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3 years ago

5

Suppose you have 13 tubes of paint. How many distinct color groupings can you make with your paint?

1 answer:

anzhelika [568]3 years ago

3 0

Answer:

32767 distinct color grouping

Step-by-step explanation:

Given data:

Total tube is 13

for distinct color, group can be 1,2,3,4,.... 15

For total number of ways we have following relation

$^nC_0 +^nC_1 +^nC_2 + .......^nC_n = 2^n$

here n = 13 so we have

$^15C_0 +^15C_1 +^15C_2 + .......^15C_{15} = 2^15$

for at least one

$= 2^{15} - 1$

$= 32768 -1$

= 32767 distinct color grouping

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Read 2 more answers

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(a). First of all, we will find the critical points of function by equating derivative with 0.

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$f'(x)=6x^{2}+6x-336$

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$f'(x)=(x+8)(x-7)$

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Since $f'(9)>0$ , therefore, function is increasing on interval $(-\infty,-8)$ .

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Since $f'(1)$ , therefore, function is decreasing on interval $(-8,7)$ .

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(c) To find inflection points, we need to check where 2nd derivative is equal to 0.

Let us find 2nd derivative.

$f''(x)=6(2)x^{1}+6$

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$12x+6=0$

$12x=-6$

$\frac{12x}{12}=-\frac{6}{12}$

$x=-\frac{1}{2}$

Therefore, $x=-\frac{1}{2}$ is an inflection point of given function.

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3 years ago