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3 years ago

Simplify (4x + 12) - (6x - 18)

Mathematics

2 answers:

bixtya [17]3 years ago

5 0

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

4*x-12-(6*x-18)=0

Step-by-step explanation:

Pull out like factors :

-2x + 6 = -2 • (x - 3)

Rama09 [41]3 years ago

4 0

Hello there!

Start by removing the parenthesis combining like terms.

(4x + 12) - (6x - 18)

4x + 12 - 6x - 18

4x - 6x + 12 - 18

Next, simplify.

-2x + 12 - 18

-2x - 6

This is the final answer and it cannot be simplified any further, I hope this was helpful!

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R is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landi

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Answer:

3/8 hope helpes

Step-by-step explanation:

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3 years ago

Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor's. A sample of 40 bab

Readme [11.4K]

Answer:

Mean weight gained of two goods is not significantly different under 0.05 or 0.01 significance level, but it is under 0.10 significance level.

Step-by-step explanation:

We need to calculate the z-statistic of the differences of sample means and compare if it is significant under a significance level.

Z-score can be calculated using the formula:

z= $\frac{X-Y}{\sqrt{\frac{s(x)}{N(x)}+\frac{s(y)}{N(y)}}}$ where

X is the mean weight gain for in the first three months after birth for babies using the Gibbs products.
Y is the mean weight gain for in the first three months after birth for babies using the competitor products
s(x) is the population standard deviation of the sample for Gibbs brand
s(y) is the population standard deviation of the sample for competitor brand
N(x) is the sample size for babies used Gibbs product
N(y) is the sample size for babies used competitor product.

putting the numbers in the formula:

z= $\frac{7.6-8.1}{\sqrt{\frac{2.3}{40}+\frac{2.9}{55}}}$ ≈ -1.51

and z-table gives that P(z<-1.51) = 0.0655

To conclude if the competitor good is significantly better, we need to choose a significance level and compare it to 0.0655.

For example, the difference in mean weight gained of two goods is not significant under 0.05 or 0.01 significance since 0.0655 is bigger than these values. But we can conclude that under 0.10 significance, competitor brand mean weight gain is significantly more than the Gibbs brand mean weight gain.

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4 years ago

A large fish tank at an aquarium needs to be emptied so that it can be cleaned. When its

VikaD [51]

Answer:

The draining time when only the big drain is opened is 2.303 hours.

The draining time when only the small drain is opened is 5.303 hours.

Step-by-step explanation:

From Physics, we know that volume flow rate ( $\dot V$ ), measured in liters per hour, is directly proportional to draining time ( $t$ ), measured in hours. That is:

$\dot V \propto \frac{1}{t}$

$\dot V = \frac{k}{t}$ (Eq. 1)

Where $k$ is the proportionality constant, measured in liters.

From statement, we have the following three expressions:

(i) Large and small drains are opened

$\dot V_{s}+\dot V_{l} = \frac{k}{2}$ (Eq. 2)

$\frac{\dot V_{s}+\dot V_{l}}{k} = \frac{1}{2}$

(ii) Only the small drain is opened

$\dot V_{s} = \frac{k}{t_{l}+3}$ (Eq. 3)

$\frac{\dot V_{s}}{k} = \frac{1}{t_{l}+3}$

(iii) Only the big drain is opened

$\dot V_{l} = \frac{k}{t_{l}}$ (Eq. 4)

$\frac{\dot V_{l}}{k} = \frac{1}{t_{l}}$

By applying (Eqs. 3, 4) in (Eq. 2) and making some algebraic handling, we find that:

$\frac{1}{t_{l}+3}+\frac{1}{t_{l}} = \frac{1}{2}$

$\frac{t_{l}+t_{l}+3}{t_{l}\cdot (t_{l}+3)} = \frac{1}{2}$

$2\cdot t_{l}+3 = t_{l}^{2}+3\cdot t_{l}$

$t_{l}^{2}-t_{l}-3 = 0$ (Eq. 5)

Whose roots are determined by the Quadratic Formula:

$t_{l,1}\approx 2.303\,h$ and $t_{l,2} \approx -1.302\,h$

Only the first roots offers a solution that is physically reasonable. Hence, the draining time when only the big drain is opened is 2.303 hours. And the time needed for the small drain is calculated by the following formula:

$t_{s} = 2.303\,h+3\,h$