All categories

3 years ago

Factor by grouping. Then supply the term that is missing below. 2mn-3m+8n-12=(m+4)(?-3) The missing term ? = _____.

1 answer:

4 0

2mn - 3m + 8n - 12

Let's group the first two terms together and the last two:

2mn - 3m and 8n - 12

In the first group, m is the greatest common factor.

m(2n - 3)

In the second group, 4 is the greatest common factor.

4(2n - 3)

Therefore, (m + 4) and (2n - 3) are our factors. Our missing term is 2n.

You might be interested in

A pew research Center project on the state of news media showed that the clearest pattern of news audience growth in 2012 came o

KengaRu [80]

Answer:

Step-by-step explanation:

Given that:

the sample proportion p = 0.39

sample size = 100

Then np = 39

Using normal approximation

The sampling distribution from the sample proportion is approximately normal.

Thus, mean $\mu _{\hat p} = p = 0.39$

The standard deviation;

$\sigma = \sqrt{\dfrac{p(1-p)}{n} }$

$\sigma = \sqrt{\dfrac{0.39(1-0.39)}{100} }$

$\sigma = 0.048$

The test statistics can be computed as:

$Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}$

$Z = \dfrac{0.3 - 0.39 }{0.0488}$

$Z = -1. 8 4$

From the z - tables;

$P (\hat p \le 0.3 ) = P(z \le -1.84)$

$\mathbf{P (\hat p \le 0.3 ) = 0.0329}$

(b)

Here;

the sample proportion = 0.39

the sample size n = 400

Since np = 400 * 0.39 = 156

Thus, using normal approximation.

From the sample proportion, the sampling distribution is approximate to the mean $\mu_{\hat p} = p = 0.39$

the standard deviation $\sigma_{\hat p} = \sqrt{\dfrac{p(1-p)}{n} }$

$\sigma_{\hat p} = \sqrt{\dfrac{0.39 (1-0.39)}{400} }$

$\sigma_{\hat p} =0.0244$

The test statistics can be computed as:

$Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}$

$Z = \dfrac{0.3 - 0.39 }{0.0244}$

$Z = -3.69$

From the z - tables;

$P (\hat p \le 0.3 ) = P(z \le -3.69)$

$\mathbf{P (\hat p \le 0.3 ) = 0.0001}$

As sample size builds up, the standard deviation of the sampling distribution decreases.

In addition to that, reduction in the standard deviation resulted in increases in the Z score, and the probability of having a sample proportion that is less than 30% also decreases.

6 0

3 years ago

What is y-6 = 2(x+5) in standard form?

vlabodo [156]