Answer:
1/10 per sec
Step-by-step explanation:
When he's walked x feet in the eastward direction, the angle Θ that the search light makes has tangent
tanΘ = x/18
Taking the derivative with respect to time
sec²Θ dΘ/dt = 1/18 dx/dt.
He's walking at a rate of 18 ft/sec, so dx/dt = 18.
After 3seconds,
Speed = distance/time
18ft/sec =distance/3secs
x = 18 ft/sec (3 sec)
= 54ft. At this moment
tanΘ = 54/18
= 3
sec²Θ = 1 + tan²Θ
1 + 3² = 1+9
= 10
So at this moment
10 dΘ/dt = (1/18ft) 18 ft/sec = 1
10dΘ/dt = 1
dΘ/dt = 1/10 per sec
Answer:
P(A' ∩ B) = 0.12
Step-by-step explanation:
Given:
P(A) = 0.41, P(B) = 0.32 and P(B' ∩ A) = 0.21
To Find:
P(A' ∩ B)
Solution:
Since, P(B' ∩ A) = P(A) - P(A ∩ B)
By substituting the values given,
0.21 = 0.41 - P(A ∩ B)
P(A ∩ B) = 0.41 - 0.21
= 0.20
Since, P(A' ∩ B) = P(B) - P(A ∩ B)
P(A' ∩ B) = 0.32 - 0.20
= 0.12
Therefore, P(A' ∩ B) = 0.12 is the answer.
Using the x-intercept and y-intercept of the equation, the graph of the equation is shown below
From the question, we are to graph the given equation
The given equation is
10.50a + 7.50c = 141
To graph the line, we will plot the variable a on the x-axis and the variable c on the y-axis of the cartesian plane.
Now, we will the determine the x-intercept and the y-intercept.
The x-intercept is the point where c = 0; and y-intercept is the point where a = 0
Determine the x-intercept
10.50a + 7.50c = 141
10.50a + 7.50(0) = 141
10.50a = 141
a = 141/10.50
a = 13.43
The x-intercept is (13.43, 0)
Determine the y-intercept
10.50(0) + 7.50c = 141
7.50c = 141
c = 141/7.50
c = 18.80
The y-intercept is (0, 18.80)
Hence, using the x-intercept and y-intercept of the equation, the graph of the equation is shown below
Learn more on Graph of equations here: brainly.com/question/4074386
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The rule of multiplication applies to the following situation. We have two events from the same sample space, and we want to know the probability that both events occur.
Rule of Multiplication If events A and B come from the same sample space, the probability that both A and B occur is equal to the probability the event A occurs times the probability that B occurs, given that A has occurred.
P(A ∩ B) = P(A) P(B|A)
