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irina1246 [14]
3 years ago
7

Suppose we want to choose 5 letters, without replacement, from 9 distinct letters. (If necessary, consult a list of formulas.) (

a) How many ways can this be done, if order of the choices is not relevant? .​
Mathematics
1 answer:
lara [203]3 years ago
5 0

Answer:

A.This is the number of combinations of 6 from 15

= 15C6

=  15! / (15-6)! 6!

= 5,005 ways.

B.  This is the number of permutaions of 6 from 15:

= 15! / (15-6)!

= 3,603,600 ways.

Step-by-step explanation:

This was someone else's work not mine sorry here's creditssss :))

brainly.com/question/15145413

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Write the polynomial in factored form. <br><br> p(x)=(x+5)(x-___)(x+___)
Rom4ik [11]

Answer:


Step-by-step explanation:

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Solution :

Part A:

First find the potential roots of p(x) using rational root theorem;

So, \text{Possible roots} =\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}

Since constant term = -60

Leading coefficient = 1

\text{Possible roots} =\pm\frac{\text{factors of 60}}{\text{factors of 1}}

\text{Possible roots} =\pm\frac{1,2,3,4,5,6,10,12,15,20,60}{1}

Thus the possible roots are  \pm1, \pm2, \pm 3, \pm4, \pm5,\pm6, \pm10, \pm12, \pm15, \pm20, \pm60

Thus from the given options the correct answers are -10,-5,3,15

Now For Part B we will use synthetic division

Out of the possible roots we will use the root which gives remainder 0 in synthetic division :

Since we can see in the figure With -5 we are getting 0 remainder.

Refer the attached figure

We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0.  All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus the quotient is x^{2} +x-12

And remainder is 0 .

So to get the other two factors of the given polynomial we will solve the quotient by middle term splitting

x^{2} +x-12=0

x^{2} +4x-3x-12=0

x(x+4)-3(x+4)=0

(x-3)(x+4)=0

Thus x-3 and x+4 are the other two factors

So , p(x)=(x+5)(x-3)(x+4)





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Answer:

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An above-ground swimming pool in the shape of a cylinder has a diameter of 18 feet and a height of 4.5 feet.If the pool is fille
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Answer:

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we know that

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