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3 years ago

4x²-17x-42 by factor

1 answer:

5 0

4x²-17x-42
=4(x²-17/4x)-42
=4[x²-17/4 x+(-17/8)²-(-17/8)²]-42
=4(x-17/8)²-289/64-42
=4(x-17/8)²-(289+2688)/64
=4(x-17/8)²-2974/64
=[(2x-34/8)²-(√2974/8)²]
=(2x-34/8 +(√2974/8))(2x-34/8-(√2974/8)
=[2x+(√2974-34)/8][2x-(√2974+34)/8]

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A random sample of 130 students is chosen from a population of 4,500 students. The mean IQ in the sample is 120, with a standard

barxatty [35]

Answer:

$120-2.614\frac{5}{\sqrt{130}}=118.85$

$120+2.614\frac{5}{\sqrt{130}}=121.15$

Step-by-step explanation:

Information given

$\bar X= 120$ represent the sample mean

$\mu$ population mean (variable of interest)

s=5 represent the sample standard deviation

n=130 represent the sample size

For this case we can't set a margin of error just with a % since they not specify 1.13% respect to something for this case we can omit this value

Confidence interval

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

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

The degrees of freedom are given by:

$df=n-1=130-1=129$

The Confidence level is 0.99 or 99%, the significance would be $\alpha=0.01$ and $\alpha/2 =0.005$ , and the critical value would be $t_{\alpha/2}=2.614$

And replacing we got:

$120-2.614\frac{5}{\sqrt{130}}=118.85$

$120+2.614\frac{5}{\sqrt{130}}=121.15$

3 0

3 years ago

What is the correct answer???

Lostsunrise [7]

Option D: $\frac{2}{5}$ is the x-coordinate

Explanation:

It is given that the coordinates of the line segment are A(3,2) and B(6,11).

Since, the line is partitioned by the point C by the ratio AC : BC = 2 : 3

The distance between the x-coordinates is 3 units.

To determine the value of the x-coordinate for point C, let us divide the value of x-coordinate from the ratio divided by the sum of ratio.

The value of x-coordinate from the ratio is 2.

Sum of the ratio is 2 +3 = 5

Thus,

The x - coordinate = value of x-coordinate from the ratio / Sum of ratio = 2/5

Substituting the values, we have,

The x - coordinate of the Point C = $\frac{2}{5}$

Thus, Option D is the correct answer.

4 0

3 years ago

Tell whether the angles are adjacent or vertical. Then find the value of x.<br><br>(Only 4-6)

eduard

Alright, lets get started.

If two angles have common side and they shares common vertex, they are called adjacent angles.

When two lines crosses each other, the opposite angles are called vertical angles as they share same vertex.

Question 4:

Two angles shown in diagram are adjacent as they are on common side.

Both the angles are on a straight line, hence

$x + 109 = 180$

Subtracting 109 from both sides

$x + 109 - 109 = 180 - 109$

$x = 71$ ° : Answer

Question 5:

Both angles shown in diagram are opposite to each other, hence vertical angles.

As they are opposite to each other, they both are equal.

$x+42= 2x + 1$

Subtracting x from both sides

$x + 42 - x = 2x + 1 - x$

$42 = x + 1$

Subtracting 1 from both sides

$42 - 1 = x + 1 - 1$

$x = 41$ ° : Answer

Question 6:

Both angles are having a common side means they are adjacent angles.

As they are on straight line, both angles will add up to 180 °.

$x+96 + 5x = 180$

$6 x + 96 = 180$

Subtracting 96 from both sides

$6x + 96 - 96 = 180 - 96$

$6x= 84$

Dividing from 6 in both sides

$\frac{6x}{6} =\frac{84}{6}$

$x = 14$ ° : Answer

Hope it will help :)

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