Any good mathematicians out there that would help me understand this concept?
1 answer:
You might be interested in
Answer:
1.15%
Step-by-step explanation:
To get the probability of m independent events you multiply the individual probability of each event. In this case we have m independent events, each one with the same probability, therefore:
This is a particlar scenario of binomial distribution problem. So the binomial distribution questions are about the number of success of m independent events, where every individual event has the same p probability. In the question we have 20 events and each event has a probability of 80%. The binomial distribution formula is:
n is the number of events
k is the number of success
p is the probability of each individual event
is the binomial coefficient
the binomial coefficient allows to find the subsets of k elements in a set of n elements. In this case there is only one subset possible since the only way to get 20 of 20 correct questions is to getting right all questions (for getting 19 of 20 questions there are many ways, for example getting the first question wrong and all the other questions right, or getting second questions wrong and all the other questions right, etc).
therefore, for this questions we have:
Answer:
The coordinates of the explosion is (3300, -2750)
Step-by-step explanation:
I have plot the points and attached to thus answer for easy understanding.
Now, from the question, since station A is the first to hear the explosion, we'll make it the foci of the parabola in the graph I attached and it will be horizontal since the distance between station C and A is much more than that between station B and A. Thus, the reason why station C will have to be the other foci with the hyperbola centred at the origin.
Now, sound travels at a speed of 1100 ft/s and station B is located 1100 ft from station A. Thus, the explosion would likely have occurred at a point on the line x = 3300ft . Since station A is 3300ft from centre C = 3300,hence C² = 3300² = 10,890,000. Since it takes 4 seconds longer for the sound to reach station C than A, the sound has traveled 4(1100)= 4400 ft.
Thus, 4400 = d1 = d2 = 2a
So,2a = 4400 and so, a =2200
a² = 2200² = 4,840,000 where d1 is the distance from station C to the explosion and d2 is the distance from station A to the explosion. To find b², let's use the equation ;
c² = a² + b² and so; b² = c² - a² = 10,890,000 - 4,840,000 = 6,050,000
Equation of hyperbola is given as;
(x²/a²) - (y²/b²) = 1
Plugging in the values of a² and b², we obtain ;
(x²/4,840,000) - (y²/6,050,000) = 1
Since we have deduced that the explosion must occur on the line x= 3300, we'll put in 3300 for x to obtain ;
(3300²/4,840,000) - (y²/6,050,000) = 1
2.25 - 1 = (y²/6,050,000)
y² = (1.25 x 6,050,000)
y² = 7562500
y = √7562500
y = ± 2750
Due to the fact that the explosion will occur at a point further from station B than from station A, the explosion will take place in quadrant 4. Thus, we will take the negative value of y which is - 2750.
So explosion will occur at the coordinate (3300, -2750)
