) equal up to 45. When the angles beside the right angle is both identical and the same, the sides that correspond with that triangle is also the same. AC is given at 9 feet, and since Angle C and B both have the same angles, AB must ALSO be a 9ft.
Now, since we know the two sides, it is very easy to find BC, or the hypotenuse of the triangle, using the Pythagorean Theorem:
, where a and b are sides, and c is the hypotenuse (or the long end) of a right triangle.
We can plug both 9s in for a and b since they're both the same, and it should equal to
9^2+9^2=c^2.
9^2 is 9*9, and that is 81. We have two of these so add them together to find 162. Since c^2 is equal to 162, we would need to square root both sides so we can find a number that equals c.

We can either plug this into a calculator, and we should get something around 12.72, and that would be the same as C if you plug that value into a calculator.
You can also simplify the radical if you know how to. 162 is 81 times 2 (example) and 81 is 9*9, so we can add that to the outside and 2 is still under the radical. But this would only make sense if you know how to do that.
Answer:
Step-by-step explanation:
Given is the hexagonal pyramid.
We know the radius of the base is same as its side.
<u>Find the base area:</u>
- A = 3√3/2a²
- A = 3√3/2*6² = 54√3
<u>Given the height and radius, find the side of the lateral triangular faces:</u>
Each of 6 triangles have sides 10, 10 and 6 units.
<u>Find the area using heron's formula:</u>
- s = P/2 = (10*2 + 6)/2 = 13
- s - a = s - b = 13 - 10 = 3
- s - c = 13 - 6 = 7

<u>Total surface area:</u>
Correct choice is B
Answer:
It will take <u><em>80 days</em></u> for the bull calf to reach a weight of 500 kilograms.
Step-by-step explanation:
Given:
The weight of a bull calf is 388 kilograms.
Now, to find the weight of bull calf of how long it will take to reach a weight of 500 kilograms, if it’s weight increases at a rate of 1 2/5 kilograms per day.
Required weight which to be increased = 500 - 388 = 112 kilograms.
Rate of weight increase = 
=
Thus, the time required = 
=
=
<em>The time required = 80 days</em>.
Therefore, it will take 80 days for the bull calf to reach a weight of 500 kilograms.