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3 years ago

Using suitable identity find 231^222-131^2

Mathematics

1 answer:

Sliva [168]3 years ago

7 0

Given:

Consider the expression is

$231^2-131^2$

To find:

The value of given expression using a suitable identity.

Solution:

We have,

$231^2-131^2$

Using the identity $a^2-b^2=(a-b)(a+b)$ , we get

$231^2-131^2=(231-131)(231+131)$

$231^2-131^2=(100)(362)$

$231^2-131^2=36200$

Therefore, the value of the given expression is $231^2-131^2=36200$ .

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3 years ago

A survey of 1,562 randomly selected adults showed that 522 of them have heard of a new electronic reader. The accompanying techn

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Answer:

a) We want to test the claim that 35% of adults have heard of the new electronic reader, then the system of hypothesis are.:

Null hypothesis: $p=0.35$

Alternative hypothesis: $p \neq 0.35$

And is a two tailed test

b) $z=\frac{0.334 -0.35}{\sqrt{\frac{0.35(1-0.35)}{1562}}}=-1.326$

c) $p_v =2*P(z$

d) Null hypothesis: $p=0.35$

e) Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

Step-by-step explanation:

Information provided

n=1562 represent the random sample selected

X=522 represent the people who have heard of a new electronic reader

$\hat p=\frac{522}{1562}=0.334$ estimated proportion of people who have heard of a new electronic reader

$p_o=0.35$ is the value to verify

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Part a

We want to test the claim that 35% of adults have heard of the new electronic reader, then the system of hypothesis are.:

Null hypothesis: $p=0.35$

Alternative hypothesis: $p \neq 0.35$

And is a two tailed test

Part b

The statistic for this case is given :

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.334 -0.35}{\sqrt{\frac{0.35(1-0.35)}{1562}}}=-1.326$

Part c

We can calculate the p value using the laternative hypothesis with the following probability:

$p_v =2*P(z$

Part d

The null hypothesis for this case would be:

Null hypothesis: $p=0.35$

Part e

The best conclusion for this case would be:

Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

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3 years ago

Using suitable identity find 231^222-131^2​

Using suitable identity find 231^222-131^2