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3 years ago

Factor completely: 16-2x^3

1 answer:

4 0

$16-2x^3=2(8-x^3)=2(2^3-x^3)\\\\\text{use}\ a^3-b^3=(a-b)(a^2-ab+b^2)\\\\=2(2-x)(2^2+2x+x^2)\\\\=\boxed{2(2-x)(4+2x+x^2)}$

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What is 32.043 in expanded form?

PtichkaEL [24]

You just have to break each number with its value.
30+2+.04+.003

7 0

3 years ago

Evaluate each expression : 12 - |-8| 7 =

I am Lyosha [343]

In guessing the expression is 12-8x7 So the answer is 28

7 0

3 years ago

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.

$\pi = 0.55$

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

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

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

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

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

$n = 1025.7$

Rounding up

n = 1026.

6 0

3 years ago

Determine the graph of the sinusoid with amplitude of 4 and period of 2π/3

DiKsa [7]

Answer:

Option b.

y = 4 sin (3x)

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The period is

T = 2π/3

This means the frequency in radians is

W = 2π/T = 3

The equation is either:

y = 4 cos(3x)

y = 4 sin (3x)

The correct answer is

Option b.

y = 4 sin (3x)

3 0

3 years ago

Y = 2x 3x-y=15 Solve By Substitution

Minchanka [31]

The answer is X=15...

6 0

3 years ago

Read 2 more answers