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3 years ago

3x + 4 = 5x + 10

Mathematics

1 answer:

IRINA_888 [86]3 years ago

8 0

Answer:

(-infinity, 2) U [-3]

Step-by-step explanation:

Step 1: we want to solve both equations for x. To do so, get the x variable by itself in both equations.

1.) 3x+4 = 5x+10

-6 = 2x (subtract 10 from both sides and 3x from both sides)

-3 = x (divide 2 from both sides)

2.) -5x + 7 > -3

-5x > -10 (subtract 7 from both sides)

x < 2

(divide both sides by -5, notice that dividing by a negative by a negative number flips the direction on > to < .)

Step 2: apply interval notation to these answers. Since x DOES equal -3 in equation one, it'll be in a bracket. On the contrary, since x has to be LESS THAN 2, it will have a parentheses.

So, our answer is: (-infinity, 2) U [-3]

*note the parentheses around infinity because something cannot equal infinity, it's not just one number*

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3 years ago

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2 years ago

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ivanzaharov [21]

Answer:

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So the answer for this case would be n=94 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma= 500$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =120 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

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$n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94$

So the answer for this case would be n=94 rounded up to the nearest integer

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2 years ago

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wariber [46]

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Hope this helps!!

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1 year ago