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3 years ago

How many solutions does the equation 3(x+2)-10=4x-6+x have?

Mathematics

2 answers:

Shtirlitz [24]3 years ago

8 0

Answer:

x=1

Step-by-step explanation:

3(x+2)-10=4x-6+x

3x+6-10=5x-6

3x-5x-4=-6

-2x-4=-6

-2x=-6+4

-2x=-2

2x=2

x=2/2

x=1

KengaRu [80]3 years ago

6 0

Answer: The answer is 1

Step-by-step explanation:

Simplifying

3(x + 2) + -10 = 4x + -6 + x

Reorder the terms:

3(2 + x) + -10 = 4x + -6 + x

(2 * 3 + x * 3) + -10 = 4x + -6 + x

(6 + 3x) + -10 = 4x + -6 + x

Reorder the terms:

6 + -10 + 3x = 4x + -6 + x

Combine like terms: 6 + -10 = -4

-4 + 3x = 4x + -6 + x

Reorder the terms:

-4 + 3x = -6 + 4x + x

Combine like terms: 4x + x = 5x

-4 + 3x = -6 + 5x

Solving

-4 + 3x = -6 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

-4 + 3x + -5x = -6 + 5x + -5x

Combine like terms: 3x + -5x = -2x

-4 + -2x = -6 + 5x + -5x

Combine like terms: 5x + -5x = 0

-4 + -2x = -6 + 0

-4 + -2x = -6

Add '4' to each side of the equation.

-4 + 4 + -2x = -6 + 4

Combine like terms: -4 + 4 = 0

0 + -2x = -6 + 4

-2x = -6 + 4

Combine like terms: -6 + 4 = -2

-2x = -2

Divide each side by '-2'.

x = 1

Simplifying

x = 1

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In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

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3 years ago

Select the correct answer. A linear function has a y-intercept of -12 and a slope of 3/2. What is the equation of the line? y =

aniked [119]

Answer:

The equation of the line is:

$y\:=\:\frac{3}{2}x\:-12$

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

m is the slope

b is the y-intercept

Given

y-intercept b = -12

slope m = 3/2

now substituting b = -12 and m = 3/2 in the slope-intercept form of line equation

$y = mx+b$

$y\:=\:\frac{3}{2}x\:+\:\left(-12\right)$

$y\:=\:\frac{3}{2}x\:-12$

Therefore, the equation of the line is:

$y\:=\:\frac{3}{2}x\:-12$

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Anon25 [30]

Answer:

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Step-by-step explanation:

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4 years ago

What number is one hundred more than 792?

Andrej [43]

One hundred more than 792 = 792 + 100

792 + 100 = 892

892 is your answer

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alexandr402 [8]

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