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3 years ago

Find the midpoint of the line segment with the given endpoints

Mathematics

1 answer:

mezya [45]3 years ago

8 0

Answer:

Option D.

Step-by-step explanation:

Hey there!

The given points are:(-4,-10) and (2,1).

Now; use midpoint formula,

$(x,y) = (\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )$

Put all values.

$(x,y) = (\frac{ -4 + 2}{2} , \frac{ - 10 + 1}{2} )$

Simplify it.

$(x,y) = ( - 1, \frac{ - 9}{2} )$

$(x,y) = (- 1,- 4 \frac{1}{2}$ )

Therefore, your required answer is Option D.

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The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (2008 data). The average c

ivanzaharov [21]

Answer:

$n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94$

So the answer for this case would be n=94 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma= 500$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =120 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The confidence2 level is 98% or 0.98 then the significance level would be $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , the critical value for this case would be $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94$

So the answer for this case would be n=94 rounded up to the nearest integer

8 0

3 years ago

Find all solutions of the given system of equations and check your answer graphically. HINT [See Examples 1-4.] (If there is no

Likurg_2 [28]

Answer:

$Infinitely\ many\ solutions\ exist.\\\\Solutions\ are\ (x,\frac{3}{4}x-1)$

Step-by-step explanation:

$Given\ equations\ are\\\\3x-4y=4.................eq(1)\\\\9x-12y=12..............eq(2)\\\\divide\ eq(2)\ by\ 3\\\\\frac{1}{3}(9x-12y=12)\\\\\Rightarrow 3x-4y=4\\\\Hence\ equations\ represent\ the\ same\ line.\\Hence\ Infinitely\ many\ solutions\ exist.\\\\3x-4y=4\\\\4y=3x-4\\\\y=\frac{3}{4}x-1\\\\Solutions\ are\ (x,\frac{3}{4}x-1)$