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san4es73 [151]
3 years ago
5

In how many orders can six people line up from left to right for a group photo?

Mathematics
2 answers:
Evgesh-ka [11]3 years ago
6 0

Answer:

We have to arrange 6 people in line

. Now, the number of ways to arrange n items = n!.

Hence, the answer is 6!=

=6×5×4×3×2×1= 720 orders

slavikrds [6]3 years ago
5 0

Answer:

720 possible orders

Step-by-step explanation:

To order 6 people in a line, let's imagine them as 6 possible spaces:

( )( )( )( )( )( )

Going from left to right, let's start with space 1.

There are 6 possibilities for space 1 as any of the 6 people could occupy that space in the line.

(6)( )( )( )( )( )

Next, since one person will have already occupied space 1, there are only 5 people left who can occupy space 2, so there are 5 possibilities for space 2:

(6)(5)( )( )( )( )

Continuing in this fashion, there are now only 4 people left so 4 possibilities for space 3 and etc.

(6)(5)(4)(3)(2)(1)

This means we have 6,5,4,3,2 and 1 possibilities for each space respectively.

Multiply them together and we have:

6x5x4x3x2x1 = 720 possible orders.

Hope this helped!

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Write the quadratic equation whose roots are 3 and -1, and whose leading coefficient is 5.
Assoli18 [71]

Answer:

5x² - 10x - 15 = 0

Step-by-step explanation:

Given that the roots are x = 3 and x = - 1, then the factors are

(x - 3) and (x + 1) and the quadratic is the product of the factors, that is

f(x) = a(x - 3)(x + 1) ← a is a multiplier

Here a = 5, thus

f(x) = 5(x - 3)(x + 1) ← expand factors using FOIL

     = 5(x² - 2x - 3) ← distribute parenthesis by 5

     = 5x² - 10x - 15

Thus equation is

5x² - 10x - 15 = 0

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Step-by-step explanation:

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Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-
Shtirlitz [24]

Answer:

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Step-by-step explanation:

Mean Value Theorem:

If f is a continuous function in a bounded interval [0,4], there is at least one value of c in (a,b) for which:

f(c) = \frac{1}{b-a}\int\limits^a_b {f(x)} \, dx

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So f(c) = c

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3 0
3 years ago
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