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4 years ago

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(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab) Which of the following shows the sum of the polynomials rewritten with like terms grouped

together? [3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2) [3a2 + (–3a2)] + (–5ab + 2b2) + (b2 + 8ab) [3a2 + 3a2] + (5ab + 8ab) + (b2 + 2b2) [3a2 + 3a2] + (5ab + 2b2) + (b2 + 8ab)

2 answers:

mr Goodwill [35]4 years ago

8 0

Answer:

Option 1st is correct

$[(3a^2+(-3a^2)]+(-5ab+8ab)+ (b^2+2b^2)$

Step-by-step explanation:

Given the expression:

$(3a^2-5ab+b^2)+(-3a^2+2b^2+8ab)$

Like terms are those which have same variable to the same powers.

Open the bracket:

$3a^2 -5ab+b^2+(-3a^2)+2b^2+8ab$

⇒ $[(3a^2+(-3a^2)]+(-5ab+8ab)+ (b^2+2b^2)$

Therefore, the sum of the polynomials rewritten with like terms grouped together is:

$[(3a^2+(-3a^2)]+(-5ab+8ab)+ (b^2+2b^2)$

Mila [183]4 years ago

6 0

<span>[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)</span><span>
</span>

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The confidence interval is $25.16 < \mu < 26.85$

Step-by-step explanation:

From the question we are given a data set

25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

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$\= x = \frac{\sum x_i}{n}$

where is the sample size with values n = 10

$\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}$

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The standard deviation is evaluated as

$\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }$

substituting values

$= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }$

$\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }$

$\sigma = 1.625$

The confidence level is given as 90% hence the level of significance is calculated as

$\alpha = 100 -90$

$\alpha =10$ %

$\alpha = 0.10$

Now the critical values of $\frac{\alpha }{2}$ is obtained from the normal distribution table as

$Z_{\frac{\alpha }{2} } = 1.645$

The reason we are obtaining the critical values of $\frac{\alpha }{2}$ instead of $\alpha$ is because we are considering two tails of the area under the normal curve

The margin of error is evaluated as

$MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

substituting values

$MOE = 1.645 * \frac{1.625 }{\sqrt{10} }$

$MOE = 0.845$

The 90%, two sided confidence interval is mathematically evaluated as

$\= x - MOE < \mu < \= x + MOE$

$26 - 0.845 < \mu < 26 + 0.845$

$25.16 < \mu < 26.85$

Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours

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