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nignag [31]
3 years ago
10

How many ways are there to choose a half dozen donuts from 10 varieties a)If there are no two donuts of the same variety.b)If th

ere are at least two varieties.c)If there must be at least one but no more than 4 glazed.
Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer:

If multiples are allowed (like "10 plain, two chocolate"), then for each of 12 donuts there are 21 possibilities.

That is 21 x 21 x 21 .... x 21 (12 terms in all) = 21^12

Step-by-step explanation:

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3 years ago
The polynomial of degree 5, P ( x ) has leading coefficient a=1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of
ser-zykov [4K]

Answer:

p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}, for r_{1} = 0

Step-by-step explanation:

The general form of quintic-order polynomial is:

p_{5}(t) = a\cdot x^{5} + b\cdot x^{4} + c\cdot x^{3} + d\cdot x^{2} + e \cdot x + f

According to the statement of the problem, the polynomial has the following roots:

p_{5} (t) = (x - r_{1})\cdot (x-3)^{2}\cdot x^{2} \cdot (x+1)

Then, some algebraic handling is done to expand the polynomial:

p_{5} (t) = (x - r_{1}) \cdot (x^{3}-6\cdot x^{2}+9\cdot x) \cdot (x+1)\\p_{5} (t) = (x - r_{1}) \cdot (x^{4}-5\cdot x^{3} + 3 \cdot x^{2} + 9 \cdot x)

p_{5} (t) = x^{5} - (5+r_{1})\cdot x^{4} + (3 + 5\cdot r_{1})\cdot x^{3} +(9-3\cdot r_{1})\cdot x^{2} - 9 \cdot r_{1}\cdot x

If r_{1} = 0, then:

p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}

5 0
3 years ago
What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)?<br> -8<br> оооо
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Answer:

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Step-by-step explanation:

desmos is extremely helpful! :)

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A dilation is applied to a triangle such that the sides of the image are 1.5 times the length of their corresponding sides in th
gtnhenbr [62]
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4 0
3 years ago
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. 25 points .please help Pythagoras theorem.​
Salsk061 [2.6K]

Answer:

  • 20 cm

Step-by-step explanation:

The bottom leg is divided into equal segments, one of them is b.

It means the bottom leg is b + b = 2b.

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<u>Solve for b:</u>

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