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3 years ago

To solve the equation 6x + 3 = 9 for x, what operations must be

Mathematics

1 answer:

Karolina [17]3 years ago

8 0

Answer:

Subtraction, and then division.

Step-by-step explanation:

We would subtract 3 on each side to undo the '3', and then divide by 6 on both sides to isolate 'x'.

$6x+3 = 9\\\\6x + 3 - 3 = 9 - 3\\\\ 6x = 6\\\\\frac{6x=6}{6}\\\\\boxed{x=1}$

Hope this helps.

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3 years ago

Rosetta wants to estimate the percentage of people who rent their home. She surveys 250 individuals and finds that 48 rent their

Andreas93 [3]

Answer:

$0.192 - 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.151$

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Step-by-step explanation:

Information given

$X= 48$ number of people who rent their home

$n= 250$ represent the sample size

$\hat p =\frac{48}{250}= 0.192$ represent the proportion of people who rent their home

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.645$

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

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

If we replace the values obtained we got:

$0.192 - 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.151$

$0.192 + 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.233$

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3 years ago