Answer:
A: 0
Step-by-step explanation:
Important to remember - total displacement is the direct distance between the start and finish points, and isn't always equal to the total distance travelled.
In the case of the table above, the hiker travels the same distance in opposite directions, which actually means they cancel each other out! Traveling 4 km to the west, then 4 km to east means you end up in the same spot, right? So your total displacement is 0! (or 4 - 4, which equals 0). Same happens with the north-south hikes - the hiker ends up in the same spot, as the displacement is equal to 6 - 6 = 0.
So, the total displacement of the hiker is 0. (Even though the hiker travelled 20 km!)
Answer:
a) P(B'|A) = 0.042
b) P(B|A') = 0.625
Step-by-step explanation:
Given that:
80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered
Of the aircraft that are discovered, 63% have an emergency locator,
whereas 89% of the aircraft not discovered do not have such a locator.
From the given information; it is suitable we define the events in order to calculate the probabilities.
So, Let :
A = Locator
B = Discovered
A' = No Locator
B' = No Discovered
So; P(B) = 0.8
P(B') = 1 - P(B)
P(B') = 1- 0.8
P(B') = 0.2
P(A|B) = 0.63
P(A'|B) = 1 - P(A|B)
P(A'|B) = 1- 0.63
P(A'|B) = 0.37
P(A'|B') = 0.89
P(A|B') = 1 - P(A'|B')
P(A|B') = 1 - 0.89
P(A|B') = 0.11
Also;
P(B ∩ A) = P(A|B) P(B)
P(B ∩ A) = 0.63 × 0.8
P(B ∩ A) = 0.504
P(B ∩ A') = P(A'|B) P(B)
P(B ∩ A') = 0.37 × 0.8
P(B ∩ A') = 0.296
P(B' ∩ A) = P(A|B') P(B')
P(B' ∩ A) = 0.11 × 0.2
P(B' ∩ A) = 0.022
P(B' ∩ A') = P(A'|B') P(B')
P(B' ∩ A') = 0.89 × 0.2
P(B' ∩ A') = 0.178
Similarly:
P(A) = P(B ∩ A ) + P(B' ∩ A)
P(A) = 0.504 + 0.022
P(A) = 0.526
P(A') = 1 - P(A)
P(A') = 1 - 0.526
P(A') = 0.474
The probability that it will not be discovered given that it has an emergency locator is,
P(B'|A) = P(B' ∩ A)/P(A)
P(B'|A) = 0.022/0.526
P(B'|A) = 0.042
(b) If it does not have an emergency locator, what is the probability that it will be discovered?
The probability that it will be discovered given that it does not have an emergency locator is:
P(B|A') = P(B ∩ A')/P(A')
P(B|A') = 0.296/0.474
P(B|A') = 0.625
Answer:
The margin of error for this estimate is of 14.79 yards per game.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
T interval
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 20 - 1 = 19
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of 
. So we have T = 2.093
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
You randomly select 20 games and see that the average yards per game is 273.7 with a standard deviation of 31.64 yards.
This means that 
What is the margin of error for this estimate?
The margin of error for this estimate is of 14.79 yards per game.
The square root of 128/5 is 5.059644
Hope this helped!
Answer:
sin
/4 * sin/6 = 1/2 *(cos /12 - cos 5/12)
Step-by-step explanation:
Formula:- sinX sinY = (1/2) [ cos (X - Y) - cos (X + Y) ]
sin(π/4)sin(π/6)
= (1/2)[cos(π/4 - π/6) - cos(π/4 + π/6)]
= (1/2)[cos(3π/12 - 2π/12) - cos(3π/12 + 2π/12)]
= (1/2)[cos(π/12) - cos(5π/12)]
