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krok68 [10]
3 years ago
11

PLEASE HELP. Which is the best interpretation of the solution set for the compound inequality? 3/2x-1<2x + 4 or 3(2/3x + 1) &

lt; 11 A. no solution B. x > -10 C. x<4 D. all real numbers.
Mathematics
1 answer:
Fudgin [204]3 years ago
5 0
(3/2)x-1<2x+4
3x-2<4x+8
-2<x+8
-10<x
x>-10

3((2/3)x + 1) < 11
(3*2/3)x+1*3<11
2x +3<11
2x<8
x<4

so the compound equality is the set of all numbers which are >-10 or <4, which are D) all real numbers
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Answer:

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And rounded up we have that n=4906

b) For this case since we don't have prior info we need to use as estimatro for the proportion \hat p =0.5

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And rounded up we have that n=6724

Step-by-step explanation:

We need to remember that the confidence interval for the true proportion is given by :  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Part a

The estimated proportion for this case is \hat p =0.76

Our interval is at 90% of confidence, and the significance level is given by \alpha=1-0.90=0.1 and \alpha/2 =0.05. The critical values for this case are:

z_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

The margin of error desired is given ME =\pm 0.01 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

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Replacing we got:

n=\frac{0.76(1-0.76)}{(\frac{0.01}{1.64})^2}=4905.83  

And rounded up we have that n=4906

Part b

For this case since we don't have prior info we need to use as estimatro for the proportion \hat p =0.5

n=\frac{0.5(1-0.5)}{(\frac{0.01}{1.64})^2}=6724  

And rounded up we have that n=6724

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Answer:

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Step-by-step explanation:

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