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sashaice [31]
2 years ago
5

HELP ME!!!! I am so Confused with this!

Mathematics
1 answer:
horsena [70]2 years ago
8 0

Answer:

C

Step-by-step explanation:

A: y=1.6X

B: y=2.5x

D: y=2x

C doesn't have a proportional relationship between X and Y

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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
How much is the orange moon counted for?<br> How much is the green circle counted for?
Vlad [161]

Answer:

green= 3 each

orange moon= 5 each

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the value of x? enter your answer in the box. x =
leonid [27]

Answer:

Step-by-step explanation:

Sum of all angles of triangle = 180

39 + 102 + x = 180

         141 + x = 180

Subtract 141 from both sides

                 x = 180 - 141

                 x = 39

4 0
2 years ago
Jason is pulling a box across the room. He is pulling with a force of 11 newtons and his arm is making a 37 angle with the horiz
MissTica

Force=10N

Angle=37

Vertical componenets:-

\\ \sf\longmapsto Fsin\theta

\\ \sf\longmapsto 10sin38

\\ \sf\longmapsto 10(0.6)

\\ \sf\longmapsto 6N

4 0
2 years ago
GM projected that 3% of their cars produced this year will be defective. If GM produced 1,698 cars that were defective, how many
serious [3.7K]

Answer:

56600 cars

Step-by-step explanation:

Below is the calculation of number of cars produced.

The percentage of cars that is defected = 3%

Number of cars that are defective = 1698 cars

The number of cars produced in a year = 1698 / 3%  

The number of cars produced in a year = 56600 cars

6 0
3 years ago
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