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zvonat [6]
3 years ago
8

if a given set has thirteen elements how many subsets have somewhere from four through eight elements

Mathematics
1 answer:
zmey [24]3 years ago
8 0
Of n elements, there are {}_nC_r=\dfrac{n!}{r!(n-r)!} ways of choosing any r elements. So the number of subsets that can be chosen from the set of 13 elements, each consisting of 4 to 8 elements, is

\displaystyle\sum_{r=4}^8{}_{13}C_r={}_{13}C_4+\cdots+{}_{13}C_8=6721

To compute the actual numbers, you have, for example,

{}_{13}C_4=\dfrac{13!}{4!(13-4)!}=\dfrac{13!}{4!9!}
=\dfrac{13\times12\times\cdots\times6\times5}{9\times8\times\cdots\times2\times1}
=\dfrac{13\times12\times11\times10}{4\times3\times2\times1}
=13\times11\times5
=715

so there are 715 ways of picking subsets of size 4. Compute the others similarly, then add them up.
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<em><u>Solution:</u></em>

Given that, I can paint 96 sq ft in 15 minutes

To find: Time taken to paint 1 square feet

From given,

96 square feet is painted in 15 minutes

Let "x" be the time taken to paint 1 square feet

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Thus it takes 0.15625 minutes to paint 1 square feet

8 0
3 years ago
Plz answer the following No scams,links or random amswers or ill report​
zvonat [6]

Answer:

f(2) = 12

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Step-by-step explanation:

<u>a)</u>

plug in x as 2

f(x) = 2^2 + 2(2) + 4

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<u>b)</u>

replace f(x) with 7

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x^2 + 2x - 3 (move 7 to other side)

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ac: -3x^2

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split b into 3x, -x

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3 0
3 years ago
(09.02 HC)
Vesna [10]
We factor the equation to get:

-(x-25)^2+361

In the form a(x-h)^2+k, the vertex is (h, k), so the vertex is (25, 361).  This means that the studio makes the most profit from selling 25 memberships, and thus makes 361 dollars.

B.  The x-intercepts are the values of x for which f(x) is 0.  This equation can be factored as (-a+6)(a-44)=0, with solutions 6 and 44.  Therefore, by selling either 6 memberships or 44 memberships, the studio breaks even, neither making nor losing money.
4 0
3 years ago
Y=x+2<br> 3x+3y=6<br> solving systems by substitution
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(

−

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3

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(

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=

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3

x

+

3

(

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x

+

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3

x

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(

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.

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y

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−

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−

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