John has 9 different flags that he wants to hang on the wall. How many different ways can the flags be arranged in a row?
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There are 362880 different of ways the flags can be arranged in a row

Step-by-step explanation:

Given

Number of flags = 9

Required

Number of arrangements

The question talks about arrangements, this means we're dealing with permutations.

Provided that all flags are distinct, each of the 9 flags can be arranged in 1! way each.

All 9 flags can be arranged in

(1!)^9 = 1 (this number is negligible)

All in all, the total 9 flags can be arranged "collectively" in a row in 9! ways

Calculating 9!

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

9! = 362880

Hence, there are 362880 different of ways the flags can be arranged in a row

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w