what is the equation for the line that is perpendicular to y=2x and passes through the point (-3, 8.5)

An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

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

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

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0

2 years ago

Write the equation of a parabola with focus at (1,-4) and a directrix at X=2

konstantin123 [22]

Answer:

The equation of a parabola is

$x = \frac{1}{4(f - h)} (y - k) ^{2} + h$

Step-by-step explanation:

(h,k) is the vertex and (f,k) is the focus.

Thus, f = 1, k = −4.

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.

Solving the system, we get h = 3/2, k = -4, f = 1.

The standard form is:

$x = - \frac{y ^{2} }{2} - 4y - \frac{13}{2}$

The general form is:

$2x + {y}^{2} + 8y + 13 = 0$

The vertex form is:

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

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.

The focal length is the distance between the focus and the vertex: 1/2.

The focal parameter is the distance between the focus and the directrix: 1.

The latus rectum is parallel to the directrix and passes through the focus: x = 1.

The length of the latus rectum is four times the distance between the vertex and the focus: 2.

The eccentricity of a parabola is always 1.

The x-intercepts can be found by setting y = 0 in the equation and solving for x.

x-intercept:

$( - \frac{13}{2} \: ,0)$

The y-intercepts can be found by setting x = 0 in the equation and solving for y.

y-intercepts:

$(0, - 4 - \sqrt{3)}$

$(0, - 4 + \sqrt{3)}$

3 0

2 years ago

URGENT!! Please help if you can!!

Leviafan [203]

Answer:

Not a function.

Step-by-step explanation:

It is not a function since it does not pass the vertical line test.

3 0

2 years ago

Read 2 more answers

SashulF [63]

<span>The correct answer would be option C. Similar polygons
Similar polygons are polygons wherein the corresponding angles are congruent and the corresponding sides are proportional with each other. Thus, having a pair of similar polygons would mean that its corresponding angles would always be congruent.</span>

3 0

3 years ago

Read 2 more answers

determine whether the triangles are similar if so what is the similarity statement and the postulate or theorem used.

zmey [24]

The triangles are similar because of the SAS postulate. The sides are proportional and angle T is equal in both.

6 0

3 years ago