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Anton [14]
3 years ago
7

Consider the following proposed proof by contradiction that for all positive integers n, 3n > 2.

Mathematics
1 answer:
laila [671]3 years ago
7 0

Answer:

The proof contains a simple direct proof, wrapped inside the unnecessary logical packaging of a proof by contradiction framework.

Step-by-step explanation:

The proof is rigourous and well written, so we discard the second answer.

This is not a fake proof by contradiction: it does not have any logical fallacies (circular arguments) or additional assumptions, like, for example, the "proof" of "All the horses are the same color". It is factually correct, but it can be rewritten as a direct proof.

A meaningful proof by contradiction depends strongly on the assumption that the statement to prove is false. In this argument, we only this assumption once, thus it is innecessary. Other proofs by contradiction, like the proof of "The square root of 2 is irrational" or Euclid's proof of the infinitude of primes, develop a longer argument based on the new assumption, but this proof doesn't.

To rewrite this without the superfluous framework, erase the parts "Suppose that the statement is false" and "The fact that the statement is true contradicts the assumption that the statement is false. Thus, the assumption that the statement was false must have been false. Thus, the statement is true."

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A data set has a normal distribution with a mean of 47 and a standard deviation of 4.6. Use this information to scale the horizo
gulaghasi [49]

Horizontal axis with 1, 2, and 3 standard deviations above the mean are 51.6, 56.2, 60.8

Horizontal axis with 1, 2, and 3 standard deviations below the mean are 42.4, 37.8, 33.2

<u>Step-by-step explanation:</u>

A data set has a normal distribution with a mean of 47 and a standard deviation of 4.6

  • Mean, M ⇒ 47
  • Standard deviation ⇒ 4.6

From this information, you have to scale the horizontal axis with the mean of this distribution and values at 1, 2, and 3 standard deviations above and below the mean.

Horizontal axis with 1, 2, and 3 standard deviations above the mean :

1 standard deviation above the mean ⇒ M + SD

⇒ 47 + 4.6 = 51.6

2 standard deviations above the mean ⇒ M + 2SD

⇒ 47 + (2 × 4.6) = 56.2

3 standard deviations above the mean ⇒ M + 3SD

⇒ 47 + (3 × 4.6) = 60.8

Horizontal axis with 1, 2, and 3 standard deviations below the mean :

1 standard deviation below the mean ⇒ M - SD

⇒ 47 - 4.6 = 42.4

2 standard deviations below the mean ⇒ M - 2SD

⇒ 47 - (2 × 4.6) = 37.8

3 standard deviations below the mean ⇒ M - 3SD

⇒ 47 - (3 × 4.6) = 33.2

8 0
3 years ago
Which side of PQR is the hypotenuse. (PQR is a right triangle)
MatroZZZ [7]

Answer:

the longest side of the triangle?

Step-by-step explanation:

3 0
3 years ago
F(r) = -(1 – 12)(r + 3)<br> What are the zeros of the function
nexus9112 [7]

Answer:

r  =   -3

Step-by-step explanation:

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

8 0
2 years ago
How to find the maximum height projectile motion?
ziro4ka [17]
Y=v(initial)*t+1/2at^2
since the velocity is zero at the maximum height then we get
y=1/2at^2
a is just acceleration due to gravity so a=g which is 9.8 m/s^2.
so y=1/2gt^2.
7 0
3 years ago
What is the slope of the line shown?<br><br> -7/9<br> 9/7<br> 7/9<br> -9/7
SpyIntel [72]

To find slope, we must find the change in y values divided by the change in x values, also called the rise/run. This is modeled below:

Slope = m = (y1 - y2)/(x1-x2) = (6-(-3))/(1 - (-6)) = (6+3)/(1+6) = 9/7

We can check that this answer is correct by consulting the graph. The graph shows a positive correlation (means that the slope should be positive), and if you count the graph unit squares, you get that the graph moves up 9 squares and over 7 squares between the two points shown, letting us know we got the right answer.

Hope this helps!

7 0
3 years ago
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