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1 year ago

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Katarina bought a package of 500 stickers. Each sheet in the package has 20 stickers.

1 answer:

Mashcka [7]1 year ago

5 0

I think there are 125 heart stickers and 375 star stickers. 20/4 = 5, so there are 5 heart stickers per sheet. there are 25 sheets in the package, 5 x 25 = 125. if the remaining stickers on a sheet are stars then there are 15 star stickers per sheet. 15 x 25 = 375.

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Show that the Fibonacci numbers satisfy the recurrence relation fn = 5fn−4 + 3fn−5 for n = 5, 6, 7, . . . , together with the in

Sonja [21]

Answer with step-by-step explanation:

We are given that the recurrence relation

$f_n=5f_{n-4}+3f_{n-5}$

for n=5,6,7,..

Initial condition

$f_0=0,f_1=1,f_2=1,f_3=2,f_4=3$

We have to show that Fibonacci numbers satisfies the recurrence relation.

The recurrence relation of Fibonacci numbers

$f_n=f_{n-1}+f_{n-2}$ , $f_0=0,f_1=1$

Apply this

$f_n=(f_{n-2}+f_{n-3})+f_{n-2}=2f_{n-2}+f_{n-3}$

$f_n=2(f_{n-3}+f_{n-4})+f_{n-3}=3f_{n-3}+2f_{n-4}$

$f_n=3(f_{n-4}+f_{n-5})+2f_{n-4}=5f_{n-4}+3f_{n-5}$

Substitute n=2

$f_2=f_1+f_0=1+0=1$

$f_3=f_2+f_1=1+1=2$

$f_4=f_3+f_2=2+1=3$

Hence, the Fibonacci numbers satisfied the given recurrence relation .

Now, we have to show that $f_{5n}$ is divisible by 5 for n=1,2,3,..

Now replace n by 5n

$f_{5n}=5f_{5n-4}+3f_{5n-5}$

Apply induction

Substitute n=1

$f_5=5f_1+3f_0=5+0=5$

It is true for n=1

Suppose it is true for n=k

$f_{5k}=5f_{5k-4}+3f_{5k-5}$ is divisible 5

Let $f_{5k}=5q$

Now, we shall prove that for n=k+1 is true

$f_{5k+5}=5f_{5k+5-4}+3f_{5k+5-5}=5f_{5k+1}+3f_{5k}=5f_{5k+1}+3(5q)$

$f_{5k+5}=5(f_{5k+1}+3q)$

It is multiple of 5 .Therefore, it is divisible by 5.

It is true for n=k+1

Hence, the $f_{5n}$ is divisible by 5 for n=1,2,3,..

8 0

2 years ago

Given: PKHE - inscribed, m∠E=120°,

Montano1993 [528]

Answer:

C is the answer they are equal.

Step-by-step explanation:

5 0

2 years ago

Se necesitan 4/7 de litro de pintura para pintar un metro cuadrado de pared, si queremos pintar 2/5 de metro cuadrado de pared,

Assoli18 [71]

Answer:

8/35 de litro

Step-by-step explanation:

De la pregunta, sabemos que se necesitan 4/7 de un litro para pintar un metro cuadrado de pared.

Ahora necesitamos saber la cantidad de pintura necesaria para pintar 2/5 de un metro cuadrado.

Digamos que la cantidad necesaria es x

Ahora hagamos una relación matemática;

4/7 pinturas 1 metro cuadrado

x pintará 2/5 metros

cuadrados por lo tanto, x * 1 = 4/7 * 2/5 = 8/35

6 0

2 years ago

What’s 4x4x2-4 in a fraction over 2

JulijaS [17]

Answer:

it should be 12/2 or 6 i believe

Step-by-step explanation:

4x4 = 8

8x2 = 16

16-4 = 12

8 0

2 years ago

An old rectangular tank with length 0.3 m could hold 154 L of water. A new similar tank has a length of 1.5 m. What is the capac

dimaraw [331]

The length of the new tank is 5 times bigger than the old one, so 154×5=770. As a result, the capacity of the new tank is 770L. Hope it help!

6 0

2 years ago

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