Answer:
x = 8
Step-by-step explanation:
All the sides are equal. So, it is an equilateral triangle. So, all angles are 60 each
6x + 12 = 60
6x = 60 - 12
6x = 48
x = 48/6
x = 8
The picture in the attached figure
we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]
step 1Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²
step 2find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²
step 3the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²
therefore
the answer isthe area of the shaded region is 44.22 units²
Answer:
P(X is greater than 30) = 0.06
Step-by-step explanation:
Given that:
Sample proportion (p) = 0.5
Sample size = 30
The Binomial can be approximated to normal with:


To find:
P(X> 30)
So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 30 lies between 29.5 and 30.5
Normal distribution:
x = 30.5,
= 25,
= 3.536
Using the z test statistics;



z = 1.555
The p-value for P(X>30) = P(Z > 1.555)
The p-value for P(X>30) = 1 - P (Z< 1.555)
From the z tables;
P(X> 30) = 1 - 0.9400
Thus;
P(X is greater than 30) = 0.06
Answer:
f(x) = x^2 -2x -8
Step-by-step explanation:
(x+2)(x-4)
FOIL
first: x*x = x^2
outer: -4x
inner: 2x
last: 2*-4x = -8
Add together
x^2 +2x-4x-8
x^2 -2x -8
This is a parabola