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2 years ago

Find the value of x in the equation: x^2 + 4 = 12

Mathematics

1 answer:

jonny [76]2 years ago

7 0

Answer:

$\sqrt{8} = 2 \sqrt{2}$

Step-by-step explanation:

In the equation we must first move 4 to the other side and change its sign

x^2 + 4 = 12

x^2 = 12 - 4

x^2 = 8

Then we find x:

x =

$x = \sqrt{8} = \sqrt{2 \times 2 \times 2} = \sqrt{ {2}^{2} \times 2 } = 2 \sqrt{2}$

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46. In the word "percent", the "cent" represents what number?

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Per cent = per 100 <== ur answer

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3 years ago

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chef daniels places her favorite recipes in a bag for 4 pasta dishes, 5 casseroles, 3 types of chili, and 8 desserts. If Chef Da

pishuonlain [190]

Answer:

1/10

Step-by-step explanation:

5/20 x 8/20 = 1/10

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3 years ago

Revolution in Russia is the lession

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Answer: The answers are in the photo. (They are color-coded.)

Step-by-step explanation:

A monarchy, democracy, and communism are different ways to run a government.

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3 years ago

Solve this equation. 25) v - 6(4v + 6) = -82

grin007 [14]

Answer:

$v = 2$

Step-by-step explanation:

Hi there! I'm glad I was able to help you solve this equation!

Let's start by simplifying both sides of the equation. It's easier to solve it this way!

$v - 6 (4v + 6) = -82$

Distribute:

$v + (-6) (4v) + (-6) (6) = -82$

$v + -24v + -36 = -82$

Combine 'like' terms:

$(v -24v) + (-36) = -82$

$-23v - 36 = -82$

Next, you'll want to add 36 to both sides of the equation.

$-23v-36 + 36 = -82 + 36$

$-23v = -46$

Finally, divide both sides by $-23$ .

$\frac{-23v}{-23} = \frac{-46}{-23}$

$v = 2$

I hope this helped you! Leave a comment below if you have any further questions! :)

7 0

3 years ago

To decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger a

Komok [63]

Answer:

The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

Step-by-step explanation:

Let the random variable X be defined as the height of chimneys in factories.

The mean height is, μ = 100 meters.

The standard deviation of heights is, σ = 12 meters.

It is provided that a random sample of n = 40 chimney heights is obtained.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample means is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

Since the sample selected is quite large, i.e. n = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.

$\bar X\sim N(\mu_{\bar x},\ \sigma^{2}_{\bar x})$

Compute the probability hat the sample mean height for the 40 chimneys is greater than 102 meters as follows:

$P(\bar X>102)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}})>\frac{102-100}{12/\sqrt{40}})$

$=P(Z>1.05)\\=1-P(Z$

*Use a z-table fr the probability.

Thus, the probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

8 0

3 years ago