Answer:
a) <u>0.4647</u>
b) <u>24.6 secs</u>
Step-by-step explanation:
Let T be interval between two successive barges
t(t) = λe^λt where t > 0
The mean of the exponential
E(T) = 1/λ
E(T) = 8
1/λ = 8
λ = 1/8
∴ t(t) = 1/8×e^-t/8 [ t > 0]
Now the probability we need
p[T<5] = ₀∫⁵ t(t) dt
=₀∫⁵ 1/8×e^-t/8 dt
= 1/8 ₀∫⁵ e^-t/8 dt
= 1/8 [ (e^-t/8) / -1/8 ]₀⁵
= - [ e^-t/8]₀⁵
= - [ e^-5/8 - 1 ]
= 1 - e^-5/8 = <u>0.4647</u>
Therefore the probability that the time interval between two successive barges is less than 5 minutes is <u>0.4647</u>
<u></u>
b)
Now we find t such that;
p[T>t] = 0.95
so
t_∫¹⁰ t(x) dx = 0.95
t_∫¹⁰ 1/8×e^-x/8 = 0.95
1/8 t_∫¹⁰ e^-x/8 dx = 0.95
1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t = 0.95
- [ e^-x/8]¹⁰_t = 0.96
- [ 0 - e^-t/8 ] = 0.95
e^-t/8 = 0.95
take log of both sides
log (e^-t/8) = log (0.95)
-t/8 = In(0.95)
-t/8 = -0.0513
t = 8 × 0.0513
t = 0.4104 (min)
so we convert to seconds
t = 0.4104 × 60
t = <u>24.6 secs</u>
Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is <u>24.6 secs</u>
Answer:
b. t = 10.5 seconds.
Step-by-step explanation:
l = 0.81t^2
90 = 0.81t^2
t^2 = 90 / 0.81
t^2 = 111
t = 10.5 seconds.
Surface area is the area of all the surfaces we can touch
2a)
1/2*5*3+1/2*4*3+6*4+6*5 which is
67.5
b) 2*(1/2*10*6)+12*6+12*10 which is
252
Answer:
The length of WX is 31 units.(third option)
Step-by-step explanation:
Given that In trapezoid WXYZ, WX║ZY and S and T are the mid points of the sides WZ and XY. We have to find the length of WX.
By trapezoid mid-segment Property,
A mid-segment of a trapezoid join the midpoints of the two non-parallel sides of trapezoid. The length of the mid-segment is the average of the lengths of the two bases and is parallel to the bases of the trapezoid.
∴ 
⇒ 
⇒ 
⇒ 
The length of WX is 31 units.(third option)
