Answer:
Probability that a 20- cubic foot block of wood has at most 1 knot P (X<=1) = 0.5918
Step-by-step explanation:
Average rate of knot= 1.4
Wavelength = 1.4
Geometric probability is given by:
P(X= K) = wavelength ^k × e^-wavelegth
P(X=0) = (1.4^0 × e^-1.4)/0!
P(X=0) = 1 × 0.2466 = 0.2466
P(X=1) = 1.4^1 × e^-1.4
P(X=1)= 1.4×0.2466= 0.3452
P(X<=1)= P(X=0) + P(X=1)
P(X<=1) = 0.2466 + 0.3452 = 0.5918
Answer:
49
Step-by-step explanation:
the number is "ab" (2 digits).
ab - 10 = 3×(a+b)
a number is actually the sum of multiplying the digits with their associated powers of 10.
a×10 + b - 10 = 3a + 3b
7a - 2b = 10
b-1 = 2×a
b = 2a + 1
7a - 2×(2a+1) = 10
7a - 4a - 2 = 10
3a = 12
a = 4
b = 2×4 + 1 = 9
Answer:
21/5
Step-by-step explanation:
Note that
108° = 90° + 18°
so
sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)
Then
sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1
by the Pythagorean identity.
