Twelve people join hands for a circle dance.In how many ways can they do this? Suppose six of these people are men, and the other six are women. In how many ways can they join hands for a circle dance, assuming they alternate in gender around the circle
Answer:
86400 ways
Step-by-step explanation:
Since the circle can be rotated, the number of ways to arrange a distinct number of n objects in a circle will be (n−1)!.
Now, if we rotate the circle with the six women, we will see that there are 5! ways with which they can be placed in the circle.
After picking the places for the women, we will now fill each gap between two women with a man.
We have 6 men. Thus, number of ways to arrange the men is 6!
Thus,number of ways they can join hands for a circle dance, assuming they alternate in gender around the circle = 5! × 6! = 86400 ways
Answer:
An exterior angle of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side of the triangle. FACTS: ... The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Answer:
25.2294 feet
Step-by-step explanation:
We can solve this question drawing a triangle using the values given and then using the law of sines. (See image attached to know how to draw the triangle and use the values).
First we need to find the third angle of the triangle, that is, the angle in the vertix where the bird is:
y + 55 + 63 = 180
y = 62°
The relation between the angles and the distances are:
25 / sin(y) = x / sin(63)
25 / 0.8829 = x / 0.8910
x = 25 * 0.8910 / 0.8829 = 25.2294 feet
Answer:
9/10
Step-by-step explanation:
to do this you would want to find a common denominator. then to divide fractions you would want to apply the keep change flip rule. keep the first fraction. change the division sign to multiplication and flip the fraction. then proceed to multiple. then you have your answer.
Step-by-step explanation:
a. (13, 6) = (1, 2)
b. (-13, 6) = (2, 2)
c. (13, -6) = (1, 3)
d.(-13, -6) = (2, 3)
