Answer:
The graph in the attached figure
Step-by-step explanation:
we have

This is the equation of the line
To graph a line we need two points
<em>Find the intercepts</em>
1) The y-intercept is the value of y when the value of x is equal to zero
For x=0


The y-intercept is the point (0,3)
2) The x-intercept is the value of x when the value of y is equal to zero
For y=0


The x-intercept is the point (-1.5,0)
To draw the graph of the line plot the intercepts and join the points
using a graphing tool
see the attached figure
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>
The answer is 6 1/4, because if you making 1/2 = 2/4, 2 + 3 = 5, the 4 stays the same, so its 5 5/4, and to make it proper, you make it 6 1/4
<u><em>Answer:</em></u>
The height of the parallelogram is 33 ft
<u><em>Explanation:</em></u>
<u>The area of the parallelogram can be calculated using the following rule:</u>
Area of parallelogram = base * height
<u>In the problem, we are given that:</u>
Area = 544.5 ft²
Base = 16.5 ft
<u>Substitute with the given values in the above equation and solve for the height as follows:</u>
Area = base * height
544.5 = 16.5 * height

Hope this helps :)