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1 year ago

Sophia bought 18 packs of lemonade each pack has 24 cans answer key

Mathematics

1 answer:

Juliette [100K]1 year ago

5 0

Answer is 432 cans in total
18 packs times 24 cans in each is 432

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Eric is two years younger than 2 times his sisters age. Write a rule that represent Eric's age a as a function of his sisters ag

Snezhnost [94]

(11•2) - 2 = Eric's Age

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2 years ago

Lincoln memorial geometrical shape

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2 years ago

Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

6 0

2 years ago

Solve 5c + 4 = -26

mr_godi [17]

<em>1) 5 c + 4 = - 26
5 c = -26 -4
5 c = -30
c = -30 / 5
c = -6 so correct option is B..

2) 3 x - x +2 = 12
2 x +2 = 12
2x = 12-2
2x = 10
x = 10/2
x= 5 so correct option is D

3 ) 3 ( x + 1 )+ 6 = 33
3x + 3 + 6 = 33
3x + 9 = 33
3x = 33-9
3x = 24
x = 24/3
x = 8 so correct option is B

4) y/-6=9
y=9 x -6
y= - 54 there is no such option i guess question is missing

5)(x + 4) /2 = 7
x +4 = 7 x 2
x + 4 = 14
x = 14-4
x = 10 so correct option is D

6)1/3 ( 2x - 8) = 4
2x/ 3 - 8 /3 = 4
2x - 8 / 3 = 4
2x - 8 = 4 x 3
2x - 8 = 12
2x = 12 + 8
2x = 20
x = 20/2
x = 10 so correct option is C

</em>