Answer:
5/18
Step-by-step explanation:
There are 9 pieces of fruit in the bowl, tangerines and 5 clementines.
Assuming that they do not put the fruit back
P (tangerine) = number of tangerines/ total = 4/9
Then John keeps his and there are 8 pieces of fruit in the bowl,
3 tangerines and 5 clementines.
P (Clementine) = number of clementines/ total = 5/8
P (tangerine, no replacement, Clementine) = P (tangerine) * P (Clementine)
= 4/9 * 5/8 =5/18
Answer:
Step-by-step explanation:
Hi there!
To get rid of the fraction , multiply both sides of the equation by 4 (the denominator:
Now, to get rid of the fraction , multiply both sides of the equation by 3 (the denominator):
I hope this helps!
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>
You can do 8*6 to find the area to be 48 ft. squared. So then we can do:
$1134/48 ft. to find the price per foot to be $23.63, or $24 rounded up
Hope this helps
For this item, we let x be the number of hours she works out and y be the total number of bananas that she will be eating after the workout. The expression that best described the given above is,
y = 5 + 2x
5 is given as the y-intercept because of the initial condition.