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>
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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>
1.6^2
It's telling you to multiply 1.6 by itself 2 times.
1.6 * 1.6 = 2.56
3 x (2/3) = 2
2 x 2 = 4
If both cats eat 3 oatmeal bowls, they should have 4 cups altogether.
2 x 23.8888 = 47.7776
4 x 23.8888 = 95.5552
47.7776 + 95.5552 = 143.3328
If one cat eats 2 fish plates and the other cat eats 4 fish plates, they use 143.3328 pounds altogether.
It will cost $30.48 to fill a 12 gallon tank.
Step-by-step explanation:
Given,
Cost of gasoline = $2.54 per gallon
Number of gallons in tank = 12 gallons
Cost of 12 gallons = Cost of gasoline per gallon * Number of gallons
Cost of 12 gallons = 2.54 * 12
Cost of 12 gallons = $30.48
It will cost $30.48 to fill a 12 gallon tank.
Keywords: multiplication
Learn more about multiplication at:
#LearnwithBrainly
Answer:
First blank: non-viable solution because the costs aren't less than the revenue
Second blank: viable solution because the costs are less than the revenue
Step-by-step explanation:
First: Insert the x into the equation and work it out to see if it is less than the y.
(30,90) x=30 y=90
y=1.5(30)+45
y=45+45
y=90
Non-Viable
Second: Insert the x into the equation and work it out to see if it is less than the y.
(60,160) x=60 y=160
y=1.5(60)+45
y=90+45
y=135
Viable
(hope this helps :P)