Since the problem doesn’t give a definite question, here are
the possible questions and answer:
P(fewer than 4 tosses)
= P(one toss) + P(two toss) + P(3 toss)
= (3/4) + (3/4)(1/4) + (3/4)(1/4)^2
= 0.984375
Expected value
= 1 / p
= 1 / (3/4)
= 4 / 3
Variance
= (1 - p) / p^2
= (1 - (3/4)) / (3/4)^2
= (1/4) / (9/16)
= 4 / 9
Standard deviation
= sqrt(Variance)
= sqrt(4 / 9)
= 2 / 3
Answer:
The concentration of HCl in the mixture is 1L of 50% HCl
Step-by-step explanation:
Here, we want to know the percentage of HCl present which refers to the its concentration.
Firstly, the total volume we have is 0.375 + 0.625 = 1 L
we can calculate the percentage as follows;
The percentage of the 25% present is 37.5%
while the percentage of the 75% present is 62.5%
When we say the percentage present, we are referring to the amounts of the total liters which is 1 present.
So the concentration of the final mixture will be;
(37.5% of 25) + (62.5% of 65)
= 9.375% + 40.625%
Adding both gives = 50%
So the concentration we have is 1L of 50% HCl
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>
Can you send pic of graph
Step-by-step explanation:
Pls
Answer:
(3x-5)*(3x-5)
Step-by-step explanation:
Perfect square trinomial is defined by the follow way
Now we can rewrite 
as 
because a squared add is equal to multiply the add by itself one time
if we make a=3x and b=-5 we can see tha the first answer is the only option that could be a perfect square triomial
