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joja [24]
4 years ago
13

Four mathematicians, three physicists, and an engineer are to be seated equally spaced around a circular table. How many differe

nt arrangements are possible if the mathematicians must all sit together (in four consecutive seats) and the physicists must all sit together (in three consecutive seats)? (As usual, two arrangements are identical if one is a rotation of the other.)
Mathematics
1 answer:
Vesna [10]4 years ago
3 0

First, we can choose the seats for the four mathematicians.  Then we seat the physicits, then the engineer.  There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer.  But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.

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The system shown is _____.<br><br> consistent<br> equivalent<br> inconsistent
mixas84 [53]

Answer:

consistent  

Solution at (3,2)

Step-by-step explanation:

A consistent and independent solution to a system of linear equations is one point

A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)

An inconsistent solution is where there is no solution, the lines do not cross

Since the lines cross at exactly one point, this is a consistent and dependent solution

The solution is at x = 3  ( 3 units to the right of the origin)

and y = 2 ( 2 units up from the origin)

(3,2)

5 0
3 years ago
Read 2 more answers
(a+b)2 ;a=1/2 and b=2
FrozenT [24]

Answer:

\frac{25}{4}

Step-by-step explanation:

a + b = \frac{1}{2} + 2 = 2 \frac{1}{2} = \frac{5}{2}, thus

(a + b)² = (\frac{5}{2} )² = \frac{5}{2} × \frac{5}{2} = \frac{5(5)}{2(2)} = \frac{25}{4}

8 0
3 years ago
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True or false: two points with the same x-coordinate are always on the same vertical line
Vesna [10]
True, you can even test it out yourself. If the domain (x) is the same then it will be a vertical line. Like if you graphed (1,2) (1,4), (1,6) it will be a vertical line on your graph. I hope this helps!
3 0
4 years ago
Simplify, write your answer in scientific notation<br> (4 x 10-6) + (3 x 10-3)
slavikrds [6]

Answer:

Step-by-step explanation: 3004 x 10⁻⁶

These numbers were written in standard forms or in scientific notation or in compressed manner

4 x 10⁻⁶ = 0.000004

3 x 10⁻₃ = 0.003

Adding the two together  gives

0.000004 + 0.003 = 0.003004

                               = 3004 x 10⁻⁶

                             

6 0
4 years ago
6x^3 - 7x^2 - 3x = 0. Show the correct steps.
Jlenok [28]

Hey there! :)

Answer:

x = -1/3, 0, 3/2.

Step-by-step explanation:

Starting with:

6x³ - 7x² - 3x = 0

Factor out a greatest common factor, or x from each term:

x(6x² - 7x - 3) = 0

Factor the expression inside of the parenthesis:

x(3x +1)(2x - 3) = 0

Use the Zero Product Property to find the solutions:

x = 0

---------

3x + 1 = 0

3x = -1

x = -1/3

-----------

2x - 3 = 0

2x = 3

x = 3/2

----------

The solutions to this equation are x = -1/3, 0, 3/2.

6 0
3 years ago
Read 2 more answers
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