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Ganezh [65]
3 years ago
7

three distinct vertices of a cube are to be randomly chosen what is the probability that they will be the vertices of an equilat

eral triangle
Mathematics
1 answer:
jasenka [17]3 years ago
3 0

The triangle formed by the vertices would be equilateral if the sides of the triangle coincide with the diagonals of the square face that defines the cube. See the attached sketch if that description is unclear.

Count the number of equilateral triangles that are possible. Such a triangle will always use up 3 vertices of the cube, and separate 1 vertex from the remaining 4. This means there are as many equilateral triangles as there are corners in the cube: 8.

Count the total number of triangles that can be made. From the 8 available vertices, we only need 3. If we fix 3 vertices, it doesn't matter in which order we connect them to make a triangle, so we count the number of combinations of 8 vertices taking 3 at a time, which is

\dbinom 83 = \dfrac{8!}{3!(8-3)!} = 56

Then the probability of forming an equilateral triangle is 8/56 = 1/7.

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Find A ∩ ( B ∪ C ).
Radda [10]

Answer:

This season, the probability that the Yankees will win a game is 0.59 and the probability that the Yankees will score 5 or more runs in a game is 0.52. The probability that the Yankees win and score 5 or more runs is 0.45. What is the probability that the Yankees will win when they score 5 or more runs? Round your answer to the nearest thousandth.

Step-by-step explanation:

7 0
3 years ago
There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.
ololo11 [35]
Let's present the given equation first. Deciphering the given code, I think the equation is (n+1)²/n+23. Then, we want to find the maximum value of n. Suppose the complete equation is:

f(n) = (n+1)²/n+23

To find the maximum,let's apply the concepts in calculus. The maxima can be determined by setting the first derivative to zero. Therefore, we use the chain rule to differentiate the fraction. For a fraction u/v, the derivative is equal to (vdu-udv)/v². 

f'(n) = [(n+23)(2)(n+1)-(n+1)²(1)]/(n+23)² = 0
[(n+23)(2n+2) - (n+1)²]/(n+23)² = 0
(2n²+2n+46n+46-n²-2n-1)/(n+23)²=0
n²+46n+45=0
n = -1, -45

There are two roots for the quadratic equation. Comparing the two, the larger one is -1. Thus, the maximum value of n is -1.
5 0
3 years ago
What is the radius of a circle with an area of 49pi
sergejj [24]
Area = π * r * r

49 = radius * radius

Radius = 7

Hope this helped☺☺
6 0
4 years ago
And our teacher has a box of 100 markers the teacher gives out silver markers to each student in the class and has 16 markers le
ad-work [718]

Answer:

12 students

Step-by-step explanation:

1. 7s+16=100

We know the teacher has 100 markers, and she gave each student 7. If we say that s is the number of students, then 7s is the number of markers she gave out. We also know that she had 16 left over.

2. 7s+16-16=100-16

Subtract 16 from both sides of the equation.

3. 7s=84

Simplify the equation.

4. 7s/7=84/7

Divide both sides by 7.

5. Simplify the equation. Since s is the number of students, we now know how many students there are in the teacher's class.

7 0
3 years ago
Find the area of the parallelogram
vovikov84 [41]

Answer:

513

Step-by-step explanation:

B×L=Area

Base=24

Length =19

24×19=513

5 0
3 years ago
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