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2 years ago

6

Julie has 30 pounds of chocolate that

1 answer:

Fudgin [204]2 years ago

7 0

Answer:

30 boxes

Step-by-step explanation:

1 box = 1 pound

x = 30 pound

30 Cross multiplied with 1

= 1 *30 =30

therefore: Julie can fill 30 boxes

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

wolverine [178]

So you're initial equation is $(2/6)*24=m$ . Well since $2/6=1/3$ , plug in 24 for the 1 in $1/3$ . So $24/3=m$ , and $24/3=8$ so $m=8$ .

7 0

3 years ago

a parking garage charges $5 for the first hour of parking and $1.75 for each additional hour. if y represents the total cost and

victus00 [196]

In this exact order:
5+1.75x=y
Sorry for the wait..Hope this helps

6 0

3 years ago

Help pls I need help lol it’s quite easy for rlly smart ppl

mr_godi [17]

Answer:

(2,1) (7,1) (7,5) (2,5)

Step-by-step explanation:

Just line up the dots on the x axis and y axis

Vertexes are the points or "corners" of the shape, and in your case, that square.

I hope this helped :D

8 0

2 years ago

Can someone please help me???????????????????

Vinil7 [7]

Answer:

C

Step-by-step explanation:

8 0

2 years ago

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