Answer:
You use the facts about a 30, 60, 90 triangle.
Step-by-step explanation:
The angles in a triangle add up to 180.
90+30+x=180
120+x=180
x=60
This is a 30-60-90 right triangle.
The side opposite the 30 degree angle is a.
The side opposite the 90 degree angle (hypotenuse) is 2a.
The side opposite the 60 degree angle is a
We know the side opposite the 90 degree angle.
2a = 12
Divide by 2.
a=6
a is the side opposite the 30 degree angle (y)
Because we know a, we can find a.
6
The square roots cancel, leaving 3.
6 times 3 is 18.
Therefore, the side opposite the 60 degree angle (x) is 18.
I'm fairly sure that the answer is an ecosystom.
Answer:
The new mean for the exam scores is 51
Step-by-step explanation:
the mean can be calculated using the formula
mean of scores = 
before the 20 points was added, the mean of the score was = 50.
Inserting this into the formula, we have:
50 = 
from this, we can compute the sum total of the scores as
sum total = 50 × 20 = 1000
when the extra 20 marks is added, the sum of the entire scores will be changed to 1000 + 20 = 1020.
Hence the new mean will be computed as (New Sum total of scores / Number of students)
= 
= 51.
∴ The new mean of the scores is = 51
Answer:
Step-by-step explanation:
It's 2.3 as the centre of a circle is twice the circumference learn the circle theorem
Material=wall+2*side and material is 40 ft so:
40=w+2s
w=40-2s
Area=ws, using w from above we get:
A=(40-2s)s
A=40s-2s^2
dA/ds=40-4s and d2A/ds2=-4
Since d2A/ds2 is a constant negative acceleration, when dA/ds=0, A(s) is at an absolute maximum.
dA/ds=0 when 4s=40, s=10 ft
And since w=40-2s, w=20 ft
So the dimensions of the pen are 20 ft by 10 ft, with the 20 ft side being opposite the wall. And the maximum possible area is thus 200 ft^2
