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3 years ago

Which equation is equivalent to the given equation? x^2 - 6x = 8

Mathematics

1 answer:

arsen [322]3 years ago

6 0

Answer:

Step-by-step explanation:

$x^2-6x=8\\\\x^2-6x+9-9=8\\\\x^2-6x+9=17\\\\(x-3)^2=17$

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The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

AURORKA [14]

The two nominal variables are related.

The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

Ownership C1 C2 C3

No 40 32 48

Yes 30 48 52

The first thing to do in order to determine if they are related or not is to state our null and alternative hypothesis

Null hypothesis

$\mathbf{H_o: Two \nomial \ variables \ are \ related}$

Alternative hypothesis

$\mathbf{H_a: Two \nomial \ variables \ are \ not \ related}$

Using the Chi-square test statistics which can be expressed by using the formula

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

Ownership C1 C2 C3 Total

No 40 32 48 120

Yes 30 48 52 130

Total 70 80 100 250

The expected values are calculated as:

$\mathsf{E_{a,b} = \dfrac{(row \ total \times column \ total )}{grand \ total }}$

$\mathsf{E_{1,1} = \dfrac{(70 \times120 )}{250 }}$

$\mathsf{E_{1,1} = 33.6}$

$\mathsf{E_{1,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{1,2} = 36.4}$

$\mathsf{E_{2,1} = \dfrac{(80 \times120 )}{250 }}$

$\mathsf{E_{2,1} = 38.4}$

$\mathsf{E_{2,2} = \dfrac{(80 \times 130 )}{250 }}$

$\mathsf{E_{2,2} = 41.6}$

$\mathsf{E_{3,1} = \dfrac{(100 \times120 )}{250 }}$

$\mathsf{E_{3,1} = 48}$

$\mathsf{E_{3,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{3,2} = 52}$

∴ Using the Chi-square test statistics, we have:

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

$X ^2 = \Bigg( \dfrac{(40-33.6)^2}{33.6}+ \dfrac{(30-36.4)^2}{36.4}+ \dfrac{(32-38.4)^2}{38.4}+ \dfrac{(48-41.6)^2}{41.6} + \dfrac{(48-48)^2}{48}+ \dfrac{(52-52)^2}{52} \Bigg)$

$X ^2 = \Bigg( \dfrac{40.96}{33.6}+ \dfrac{40.96}{36.4}+ \dfrac{40.96}{38.4}+ \dfrac{40.96}{41.6} + \dfrac{0}{48}+ \dfrac{0}{52} \Bigg)$

$X ^2 = \Bigg( 1.2190+ 1.1253+ 1.0667+ 0.9846+0+ 0 \Bigg)$

$\mathbf{X ^2 =4.3956}$

The degree of freedom df = ((r - 1) × (c - 1))

= (3 - 1) (2 -1 )

= 2 × 1

= 2

∴

Assuming the level of significance = 5%

The p-value of the Chi-square test statistics at df of 2 is:

= $\mathbf{P(X^2 > 4.3956) \implies 0.111}$

Therefore, we can conclude that since the p-value (0.111) is greater than the level of significance (0.05), we fail to reject the null hypothesis.

Hence, the two nominal variables are related.

Learn more about Chi-square test statistics here:

brainly.com/question/2365682?referrer=searchResults

7 0

3 years ago

WILL MARK BRAINLIEST IF ANSWER IS CORRECT <br><br> Solve<br><br> 20÷4+2•5

Bingel [31]

Answer: the answer is 8

Step-by-step explanation:

Hope this helped.

8 0

2 years ago

Read 2 more answers

Please help mee! <br> no links :(

Cerrena [4.2K]

Answer:

a=0.62, b=7/9, c=10/9

Step-by-step explanation:

Brainliest would be appreciated

5 0

3 years ago

Read 2 more answers

Which of the following are alternate interior angles? Select all that apply.

goblinko [34]

Option C: ∠2 and ∠8

Option E: ∠3 and ∠5

Solution:

Two parallel lines cut by a transversal.

Option A: ∠5 and ∠4

∠4 is not interior of parallel lines.

Hence it is not true.

Option B: ∠6 and ∠5

∠6 is not interior of parallel lines.

Hence it is not true.

Option C: ∠2 and ∠8

∠2 and ∠8 lies in the interior of the parallel lines.

∠2 and ∠8 lies in alternate of the transversal line.

Therefore, ∠2 and ∠8 are alternate interior angles.

Hence it is true.

Option D: ∠8 and ∠1

∠1 is not interior of parallel lines.

Hence it is not true.

Option E: ∠3 and ∠5

∠3 and ∠5 lies in the interior of the parallel lines.

∠3 and ∠5 lies in alternate of the transversal line.

Therefore, ∠3 and ∠5 are alternate interior angles.

Hence it is true.

Therefore ∠2 and ∠8, ∠3 and ∠5 are alternate interior angles.

6 0

3 years ago

Hannah is going to roll two dice.

krok68 [10]

Answer:

14 /36

Step-by-step explanation:

1. 2. 3. 4. 5. 6.

1 1,1. 1,2. 1,3. 1,4 1,5. 1,6

2. 1,2. 2,2. 2,3. 2,4. 2,5. 2,6

3 1,3. 3,2. 3,3 3,4. 3,5. 3,6

4 1,4. 2,4. 3,4. 4,4. 4,5. 4,6

5. 1,5. 2,5. 3,5. 4,5. 5,5. 6,5

6 1,6. 2,6. 3,6. 4,6. 5,6. 6,6

There are 36 possible outcomes, and 14 of those meet your constraint/what the question is asking.

Hope this helps!

8 0

4 years ago