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3 years ago

Given 3(x-2)=6, then x is equal to: Select one: A.5 b.4 c. 2 d.6

Mathematics

1 answer:

Gnoma [55]3 years ago

5 0

Answer:

$\boxed {\boxed {\sf B. \ 4}}$

Step-by-step explanation:

We are given the following equation.

$3(x-2)=6$

We are solving for x, so we must isolate the variable using the inverse operation.

(x-2) is being multiplied by 3. The inverse operation of multiplication is division, so we divide both sides of the equation by 3.

$\frac {3(x-2)}{3}= \frac{6}{3}$

$(x-2)= \frac{6}{3}$

$(x-2)= 2$

2 is being subtracted from x. The inverse operation of subtraction is addition, so we add 2 to both sides of the equation.

$(x-2)+2= 2+2$

$x=2+2$

$x=4$

Check the answer by plugging 4 in for x in the original equation.

$3(x-2)= 6$

$3(4-2)= 6$

$3(2)= 6$

$6=6$

This checks out, so we know our answer is correct. x is equal to 4 and choice B is correct.

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Marizza181 [45]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25$

And rounded up we have that n=421

Step-by-step explanation:

We know that the sample proportion have the following distribution:

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

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:

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

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)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We assume that a prior estimation for p would be $\hat p =0.5$ since we don't have any other info provided. And replacing into equation (b) the values from part a we got: