9514 1404 393
Answer:
779.4 square units
Step-by-step explanation:
You seem to have several problems of this type, so we'll derive a formula for the area of an n-gon of radius r.
One central triangle will have a central angle of α = 360°/n. For example, a hexagon has a central angle of α = 360°/6 = 60°. The area of that central triangle is given by the formula ...
A = (1/2)r²sin(α)
Since there are n such triangles, the area of the n-gon is ...
A = (n/2)r²sin(360°/n)
__
For a hexagon (n=6) with radius 10√3, the area is ...
A = (6/2)(10√3)²sin(360°/6) = 450√3 ≈ 779.4 . . . . square units
The rectangle with 6 rows has 30 people in the whole rectangle. The rectangle with 9 rows has 45 people.
6 x 5 =30
9 x 5 =45
30+45 =75 people
Answer:
The error is that 2 should have been added to both sides, 7 = x
Step-by-step explanation:
The first sampling method is Convenient Sampling. It is biased sampling and it is not representative of a random sample.
The second sampling method is Systematic Sampling. If this method of sampling is drawn from the population, it is an efficiently randomized sampling method.
Let us review the given answers.
1. Both samples should be exactly the same.
INCORRECT
2. Neither sample will be representative.
Because the second sampling method can be random, this answer is
INCORRECT.
3. The first sampling method, ..., is the most representative,
INCORRECT
4. The second sampling method, ..., is the most representative.
CORRECT
Estimate tree height: 50 ft
First, you'd have to get the hypotenuse of the smaller triangle to get the base of the bigger triangle. This can easily be done using Pythagorean theorem (15^2 + 5^2 = hyp^2). The hyp of smaller triangle/base of bigger triangle is 15.81 ft. Then you'd also want to get the angle adjacent to the 5 ft leg, and opposite the 15 ft leg of the smaller triangle to get one of the two remaining angles of the bigger triangle. This can be done via sohcahtoa, using the TOA part. The inverse tangent of opposite/adj leg will give you the angle you're looking for (71.6 deg). With that, you'll know that the remaining angle is 18.4 deg (sum of all angles is 180). You can solve for the height of the tree/hypotenuse of the bigger triangle by using SOH. Sine of 18.4 is equal to 15.81/hypotenuse. Solving for that will give you around 50 ft.