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fomenos
3 years ago
15

X-y=0 and 5x-2y=6 solve by elimination

Mathematics
1 answer:
Elena-2011 [213]3 years ago
6 0

Answer:

(2,2)

Step-by-step explanation:

first take x-y=0 and multiply it by -5 you will then get this

-5x+5y=0

5x-2y=6

add those together

3y=6

divide by 3

y=2

now plug 2 in for y

x-2=0

add 2 to both sides

x=2

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The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of th
Ilia_Sergeevich [38]

Answer:

(0.0757;0.1403)

Step-by-step explanation:

1) Data given and notation

Republicans =115

Democrats=331

Independents=54

Total= n= 115+331+54=500

\hat p_{ind}=\frac{54}{500}=0.108

Confidence=0.98=98%

2) Formula to use

The population proportion have the following distribution

\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

The confidence interval for the population proportion is given by this formula

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

We have the proportion of independents calculated

\hat p_{ind}=\frac{54}{500}=0.108

We can calculate \alpha=1-conf=1-0.98=0.02

And we can find \alpha/2 =0.02/2=0.01, with this value we can find the critical value z_{\alpha/2} using the normal distribution table, excel or a calculator.

On this case z_{\alpha/2}=2.326

3) Calculating the interval

And now we can calculate the interval:

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0.108 + 2.326\sqrt{\frac{0.108(1-0.108)}{500}}=0.1403

So the 98% confidence interval for this case would be:

(0.0757;0.1403)

7 0
3 years ago
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