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3 years ago

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What is the solution to 8(2x + 3) = 48?

1 answer:

Tom [10]3 years ago

6 0

You have to start by using the distributive property. So you take the number next to the parentheses which is “8” and you multiply it with “2x”. This gives you “16x”. Then you multiply “8” with “3” and that gives you “24”. You now have the equation “16x + 24 = 48”.
The next step is to subtract “24” with “48”. This leaves you with “24”. Then you now have “16x = 24” as your new equation. The last step is to divide “16x” with “16”, this cancels it out with itself. Then you divide “24” with “16” and you get 1.5. So “X” equals 1.5 or you can convert it into a fraction witch gives you “3/4”.

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The third step would be calculate the standard deviation for the differences, and we got:

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The next step is calculate the statistic given by :

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And the correct option would be:

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Step-by-step explanation:

We assume the following notation:

x=test value after , y = test value before

x: 34 39 28 33 27 23 35 33

y: 32 35 34 33 28 28 35 32

The system of hypothesis for this case is given by:

Null hypothesis: $\mu_y- \mu_x = 0$

Alternative hypothesis: $\mu_y -\mu_x \neq 0$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: 2, 4, -6, 0, -1, -5, 0, 1

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{29}{8}=-0.625$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.378$

The next step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.625 -0}{\frac{3.378}{\sqrt{8}}}=-0.523$

And the correct option would be:

a. t = -0.523

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