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4 years ago

12

Negative four times a number plus nine is no more than the number minus twenty one

2 answers:

marysya [2.9K]4 years ago

8 0

N is no more than six

Allushta [10]4 years ago

3 0

4x+9 =< x-21
<span>-4x-x +9 =< x-x-21 </span>
<span>-5x +9 =< -21 </span>
<span>-5x +9-9 =< -21-9 </span>
<span>-5x =< -30 </span>
<span>-5x/-5 =< -30/-5 (DANGER divide by neg affects direction of inequality) </span>
<span>x =< 6 </span>
<span>CHECK sign </span>
<span>-4x+9 =< x-21 </span>
<span>-4*6+9 =< 6-21 </span>
<span>-24+9 =<-15 </span>
<span>-15 =<-15 </span>

<span>-4*7+9 =< 7-21 </span>
<span>-28+9 =< 7-21 </span>
<span>-19 =< -14 false </span>

<span>-4*5+9 =< 5-21 </span>
<span>-20+9 =< -16 </span>
<span>-11 =< -16 true </span>

<span>so </span>
<span>x =< 6 is correct. </span>

<span>I use =< since eq would NO MORE THAN.</span>

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$\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29$

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Step-by-step explanation:

For this case we have the following data given:

2.3 3.1 2.8

1.7 0.9 4.0

2.1 1.2 3.6

0.2 2.4 3.2

Since the data are assumedn normally distributed we can find the standard deviation with the following formula:

$\sigma =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}$

And we need to find the mean first with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29$

And then we can calculate the deviation and we got:

$s=1.09$

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