25% just like money 25 50 75 1.00 same thing just going from .25 to .5 so 25%
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
1025
Step-by-step explanation:
3075/3=1025
Answer:
Step-by-step explanation:
x^2 = 64
√x² = √64
x = 8, -8
answer is B
Answer:
B, Work with the math instructors to create a list of students currently taking a math class. Randomly select
Step-by-step explanation:
Let's think of each scenario at a time.
(A) We select 100 students enrolled in college randomly that should be fine because we are taking only students that can take classes. this rules out faculty members and any other persons but also there may be students that will never take any math course as part of their study plan, this is ruled out on that basis.
(B)if we take 100 students from the list of math instructor, that will ensure that we have taken students that are taking math class now, and math is part of their study plan, seems fine.
(C) visiting cafeteria randomly on multiple days will give us random persons that may not even be enrolled in university. this can be ruled out on that basis.
(D)Ten class at random and surveying each student in every class will make sampling size large or small depending on students enrolled in each of the class this will not give us reliable results.
We can conclude that (B) is the beast method for obtaining reliable results.
