Solve the equation. 3x-3(4+x)=3/4(3x+2)-1

Mathematics

1 answer:

bonufazy [111]1 year ago

8 0

Answer:

$x=\frac{10}{3}$

Step-by-step explanation:

$3x-3(4+x)=\frac{3}{4}(3x+2)-1$

Solve the parenthesis ↑

$3x-12+3x=\frac{9}{4}x+\frac{6}{4}-1$

Multiply everything by 4 to get rid of the denominators.

$\frac{12x}{4}-\frac{48}{4}+\frac{12x}{4}=\frac{9}{4}x+\frac{6}{4}-\frac{4}{4}$

Rid the denominators.

$12x-48+12x=9x+6-4$

Solve.

$12x+12x-9x=6-4+48$

$15x=50$

$x=\frac{50}{15}$

Simplify.

$x=\frac{10}{3}$

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The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked

Serggg [28]

Answer:

a) The 99% confidence interval would be given by (24.409;24.979)

b) n=464

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=47-1=46$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,46)".And we see that $t_{\alpha/2}=2.01$