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Ulleksa [173]
3 years ago
6

In how many ways can 6 people line up on a bus if 3 specific

Mathematics
1 answer:
astra-53 [7]3 years ago
6 0
More info needed smh gd
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Find the generating function for the sequence 1,-2,4,-8, 16, ...
kirill [66]

Answer:

  a(x)=\dfrac{1}{1+2x}

Step-by-step explanation:

The generating function a(x) produces a power series ...

  a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots

where the coefficients are the elements of the given sequence.

We observe that the given sequence has the recurrence relation ...

  a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}

This can be rearranged to ...

  a_n+2a_{n-1}=0

We can formulate this in terms of a(x) as follows, then solve for a(x).

\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}

The generating function is ...

  a(x) = 1/(1+2x)

3 0
3 years ago
Read 2 more answers
When Theresa got her puppy, it weighed 6 ponds less than 2/3 of its weight now. If the puppy weighed 4 pounds when she first rec
sesenic [268]

Answer:

15 lb

Step-by-step explanation:

let the current weight of the puppy be X, the  initial weight of the puppy is 4lb or \frac{2}{3}X-6\ lb, (6 lb less 2/3 X) .

#We equate the current weight to the initial weight to determine X:

4\ lb=\frac{2}{3}X-6\ lb\\\\10 \ lb=\frac{2}{3}X\\\\X=15

Hence, the current weight of the puppy is 15 lb

5 0
4 years ago
The distance from town a to town b is 5 miles and the distance from town b to town c is 4 miles. which of the following could No
Radda [10]
A. 1 because a to b is 5 miles and b to c is 4 miles so it couldn't be 1 mile
6 0
3 years ago
Need help ASAP ......
ZanzabumX [31]

Answer:

a= 74

c= 10

d= 25

e= 10

f=16

g= 90

h= 24

j= 26

k= 154

m= 70

n= 170

p= 156

r= 154

s= 129

t= 148

v= 55

w= 41

x= 55

y= 24

z= 106

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Determine which ratio forms a proportion with 20/24 by writing the ratios in simplest form
Stella [2.4K]
5/6, I'm pretty sure.
7 0
4 years ago
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