Answer:
129.3 in²
Step-by-step explanation:
The shaded segment is calculated as
area of sector ABC - area of triangle ABC
area of sector = area of circle × fraction of circle
A = πr² ×
= π × 18² ×
= 324π × = 54π in²
area of Δ ABC = × 18 × 18 × sin60° ≈ 40.30 in²
Then
shaded area = 54π - 40.30 ≈ 129.3 in² ( to the nearest tenth )
Answer:100mm
Step-by-step explanation:
Answer:B
Step-by-step explanation: Alternate exterior angles theorem
Answer:
see explanation
Step-by-step explanation:
consecutive even integers have a difference of 2 between them
for example 2, 4, 6 are 3 consecutive even integers
In general if we let the first integer be k then the next 2 integers are
k + 2 and k + 4
the sum of these equals 4 times the first integer, that is 4k, hence
k + k + 2 + k + 4 = 4k
3k + 6 = 4k ( subtract 3k from both sides )
6 = k
the 3 consecutive integers are
k = 6
k + 2 = 6 + 2 = 8
k + 4 = 6 + 4 = 10
that is 6, 8 and 10
note that sum = 6 + 8 + 10 = 24
and 4 × 6 = 24
confirming the sum of the 3 integers equals 4 times the first integer
Answer:
Minimum: 50
Lower Quartile: 59
Median: 66
Upper Quartile: 74
Maximum: 92
Step-by-step explanation:
50, 55, 58, 60, 62, 64, 68, 70, 72, 76, 84, 92
Minimum: 50
Lower Quartile: (58 + 60)/2 = 59
Median: (64 + 68)/2 = 66
Upper Quartile: (72 + 76)/2 = 74
Maximum: 92