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3 years ago

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A Florida neighborhood is comprised of a total of 250 houses of which 12% are in foreclosure. A random sample of 91 homes from t

his neighborhood was selected. The standard error of the proportion is ________.

1 answer:

natka813 [3]3 years ago

6 0

Answer:

the standard error of the proportion is 0.0272

Step-by-step explanation:

We have that if the sample size is greater than 5% of the entire population, a finite population correction factor (fpc) is multiplied with the standard error :

fpc = $\sqrt{\frac{N -n}{N -1} }$

We know that N = 250 n = 91, replacing:

fpc = $\sqrt{\frac{250 - 91}{250 -1} }$

fpc = 0.799

Now, the formula would then be:

SE = $\sqrt{\frac{p * (1 -p)}{n} }$ *fpc

Now replacing, knowing that p = 0.12

SE= $\sqrt{\frac{0.12 * (1 - 0.12)}{91} }$ *0.799

SE = 0.0272

So the standard error of the proportion is 0.0272

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tyler has a rectangular garden measuring 12m by 20 m that he wants to split diagonally from corner to corner using a fence. how

adelina 88 [10]

Answer:

23.3

(or $4\sqrt{34}$ (let me know if you wanted this one and is you want it explained) lol)

Step-by-step explanation:

To find the length of the fence, use the Pythagorean theorem because, if you cut a rectangle diagonally, you will create two right triangles, and this formula only works with right triangles:

$a^{2} +b^{2} =c^{2}$

Insert values:

$12^{2} +20^{2} =c^{2}$

Solve for c:

Evaluate exponents

$144+400=c^2$

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$544=c^2$

Find the square root of both

$\sqrt{544} =\sqrt{c^2}\\\\\sqrt{544} =c\\\\23.324=c\\\\c=23.3$

The fence needs to be approximately 23.3 m.

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3 years ago

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What does dilation of a triangle mean?

NikAS [45]

Answer: Dilation is a technique for creating similar figures. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. (Outwards if the scale factor is bigger than 1.) Move the points A, B, and C to change the shape of the triangle.

Step-by-step explanation:

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1 year ago

30% of Number A is the same as 40% of Number B.

Goryan [66]

30% of number A means

$\dfrac{30A}{100}=\dfrac{3A}{10}$

similarly, 40% of number B means

$\dfrac{40B}{100}=\dfrac{2B}{5}$

These must be equal, so we have

$\dfrac{3A}{10}=\dfrac{2B}{5}$

Multiply both sides by 10 to get

$3A=4B \iff A=\dfrac{4B}{3}$

So, you can choose any number for A, and then you multiply it by 4/3 to get B. There are infinitely many solutions to this equation.

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3 years ago

Х<br> 6 - 5 = (-13)<br> What does x equal?

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Answer:

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3 years ago

Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

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3 years ago