Answer:
140°
Step-by-step explanation:
<3 = 40 because they are vertical angles
<3 +<4 = 180 because they are same side interior angles
40 + <4 = 180
Subtract 40 from each side
40-40 + <4 = 180-40
<4 = 140
Answer:
2(5000000x1256y+400−a)
Step-by-step explanation:
4b+20 because you disrepute the 4
Answer:
a) 0.122
b) 3.35 × 10⁻⁴
c) 0.1071
Step-by-step explanation:
Here we have the Poisson process given by
Where:
λ = Rate = 4 bites/hour and
t = Length of time that is
Mean = λt
Where k = 6 fishes bites and t = 2 hours we have
b) The probability that he fails to catch any fishes during the first two hours is the probability t that he catches 0 fish as follows
(c) Here we have
For 1 fish caught in two times we have first time no fish and second time he caches a fish gives
0.122×(1-0.122) = 0.1071
Answer:
sin θ/2=5√26/26=0.196
Step-by-step explanation:
θ ∈(π,3π/2)
such that
θ/2 ∈(π/2,3π/4)
As a result,
0<sin θ/2<1, and
-1<cos θ/2<0
tan θ/2=sin θ/2/cos θ/2
such that
tan θ/2<0
Let
t=tan θ/2
t<0
By the double angle identity for tangents
2 tan θ/2/1-(tanθ /2)^2 = tanθ
2t/1-t^2=5/12
24t=5 - 5t^2
Solve this quadratic equation for t :
t1=1/5 and
t2= -5
Discard t1 because t is not smaller than 0
Let s= sin θ/2
0<s<1.
By the definition of tangents.
tan θ/2= sin θ/2/ cos θ/2
Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.
cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2
Solve for s.
s/-√1-s^2 = -5
s^2=25(1-s^2)
s=√25/26 = 5√26/26
Therefore
sin θ/2=5√26/26=0.196....
