Unfortunately I still have school could anybody help me please? MATH 2 Standard G-SRT.8.1
1 answer:
Answer:
t = 6
∠BAC = ∠EAD = 6°
∠BCA = ∠ABC = ∠AED = ∠EDA = 87°
Step-by-step explanation:
From inspection of the diagram, we can see that there are 2 triangles inside a circle. One of the vertices of both triangles is at the center of the circle. The other vertices of both triangles are on the circumference of the circle.
The dashes on the line segments (chord) mean they are <u>equal in length</u>.
⇒ BC = DE
The legs of both triangles are the radius of the circle.
Therefore, ΔABC = ΔAED
This means the ∠BAC = ∠EAD, therefore:
⇒ 6t - 12 = 18 - 4t
⇒ 10t - 12 = 18
⇒ 10t = 30
⇒ t = 3
Substituting the found value of t into one of the expressions to find ∠BAC and ∠EAD:
⇒ ∠BAC = ∠EAD = 6(3) - 12 = 6°
Triangles ΔABC and ΔAED are both isosceles triangles (as they have 2 sides of equal length: the radii).
Therefore, the remaining 2 angles in each triangle will be <u>equal</u>.
The sum of interior angles of a triangle = 180°
⇒∠BAC + 2(∠BCA) = 180°
⇒ 6° + 2(∠BCA) = 180°
⇒ 2(∠BCA) = 174°
⇒ ∠BCA = 87°
Therefore, as ∠BCA = ∠ABC = ∠AED = ∠EDA
all the other angles are 87°
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Answer:
a) time=
b)
c)
Step-by-step explanation:
Definitions and concepts
The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:
And the parameter represent the average ocurrence rate per unit of time.
The exponential distribution is useful when we want to describ the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time btween two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:
a. What is the expected time you would have to wait to see ten birds arrive?
The original rate for the Poisson process is given by the problem "rate of six per hour" and on this case since we want the expected waiting time for 10 birds we have this:
time=
b. What is the probability that the elapsed time between the second and third birds exceeds fifteen minutes?
Assuming that the time between the arrival of two birds consecutive follows th exponential distribution and we need that this time exceeds fifteen minutes. If we convert the 15 minutes to hours we have 15(1/60)=0.25 hours. And we want to find this probability:
And we can use the result obtained from the definitions and we have this:
c. If you have already waited five minutes for the first bird to arrive, what is the probability that the bird will arrive within the next five minutes?
First we need to convert the 5 minutes to hours and we got 5(1/60)=0.0833h. And on this case we want a conditional probability. And for this case is good to remember the "Markovian property of the Exponential distribution", given by :
Since we have a waiting time for the first bird of 5 min = 0.0833h and we want that the next bird will arrive within 5 minutes=0.0833h, we can express on this way the probability of interest:
And using the Markovian property we have this:
<h3>Answer: Choice D</h3>
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Explanation:
The inequality sign has an "or equal to", which means the boundary line will be solid. We can rule out choices B and C because they have dashed boundary lines.
A solid boundary line means that points on the boundary are part of the solution set.
Now let's see what happens when we plug in a point like (x,y) = (4,0). This will tell us how to shade the blue region.
This is false because -20 is not larger than -1. It's the other way around.
This tells us the point (4,0) is not in the blue shaded region, and it's not on the boundary line either. We can rule out choice A because of this.
The only thing left is choice D, which is the final answer. I recommend plugging a point from this region into the inequality to confirm we have a true statement.