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swat32
3 years ago
14

Without solving explain why the equations do not have solutions​

Mathematics
1 answer:
Talja [164]3 years ago
5 0
<h2>Examining the equation</h2>

We have 2 terms:

\sqrt{x+2} and \sqrt{4x+1}

For the sum of these to equal a negative number, in this case -3, one of these terms would have to be negative.

<h2>So what's the problem?</h2>

The function \sqrt{x} (square root of x) only returns positive values!

(See the attached image for a graph of \sqrt{x})

Since neither of the terms can be negative, it can't be equal to -3. In other words, no matter what we put as x, we can't solve the solution, so we say that the equation <em>does not have any solutions.</em>

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A chocolate factory produces mints that weigh 10 grams apiece. The standard deviation of the weight of a box of 10 mints is 3 gr
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The confidence that the box you bought did not come from the factory is 90 %.

<u>Step-by-step explanation:</u>

Since we have given that

Population Mean weight (\mu)= 10 grams a piece

Standard deviation of the weight of a box = 3 grams

Number of mints = 10

We need to buy a box of mints that weighs 95 grams.

Sample mean is given by

x = \frac{95}{10}=9.5 grams .

First we find out the standard error which is given by

s=\frac{\sigma}{\sqrt{n}}\\\\=\frac{3}{\sqrt{10}}\\\\= 0.94868

Since it is normal distribution, so, we will find z-score.

z=\frac{x-\mu}{s}\\\\z=\frac{9.5-10}{0.94868}\\\\z=-0.527\\\\

z = - 0.53

The area to the left of a z-score of -0.53 = 0.29805.

So, it may be 90% or 95 % confidence.

For 95% confidence level,

\alpha=\frac{1-0.95}{2}=0.025

Similarly,

For 90% confidence level,

\alpha=\frac{1-0.90}{2}=0.05

The value is much smaller than 0.05.  

So, we will get 90% confidence and the critical value = 1.645

Margin of error is given by

(Standard deviation) \times (critical\ value) = 0.94868 \times 1.645

                                                              =1.56

So, confidence interval will be

                          (10-1.56,10+1.56)

                              =(8.44,11.56)

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3 years ago
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