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3 years ago

If x³ + 2x and x³ − 7x² + 4x +2 + k have a common linear polynomial factor, then the value of k is what?

Mathematics

1 answer:

Georgia [21]3 years ago

8 0

Answer:

k = -2

Step-by-step explanation:

Factor x³ + 2x:

x³ + 2x = x(x² + 2)

1. The common factor is x, then:

2 + k = 0 ⇒ k = -2 (all the rest are divisible by x)

2. Factor x² + 2 is not linear therefore we discard it.

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Answer:

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Let us suppose we have data on the absorbency of paper towels that were produced by two different manufacturing processes. From

maksim [4K]

Answer:

The 95% CI for the difference of means is:

$-155.45 \leq \mu_1-\mu_2 \leq -44.55$

Step-by-step explanation:

The question is incomplete:

"Find a 95% confidence interval on the difference of the towels mean absorbency produced by the two processes. Assumed that the standard deviations are estimated from the data. Round to two decimals places."

Process 1:

- Sample size: 10

- Mean: 200

- S.D.: 15

Process 2:

- Sample size: 4

- Mean: 300

- S.D.: 50

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$M_d=M_1-M_2=200-300=-100$

The standard deviation can be estimated as:

$\sigma_d=\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\\\\\sigma_d=\sqrt{\frac{15^2}{10}+\frac{50^2}{4}} =\sqrt{22.5+625}=\sqrt{647.5}=25.45$

The degrees of freedom are:

$df=n_1+n_2-2=10+4-2=12$

The t-value for a 95% confidence interval and 12 degrees of freedom is t=±2.179.

Then, the confidence interval can be written as:

$M_d-t\cdot \sigma_d\leq \mu_1-\mu_2 \leq M_d+t\cdot \sigma_d\\\\-100-2.179*25.45\leq \mu_1-\mu_2 \leq -100+2.179*25.45\\\\-100-55.45 \leq \mu_1-\mu_2 \leq -100+55.45\\\\ -155.45 \leq \mu_1-\mu_2 \leq -44.55$

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3 years ago

The perimeter of a triangle is 42 yards. The first side is 5 yards less than the second side, and the third side is 2 yards less

Maru [420]

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Answer:

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Answer:

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