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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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a pile of coins, consisting of dimes and quarters only, is worth 4 dollars and 55 cents. there are 7 more dimes than quarters in
Lady_Fox [76]

11 quarters and 18 dimes

Hope this helps! :D

7 0
2 years ago
There are 20 machines in a factory. 7 of the machines are defective.
adelina 88 [10]

Answer:

0.1225

Step-by-step explanation:

Given

Number of Machines = 20

Defective Machines = 7

Required

Probability that two selected (with replacement) are defective.

The first step is to define an event that a machine will be defective.

Let M represent the selected machine sis defective.

P(M) = 7/20

Provided that the two selected machines are replaced;

The probability is calculated as thus

P(Both) = P(First Defect) * P(Second Defect)

From tge question, we understand that each selection is replaced before another selection is made.

This means that the probability of first selection and the probability of second selection are independent.

And as such;

P(First Defect) = P (Second Defect) = P(M) = 7/20

So;

P(Both) = P(First Defect) * P(Second Defect)

PBoth) = 7/20 * 7/20

P(Both) = 49/400

P(Both) = 0.1225

Hence, the probability that both choices will be defective machines is 0.1225

4 0
3 years ago
Which of the following functions is graphed below.
Valentin [98]

Answer: Option A

y=\left \{ {{x^2 +2;\ \ x

Step-by-step explanation:

In the graph we have a piecewise function composed of a parabola and a line.

The parabola has the vertex in the point (0, 2) and cuts the y-axis in y = 2.

The equation of this parabola is y = x ^ 2 +2

Then we have an equation liney = -x + 2


Note that the interval in which the parabola is defined is from -∞ to x = 1. Note that the parabola does not include the point x = 1 because it is marked with an empty circle " о ."

(this is x< 1)

Then the equation of the line goes from x = 1 to ∞ . In this case, the line includes x = 1 because the point at the end of the line is represented by a full circle .

(this is x\geq 1)

Then the function is:

y=\left \{ {{x^2 +2;\ \ x

7 0
3 years ago
The cost of 9 scares is $78.75 what is the unit price ?
Vlad [161]

Answer:

$8.75

Step-by-step explanation:

5 0
2 years ago
A university hired you as a lab assistant after you graduated. Your starting salary is $41,500 and your salary will increase by
VladimirAG [237]

Answer:

$67,000

Step-by-step explanation:

41,000*(1,700*15)=67,000

5 0
3 years ago
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