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just olya [345]
3 years ago
11

Kai calculates that he spends 15% of the school day in science class. If he spends 42 minutes in science class, how many minutes

does Kai spend in school each day? Can someone tell me how to do that with fractions and cross products or something

Mathematics
1 answer:
MissTica3 years ago
6 0
You need to first multiply 100 by 42 then divide by 15

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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
3 years ago
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a​ single-strand electric
allochka39001 [22]
I'm fairly certain that using that wire you can have the same area no matter what dimensions there are, but if you do the square root, or \sqrt{} of 19,001,900 then you get 4359.11688. So your dimensions are 4359.11688 x 4359.11688. To get area, do length x width to get <span>1.9*1 0^{7}.

Hope this helped! If it did, please give me a good rating and mark me brainiest.<span /></span>
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Solve the rational equation quantity 3 times x minus 5 end quantity divided by 7 equals four sevenths. A: f(n) = f(n − 1) ⋅ 0.3
KengaRu [80]

Answer:

2.8 < x -0

Step-by-step explanation:

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2 years ago
A rotation is a transformation where an object move
ICE Princess25 [194]

Let's rephrase this:

Here:

There are 3 geometric transformations:

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Shapes are rotated or turned around an axis.

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3. Translation

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Melinda spends $5 at each of the 14<br> stores she visits. How much money did she spend ?
Paha777 [63]

Answer:

$70

Step-by-step explanation:

5 dollars * 14 stores= $70

4 0
3 years ago
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