Write the opposite of – 1/2 explain.

Show that 2 - sqrt(2) is irrational

babunello [35]

Answer:

This proof can be done by contradiction.

Let us assume that 2 - √2 is rational number.

So, by the definition of rational number, we can write it as

$2 -\sqrt{2} = \dfrac{a}{b}$

where a & b are any integer.

⇒ $\sqrt{2} = 2 - \dfrac{a}{b}$

Since, a and b are integers $2 - \dfrac{a}{b}$ is also rational.

and therefore √2 is rational number.

This contradicts the fact that √2 is irrational number.

Hence our assumption that 2 - √2 is rational number is false.

Therefore, 2 - √2 is irrational number.

3 0

2 years ago

A national grocery store chain wants to test the difference in the average weight of turkeys sold in Detroit and the average wei

Arte-miy333 [17]

Answer:

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

The null hypothesis is accepted .

Assume the population variances are approximately the same

Step-by-step explanation:

Explanation:-

Given data a random sample of 20 turkeys sold at the chain's stores in Detroit yielded a sample mean of 17.53 pounds, with a sample standard deviation of 3.2 pounds

The first sample size 'n₁'= 20

mean of the first sample 'x₁⁻'= 17.53 pounds

standard deviation of first sample S₁ = 3.2 pounds

Given data a random sample of 24 turkeys sold at the chain's stores in Charlotte yielded a sample mean of 14.89 pounds, with a sample standard deviation of 2.7 pounds

The second sample size n₂ = 24

mean of the second sample "x₂⁻"= 14.89 pounds

standard deviation of second sample S₂ = 2.7 pounds

Null hypothesis:-H₀: The Population Variance are approximately same

Alternatively hypothesis: H₁:The Population Variance are approximately same

Level of significance ∝ =0.05

Degrees of freedom ν = n₁ +n₂ -2 =20+24-2 = 42

Test statistic :-

$t = \frac{x^{-} _{1} - x_{2} }{\sqrt{S^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }$

where $S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2}S_{2} ^{2} }{n_{1} +n_{2} -2}$

$S^{2} = \frac{20X(3.2)^2+24X(2.7)^2}{20+24-2}$

substitute values and we get S² = 40.988

$t= \frac{17.53-14.89 }{\sqrt{40.988(\frac{1}{20} }+\frac{1}{24} )}$

t = 1.3622

Calculated value t = 1.3622

Tabulated value 't' = 2.081

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

Conclusion:-

The null hypothesis is accepted

Assume the population variances are approximately the same.

6 0

2 years ago

A line has a slope of 3 and a y-intercept of 5. What is its equation in slope-intercept form? Write your answer using integers,

s344n2d4d5 [400]

Answer:

$y=3x+5$

Step-by-step explanation:

The problem is asking for slope-intercept form, luckily, they gave us both of those things.

Slope-intercept form: $y=mx+b$ , where $m=$ slope and $b=$ y-intercept.

So,

$y=3x+5$

Hope this helps!

7 0

3 years ago

Which expressions are equivalent to z+(z+6)

Nezavi [6.7K]

Answer:

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

(2*2)^2-(3+(2*2)/(6-4) EXPLAINED PLEASE

Eva8 [605]

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The solution of the given expression (2×2)² - [3+(2×2)]/(6-4) is 14.

<h3>What is PEMDAS?</h3>

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.

As per the rule of PEMDAS, the given expression can be simplified as shown below.

(2×2)² - [3+(2×2)]/(6-4)

Step 1: Solving Parenthesis,

= 4² - (3+4) / (2)

= 4² - 4/2

Step 2: Solving exponents,

= 16 - 4/2

Step 3: Solving Divisions,

= 16 - 2

Step 4: Solving Subtraction,

= 14

Hence, the solution of the given expression (2×2)² - [3+(2×2)]/(6-4) is 14.

Learn more about PEMDAS here:

brainly.com/question/36185

#SPJ1

6 0

1 year ago