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3 years ago

4a-3(a-2)=2(3a-2) How do you do this?

Mathematics

1 answer:

Alexxandr [17]3 years ago

7 0

Answer:

a=2

Step-by-step explanation:

4a-3(a-2)=2(3a-2)

4a-3a+6=a-4

a+6=6a-4

a-6a=-4-6

-5a=-10

divide both sides by -5

a=2

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According to a poll, 76% of California adults (385 out of 506 surveyed) feel that education is one of the top issues facing Cali

lina2011 [118]

Answer:

The error bound is 3.125%.

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 interval $1-\alpha$ , 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 $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

A sample of 506 California adults.. This means that $n = 506$ .

76% of California adults (385 out of 506 surveyed) feel that education is one of the top issues facing California. This means that $\pi = 0.76$

We wish to construct a 90% confidence interval

So $\alpha = 0.10$ , z is the value of Z that has a pvalue of $1 - \frac{0.10}{2} = 0.95$ , so $z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 - 1.645\sqrt{\frac{0.76*0.24}{506}} = 0.7288$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 + 1.645\sqrt{\frac{0.76*0.24}{506}} = 0.7913$

The error bound of the confidence interval is the division by 2 of the subtraction of the upper limit by the lower limit. So:

$EBM = \frac{0.7913 - 0.7288}{2} = 0.03125$

The error bound is 3.125%.

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3 years ago

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3 years ago

The product of (a + b)(a − b) is a2 − b2. (1 point) Sometimes Always Never

jenyasd209 [6]

ANSWER

$\boxed{Always}$
EXPLANATION

The given product is

$( a - b)(a + b)$

This is always equal to

${a}^{2} - {b}^{2}$

The identity

$( a - b)(a + b) = {a}^{2} - {b}^{2}$

is called difference of two squares.

We can verify this by simply expanding the brackets using the distributive property to obtain,

$( a - b)(a + b) = a(a + b) - b(a + b)$

$( a - b)(a + b) = {a}^{2} + ab - ab- {b}^{2}$

This simplifies to

$( a - b)(a + b) = {a}^{2} - {b}^{2}$

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Step-by-step explanation:

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