Answer:
Step-by-step explanation:
To find the distance between two points, and
, you can use the following distance formula:
Plugging in the points from the problem, you'll get the following:
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1 answer:
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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.
Answer:
Option (c) is correct.
The approximate total area of the plastic triangles on the spinner is 2 × 3.9 square centimeters = 7.7 square centimeters
Step-by-step explanation:
Given:A spinner for a board game consists of a cardboard circle with two plastic arrows anchored to its center. The arrows are congruent isosceles triangles connected at their bases.
also, Given: The base of each triangle measures 2 centimeters and the perimeter of each triangle is 10 centimeters.
We have to find the approximate total area of the plastic triangles on the spinner.
Perimeter of triangle is the sum of sides.
Since given the triangle to be isosceles .
Let the two equal side be x cm, then,
Perimeter of given triangle = 1 0
⇒ x + x + 2 = 1 0
⇒ 2x = 8
⇒ x = 4
Thus, side of triangle is 4 cm.
Now we find the area of isosceles triangle.
We first find the height, using Pythagoras theorem,
Putting values, we get,
Solving we get,
Thus, area of one isosceles triangle
area of one isosceles triangle
On solving we get,
Approximate area of one plastic triangles on the spinner is 3.9 square centimeters.
Thus, the approximate total area of the plastic triangles on the spinner is 2 × 3.9 square centimeters = 7.7 square centimeters
Option (c) is correct.