1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zhuklara [117]
3 years ago
6

Suppose you choose a team of two people from a group of n > 1 people, and your opponent does the same (your choices are allow

ed to overlap). Show that the number of possible choices of your team and the opponent’s team equals Pn−1 i=1 i 3 .
Mathematics
1 answer:
jonny [76]3 years ago
4 0

Answer:

The number of possible choices of my team and the opponents team is

 \left\begin{array}{ccc}n-1\\E\\n=1\end{array}\right     i^{3}

Step-by-step explanation:

selecting the first team from n people we have \left(\begin{array}{ccc}n\\1\\\end{array}\right)  = n possibility and choosing second team from the rest of n-1 people we have \left(\begin{array}{ccc}n-1\\1\\\end{array}\right) = n-1

As { A, B} = {B , A}

Therefore, the total possibility is \frac{n(n-1)}{2}

Since our choices are allowed to overlap, the second team is \frac{n(n-1)}{2}

Possibility of choosing both teams will be

\frac{n(n-1)}{2}  *  \frac{n(n-1)}{2}  \\\\= [\frac{n(n-1)}{2}] ^{2}

We now have the formula

1³ + 2³ + ........... + n³ =[\frac{n(n+1)}{2}] ^{2}

1³ + 2³ + ............ + (n-1)³ = [x^{2} \frac{n(n-1)}{2}] ^{2}

=\left[\begin{array}{ccc}n-1\\E\\i=1\end{array}\right] =   [\frac{n(n-1)}{2}]^{3}

You might be interested in
Ray BD bisects ABC so that m 2DBC = (x + 6)° and m ZABD = (2x – 12). What is x?
Ludmilka [50]
C 16 is correct Bc if u solve it out it Becomes to 16 put -6 under 2 and 12 cross out 2-6 and add 12 and 6 witch gives u 16.
5 0
3 years ago
The length of the midsegment of a triangle is always half the length of the side it is parallel to true or false
Vladimir [108]
True. The midsegment of a triangle is halfway up the triangle, and since the top half and the full triangle are similar triangles, its dimensions are proportional.

This means half the height will give half the base (midsegment). So the midsegment is always half the length of the side it's parallel to.
3 0
3 years ago
Four pounds of bananas cost $1.96 . How much does it cost per pound ?
Troyanec [42]
1.96 divided by 4 is 48.5 cents round it to get 49 cents
so 49 cents per pound

7 0
3 years ago
Express 5/4 as a mixed number and show the work
SCORPION-xisa [38]

Answer:

5/4 as a mixed number = 1\frac{1}{4}

5 0
3 years ago
Which equation could have the graph shown below? y = (x – 4)(x – 1)(2 + x)(3 + x) y = (x – 4)(1 – x)(2 + x)(3 + x) y = (x + 4)(x
Paul [167]
These functions are expressed in the factored form: what this means is that say for the first one y=(x-4)(x-1)(2+x)(3+x) ... when x=4, the first bracket becomes 0. Same for x=1, x=-2, x=-3 ... 

If you were to graph this, you would see that the function's line interesects the x-axis at these points... when x=4, when x=1, etc etc.

Thus, take a look at the zeroes of the graph. At which x points do they interscet the x-axis? You can determine the equation of your graph by this.
7 0
3 years ago
Other questions:
  • At the city museum, child admission is $5.70 and adult admission is $9.50. on Friday, 155 tickets were sold for a total sales of
    8·2 answers
  • Anastasia gets overtime (time and a half) for every hour she works over 40 hours. If her hourly pay is $28.50, how much would sh
    14·1 answer
  • The sum of the square of a positive number and the square of 3 more than the number is 89. What is the​ number?
    6·1 answer
  • Divide 28 photos into two groups so the ratio is 2 to 5. Write your answer as a ratio
    14·1 answer
  • What is the general solution of dt/dz=20z^3?
    13·1 answer
  • What is the amount of change from 20 to 36
    15·2 answers
  • Jimmy has a collection of 1400 baseball cards. Of these cards, 15%, are
    12·1 answer
  • I need help can someone tell me how to do this plz
    14·2 answers
  • . If a landfill has a density of 1,200 pounds per cubic yard, what would be the volume required for 15- years worth of MSW to th
    13·1 answer
  • Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!