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2 years ago

4(-4x - 3) > 36 with the steps

Mathematics

2 answers:

Lena [83]2 years ago

8 0

Answer is x < -3

4(-4x-3) > 36

Expand the brackets

-16x - 12 > 36

Rearrange the inequality to get x on its own

-16x > 36 + 12

-16x > 48

Divide both sides by -16 in order to get x on its own. When dividing both sides of the inequality by a negative number, flip the inequality sign (as this is one of the laws of inequalities)

x < 48/-16

x < -3

Sergeu [11.5K]2 years ago

5 0

Answer:

x < -3

Step-by-step explanation:

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

−4x−3> 36/4

Divide 36 by 4 to get 9.

−4x−3>9

Add 3 to both sides.

−4x>9+3

Add 9 and 3 to get 12.

−4x>12

Divide both sides by −4. Since −4 is negative, the inequality direction is changed.

x< 12/-4

Divide 12 by −4 to get −3.

x < -3

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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

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Answer:

The 95% CI for the difference of means is:

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

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>"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."</em>

Process 1:

- Sample size: 10

- Mean: 200

- S.D.: 15

Process 2:

- Sample size: 4

- Mean: 300

- S.D.: 50

The difference of the sample means is:

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

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:

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