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yKpoI14uk [10]
3 years ago
8

A class of 32 students is organised in 33 teams every team consists of 3 students and there are no identical teams . show that t

here are two teams with exactly one common student
Mathematics
1 answer:
Tresset [83]3 years ago
6 0

Answer:

Step-by-step explanation:

Let's start by making up as many teams as we can with the 32 student. Given that each team is different, we can make 10 teams of 3 each. (we still have 23 more teams to make).

The last two people make a team of only 2. No matter which student from the 30 other students is picked, the team of two and the one the student is coming from will have one student in common. Though there are more borrowings that take place (many more), the results remain as stated. At least 2 teams will have 1 person in common.

The method is called the pigeon hole method.

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Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of −3
RSB [31]

Answer:

\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}

Step-by-step explanation:

Hello,

Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).

   \Large \boxed{k(x+3)(x+1)(x-2)}

We know that the point (1,10) is on the graph of this function, so we can say.

k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}

Then the solution is:

\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

8 0
3 years ago
Which three lengths CANNOT be the lengths of the sides of a triangle
kogti [31]

Answer:

I believe 21 cm

Step-by-step explanation:

4 0
2 years ago
Does anyone know the answer for the question below.
8090 [49]

Answer: option C

Step-by-step explanation:

The diagram of the triangle is shown in the attached photo. The triangle is a right angle triangle ABC

Assuming the given angle is #,

Recalling the trigonometric ratio,

tan # = opposite / adjacent

If tan # = 4, it means

opposite / adjacent = 4/1

Therefore, opposite = 4 and adjacent = 1

Applying Pythagoras theorem,

Hypotenuse^2 = opposite ^2 + adjacent ^2

Hypotenuse = AC

Opposite = 4

Adjacent = 1

AC^2 = 4^2 + 1^2 = 17

AC = ± √17

To determine cos #, we would apply another trigonometric ratio,

Cos# = adjacent /hypotenuse

Cos# = 1/±√17

Cos # =-1 /√17 or 1/√17

8 0
2 years ago
Simplify the trigonometric expression. 1/1+ sin theta + 1/1-sin theta A, 2 cos^2 theta B. 2 sec^2 theta C. 2 csc^2 theta D. 2 co
Ganezh [65]
So the problem ask to simplify the trigonometric function in your problem and base on the expression and using the theory in simplifying trigonometric function, the answer would be letter B. 2 sec^2 theta. I hope you are satisfied with my answer and feel free to ask for more  
3 0
2 years ago
What is continuous​ compounding? how does the apy for continuous compounding compare to the apy​ for, say, daily​ compounding? e
aliya0001 [1]
Continuous compounding is the mathematical limit that compound interest can reach.

It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A  every infinitesimally small  instant.
The limit  of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).

Say we invest  $1000  at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-

1000 ( 1 + 0.02/365)^365 = $1020.20

with continuous compounding this will be 

1000 * e^1  =  $2718.28  
4 0
3 years ago
Read 2 more answers
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