Answer:
1.5:2.25 because there is 1.5 quarts of juice and 2.25 quarts of ginger ale and the you put that with the to sign and there you have it
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:
x = 15
Step-by-step explanation:
2 = -7/4 + 1/4x
+7/4 +7/4 Add 7/4 to both sides
15/4 = 1/4x Divide both sides by 1/4
15 = x
If this answer is correct, please make me Brainliest!
Answer:
48
Step-by-step explanation:
The mean of a number is the sum of all the numbers divided by how many numbers there are. We can set up this formula: 
.
When we plug our values into this equation, we get: 
. Solving this equation gets us sum = 6 * 8 = 48
Step-by-step explanation:
the average change rate is simply the change of the functional values in a given interval relative to the change of the input values.
in short
(f ( interval upper limit) - f (interval lower limit) ) /
(interval upper limit) - (interval lower limit)
and you know that f (x) is usually also called y (the functional result variable).
so, the upper limit is 0, the lower limit is -2.
y (or f (x)) is 6 and 10 at these points.
and we get
(6 - 10) / (0 - -2) = -4 / 2 = -2
