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KiRa [710]
3 years ago
7

Consider the following theorem and proof.Theorem: The number âš2 is not rational number.Proof: Let's suppose âš2 is a rational n

umber.Then we can write âš2 = a/b where a, b are whole numbers, b not zero.We additionally assume that a/b is simplified to lowest terms, i.e., a and b have no common factors. Both of the numbers a and b cannot be even.From the equality âš2 = a/b it follows that 2 = a2/b2 .So, a2 = 2 · b2. Showing that the square of a is an even number since it is two times something.From this we know that a itself is also an even number.In symbols, a = 2k where k is a natural number. If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:2=(2k)2/b22=4k2/b22*b2=4k2b2=2k2Showing that b2 is even because it is 2 times a number.This implies that b itself is also even.Therefore the supposition made in the first line cannot be true and we can conclude that the number âš2 is not rational number.thereforeThe statement "Both of the numbers a and b cannot be even." is justified by the fact that The assumption that âš2 is a rational number. The assumption that a/b is simplified lowest terms. The assumption that âš2 is an irrational number. The fact that b divides a evenly. The fact that a and b are whole numbers.
Mathematics
1 answer:
ololo11 [35]3 years ago
7 0

Answer:

The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms

Step-by-step explanation:

We need to  show that the √2 is an irrational number.

And from the given steps of proof stated in the question, we need to find the assumption that justifies the fact : " Both of the number a and b cannot be even".

First take the given options :

Option a : √2 is a rational number

√2 being an rational or irrational has no relation of a and b to be even or odd. So, this option is rejected.

Option B : a/b is simplified lowest terms

This shows that a and b are not even because if a and b are even then a/b can be simplified in other lowest term.

Option c : √2 is a irrational number

Similarly, By using the inverse part of Option A, option c is also rejected.

Option d : The fact that b divides a evenly

This only shows that the a is even. This does not give any idea about b is even or not. So option D is also rejected.

Option E : The fact that a and b are whole numbers

This fact does not imply that the a and b are even or odd. So option E is also rejected.

Hence, The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms

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Answer: 2285

Step-by-step explanation:

Formula to find the sample size is given by :-

n=p(1-p)(\dfrac{z_c}{E})^2

, where p = prior estimate of population proportion.

E= Margin of error.

z_c = z-value for confidence interval of c.

Given : Confidence interval : 95%

From the z-value table , the z-value for 95% confidence interval = z_c=1.96

The General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal.

i.e. the prior estimate of population proportion of US residents thought marijuana should be made legal : p=0.61  

 [∵ sample proportion is the best estimate for population proportion.]

Margin of error : E= 2%=0.02

Now, the required minimum sample size would be :-

n=0.61(1-0.61)(\dfrac{1.96}{0.02})^2

Simplify ,

n=0.2379\times9604=2284.7916\approx2285

Thus , we need to survey <u>2285</u> Americans .

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3 years ago
Find the prime factorization of 72.​
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Answer:

2^3×3^2

and yh

Step-by-step explanation:

2×2×2×3×3

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Hey can you please help me posted picture of question
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We have to take out the greatest common factor from the given polynomial to factorize the expression. If you observe the terms of the polynomial, the greatest factor that is common to all the terms is 4 x^{4}. So taking it out as common, the factorization of the polynomial will be:

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So the option C gives the correct answer
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3 years ago
Please help, At a festival 2/7th of the number of girls was equal to 3/5th of the number of boys.
fenix001 [56]

Answer:

465

Step-by-step explanation:

Let the number of girls at the festival be--------- g

Let the number of boys at the festival be---------b

The conditions are;

2/7 g = 3/5 b ---------------(i)

g-b= 165 ---------------------(ii)---------make g the subject of the expression

g= 165 +b---------------------(iii)--------use this equation in (i)

2/7 (165 +b)= 3/5 b -------multiply both sides by 7

7*2/7(165+b) =3/5*7 b

2(165+b)=21/5 b ------multiply both sides by 5

5*2(165+b) = 21/5*5*b

10(165+b) = 21 b -------open brackets

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1650 = 11 b -----divide both sides by 11

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Total number of children at the festival = 150+315 =465

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