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3 years ago

Make x the subject of h = 4(x + 3y) + 2 Plz help

Mathematics

1 answer:

wlad13 [49]3 years ago

5 0

Answer:

$x=\frac{h}{4}-3y-\frac{1}{2}$

Step-by-step explanation:

This equation has "h" as the subject. Now, making "x" the subject means to use algebra and re-arrange the equation so we have "x = SOMETHING".

First, we will use distributive property on the RHS of the equation. The distributive property is:

$a(b+c)=ab+ac$

So, we have:

$h=4(x+3y)+2\\h=4x+12y+2$

Since we want "x" as the subject, we put "x" term on one side and everything else on another and solve for x. Shown below:

$h=4x+12y+2\\4x=h-12y-2\\x=\frac{h-12y-2}{4}\\x=\frac{h}{4}-3y-\frac{1}{2}$

This is the answer.

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Why does a rectangle with different side lengths have only 2 lines of symmetry?

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Answer:

C. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection

Step-by-step explanation:

A. isn't correct because all four sides aren't congruent, only the pair of opposite sides are congruent. Sense only opposite side are congruent you can only reflect the opposite sides onto each other and not diagonally meaning B. and D. are incorrect leaving C. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection as the correct answer

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3 years ago

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Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student

AysviL [449]

Answer:

The mean calculated for this case is $\bar X=584$

And the 95% confidence interval is given by:

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

Step-by-step explanation:

Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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 mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=584$

The sample deviation calculated $s=86.776$

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

$df=n-1=5-1=4$

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 tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that $t_{\alpha/2}=2.776$