If the volume of a cube is 27 metre cube find one of side

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time coll

ICE Princess25 [194]

Answer:

a) n = 1037.

b) n = 1026.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

(a) Assume that nothing is known about the percentage to be estimated.

We need to find n when M = 0.04.

We dont know the percentage to be estimated, so we use $\pi = 0.5$ , which is when we are going to need the largest sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 2.575*0.5$

$(\sqrt{n}) = \frac{2.575*0.5}{0.04}$

$(\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}$

$n = 1036.03$

Rounding up

n = 1037.

(b) Assume prior studies have shown that about 55% of full-time students earn bachelor's degrees in four years or less.

$\pi = 0.55$

So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 2.575\sqrt{\frac{0.55*0.45}{n}}$

$0.04\sqrt{n} = 2.575*\sqrt{0.55*0.45}$

$(\sqrt{n}) = \frac{2.575*\sqrt{0.55*0.45}}{0.04}$

$(\sqrt{n})^{2} = (\frac{2.575*\sqrt{0.55*0.45}}{0.04})^{2}$

$n = 1025.7$

Rounding up

n = 1026.

6 0

3 years ago

What is the domain of {(1,0),(-5,7),(-4,-7),(-7,-4)}

olasank [31]

D(1,-5,-4,-7) R(0,7,-7,-4) Domain are your x values and range is your y values

7 0

2 years ago

The _____ _____, denoted ModifyingAbove p with caretp, is given by the formula ModifyingAbove p with caretpequals=_____, wher

Vlada [557]

Answer:

The sample proportion, denoted by ^p, is given by the formula ^p= $\frac{x}{n}$ , where x is the number of individuals with a specified characteristic in a sample of n individuals.

Step-by-step explanation:

Sample proportion is used to determine sample mean, sample standard error and test the hypotheses about the population.

sample mean can be stated as p and sample standard error can be found using the equation $\sqrt{\frac{p*(1-p)}{n} }$ where

n is the sample size

p is the sample proportion

And if n×p×(1-p)≥10, then sample is assumed large enough to assume normal distribution and apply statistical test.

3 0

3 years ago

How would you do this as a decimal number ?

Contact [7]

Answer:

-5.875

Step-by-step explanation:

5 0

3 years ago

Please help The perimeter of a rectangular shape electronic keyboard is 14 ft. Its width is 3 ft longer than its depth

kipiarov [429]

Answer:

Width = 6ft Area = 54 sq ft

Step-by-step explanation:

First, re-read the problem until you understand it and can put it into your own words. I re-wrote it like this: "Find the area of a rectangle by first finding the length (L) and the width (W)." [note that I added "find L and W," but that is how I'm going to solve the problem; I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).

Translate the problem:

"The length of a rectangle is 3 ft longer than its width" means

L = 3 + W (eq1)

"the perimeter of the rectangle is 30 ft" means

P = 30 (eq2)

So, now the math is easy, just find L and W so we can compute the area:

P = 30 = 2L + 2W (eq3; from eq2 and the formula for P)

30 = 2(3+W) + 2W (use eq1 to substitute for L)

30 = 6 + 2W + 2W (distribute)

30 = 6 + 4W (collect terms)

24 = 4W (subtract 6 from both sides)

6 ft = W (divide both sides by 4)

Use the easiest equation (either eq1 or else eq3) to find L:

L = 3 + W (eq1)

L = 3 + 6

L = 9 ft

What is the area (A)?

A = L*W

A = (9 ft)*(6 ft)

A = 54 sq ft

3 0

2 years ago

If the volume of a cube is 27 metre cube find one of side​

If the volume of a cube is 27 metre cube find one of side