∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.
Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².
∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find
![\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm](https://tex.z-dn.net/?f=%5Csin%2830%5E%5Ccirc%29%20%3D%20%5Cdfrac%7Bh%7D%7B4%5C%2C%5Crm%20cm%7D%20%5Cimplies%20h%3D%202%5C%2C%5Crm%20cm)
where
is the length of the altitude originating from vertex O, and so
![\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%20b2%5Cright%29%5E2%20%2B%20h%5E2%20%3D%20%284%5C%2C%5Cmathrm%7Bcm%7D%29%5E2%20%5Cimplies%20b%20%3D%204%5Csqrt3%20%5C%2C%5Crm%20cm)
where
is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².
So, the total area of the shaded region is
(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²
Answer:
answer is 24 :)
Step-by-step explanation:
# of apples
3/8(a)=# of oranges
p=# of pears
3/4(p)=# of oranges
(3/8)a=(3/4)p
(3/8)/(3/4)=p/a
(3/8)(6/8)=p/a
3/6=p/a
1/2=p/a
the ratios of pears to apples is 1 to 2
for every 1 pear there are 2 apples
if there are 4 pears there are 8 apples
there are 8 apples
(3/8)(8)=3 oranges
there are 4 pears
(3/4)(4)=3 oranges again
8 apples, 3 oranges, 4 pears
15 pieces of fruit and 3 are oranges
ratio is 3/15=1/5
4/5/2015 | Arthur D.
Answer:
a. Mean
a. 79 points is an outlier, and the mean is most responsive to outliers.
Step-by-step explanation:
17, 14, 30, 24, 21, and 14
Let's calculate the measure of central tendency of the numbers first.
Mean = 120/6
Mean = 20
For Median
Let's arrange the numbers in ascending order
14,14,17,21,24,30
The median is 17 and 21
Median value =( 17+21)/2
Median = 38/2
Median = 19
Mode = 14.
After 79 was added.
Mean =( 120+79)/7
Mean = 199/7
28.43
For Median
14,14,17,21,24,30,79
Median= 21
Mode = 14
The value that changed the most was the mean value.