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Answer:
The distance of the helicopter from the bristol is approximately 1<u>2.81 miles</u>
Step-by-step explanation:
Given:
Helicopter flies 10 miles east of bristol.
Then the helicopter flies 8 miles North before landing.
To find the direct distance between the helicopter and bristol.
Solution:
In order to find the distance of the helicopter from the bristol before landing, we will trace the path of the helicopter
The helicopter is first heading 10 miles east of bristol and then going 8 miles due north.
On tracing the path of the helicopter we find that the direct distance of the helicopter from the bristol is the hypotenuse of a right triangle formed by enclosing the path of the helicopter.
Applying Pythagorean theorem to find the hypotenuse of the triangle.
Taking square root both sides.
Thus, the distance of the helicopter from the bristol is approximately 12.81 miles
Answer:
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Step-by-step explanation:
The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
8 covered buckets, so N = 8.
4 buckets are selected, so n = 4.
2 contain a ball, which means that k = 2.
Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.
This is P(X = 2). So
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.