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3 years ago

PLEASE HELP WILL GIVE BRAINIEST!!!

Mathematics

1 answer:

scZoUnD [109]3 years ago

7 0

Answer:

Step-by-step explanation:

hello :

let :

y : the length , x : the width , A : the area, x and y positifs numbers (y>x)

you have the system : xy=180....(*)

y=x+8...(**)

put the value for y by (**) in to(*) : (x+8)x=180

x²+8x-180 =0......a=1 b=8 c = -180

∆ = b²- 4ac

∆ = 8²- 4(1)(-180)=384=28²

X1 = ( -b - √∆)/2a = (-8-28)/2 = -15 refused

X2= ( -b + √∆)/2a = (-8+28)/2 = 10

x=10 but : y=x+8

y = 10+8 =18

The length of the rectangle is...18...cm.

The width of the rectangle is...10...cm.

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3 years ago

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

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Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

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

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: